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Finding Common Mistakes In Modelling With Mathematical Formalisms Using LLMs
Lilian Killich, Marko Schmellenkamp, Fabian Vehlken, Thomas Zeume
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Abstract
Abstract:Modelling with mathematical formalisms like logical formulas, mathematical equations, or regular expressions is an important yet challenging task for students of computer science and other STEM disciplines. Identifying common mistakes occurring in this context is an important step towards helping struggling students by providing targeted high-quality feedback, e.g. in interactive learning systems. We present a tool-supported workflow that allows to (1) identify candidates for common mistakes that explain many student mistakes in large educational data sets, (2) cluster candidates according to similarities, and (3) visualize resulting clusters for instructors and CS education researchers. The visualization is designed to help researchers to identify common modelling mistakes. The candidates for common mistakes are represented by bug fixing transformations that translate incorrect formalizations into correct formalizations; they are generated by an LLM and validated algorithmically. We show that this approach works well by reproducing common mistakes in propositional logic modelling that were identified by hand in the literature; showing that, unlike other algorithmic approaches, the LLM-based approach is suitable for very large sets of data; and applying it to multiple other formalisms to showcase it generalizes beyond propositional logic.
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- Source: https://arxiv.org/abs/2609.17111v1
- Canonical: https://arxiv.org/abs/2609.17111v1
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Finding Common Mistakes In Modelling With Mathematical Formalisms Using LLMs DOI: X.XXXXXXXConference: Make sure to enter the correct conference title from your rights confirmation email; June 03–05, 2018; Woodstock, NYISBN: 978-1-4503-X-X/2018/06CCS: Theory of computation LogicCCS: Social and professional topics Computer science education Lilian Killich email: lilian.killich@rub.de Affiliation: Ruhr University Bochum, Bochum, Germany , Marko Schmellenkamp email: marko.schmellenkamp@rub.de Affiliation: Ruhr University Bochum, Bochum, Germany , Fabian Vehlken email: fabian.vehlken@rub.de Affiliation: Ruhr University Bochum, Bochum, Germany and Thomas Zeume email: thomas.zeume@rub.de Affiliation: Ruhr University Bochum, Bochum, Germany 2018 Abstract. Modelling with mathematical formalisms like logical formulas, mathematical equations, or regular expressions is an important yet challenging task for students of computer science and other STEM disciplines. Identifying common mistakes occurring in this context is an important step towards helping struggling students by providing targeted high-quality feedback, e.g. in interactive learning systems. We present a tool-supported workflow that allows to (1) identify candidates for common mistakes that explain many student mistakes in large educational data sets, (2) cluster candidates according to similarities, and (3) visualize resulting clusters for instructors and CS education researchers. The visualization is designed to help researchers to identify common modelling mistakes. The candidates for common mistakes are represented by bug fixing transformations that translate incorrect formalizations into correct formalizations; they are generated by an LLM and validated algorithmically. We show that this approach works well by reproducing common mistakes in propositional logic modelling that were identified by hand in the literature; showing that, unlike other algorithmic approaches, the LLM-based approach is suitable for very large sets of data; and applying it to multiple other formalisms to showcase it generalizes beyond propositional logic. Keywords: modelling, logical formulas, mathematical formalisms, common mistakes, large language model 1. Introduction and Motivation Learning to model scenarios with mathematical formalisms such as logical formulas, mathematical equations and terms, regular expressions, and many others, is an important aspect when introducing students to mathematical foundations in computer science and other STEM disciplines. A typical learning objective is that students can model scenarios given in natural language within the intended formalism. In this paper we address the question: Suppose we are given a large data set of student modelling attempts. How can common modelling mistakes be identified? Identifying common mistakes is a preliminary step for understanding students’ struggles, exploring their invalid conceptions, and ultimately providing advice and feedback in modelling assignments. Knowing common mistakes also helps to craft specific advice and feedback in interactive learning systems. We aim for a workflow for identifying common modelling mistakes that supports CS education researchers and educators with adequate algorithmic tools, so that mistakes can be identified from large scale data sets. Our starting point for an algorithmic approach is the observation that the syntax of many mathematical formalisms is specified by a context-free grammar and therefore each formalization is associated with a syntax tree. For such formalisms, modelling mistakes are reflected in differences between the syntax trees of correct and incorrect formalizations. A key idea for answering the above question is that common mistakes can now be found by identifying “bug fixing transformations” that explain differences between syntax trees (Neider et al., 2025). We provide examples of this idea for two different formalisms. Example 1.1 (Modelling with propositional logic formulas). A typical assignment when learning propositional logic is the translation of natural language statements such as “Anna goes to the cinema, but Bob only goes if Celine does.” into formulas. A correct propositional formula is A∧(B→C)A (B→ C), while a frequent mistake by students is to model the statement by A∧(C→B)A (C→ B). The difference is reflected in the syntax trees:∧ → , and ∧ → . A similar difference occurs for the statement “The user interface is not working properly only if the database or the back end are not working properly.” modelled by ¬U→(¬D∨¬B) U→( D B) with frequent mistake (¬D∨¬B)→¬U( D B)→ U and the following syntax trees:→∨ ¬ ¬ ¬ , and →¬ ∨ ¬ ¬ . The differences in both examples are captured by a bug fixing transformation that captures the mistake and locally modifies the incorrect trees to correct trees: → 2Y_2Y1Y_1 ↝ → 1Y_1Y2Y_2 This bug fixing transformation matches the two examples from above as follows: the pattern on the left hand side can be mapped into a subtree of the syntax tree of the incorrect formalizations, and rearranging the subtree according to the right hand side of the transformation yields the correct formalizations (see (Neider et al., 2025) for precise semantics). This transformation captures the common mistake that students model “only if” statements with an implication in the wrong direction. It can be used, for instance, to automatically identify this mistake in student attempts and provide feedback (Geck et al., 2018). Example 1.2 (Modelling with regular expressions). For the assignment “Provide a regular expression for the language of words over the alphabet a,b,c\a,b,c\ in which a appears as first and last letter, but nowhere else.” with correct formalization a(b∗c∗)∗a(b^*c^*)^*a and frequent mistake a(b∗c∗)a(b^*c^*)a with syntax trees ∘ ∘ ∗*c∗*bbaa and ∘ ∗*∘ ∗*c∗*bbaa, the difference between the trees can be described by ∘ ∗*Y2Y_2∗*Y1Y_1 ↝ ∗*∘ ∗*Y2Y_2∗*Y1Y_1 Contributions We present a tool-supported workflow (see Figure 1) that allows to (1) identify candidates for common mistakes by finding bug fixing transformations that explain many student mistakes in large educational data sets, (2) cluster candidates according to similarities, and (3) visualize resulting clusters for instructors and CS education researchers. The visualization is designed to help researchers to identify common modelling mistakes. We note that while candidates identified in Step (1) explain frequent structural differences between syntax trees of correct and incorrect formalizations, it is not guaranteed that these differences correspond to actual conceptual mistakes. Therefore, structuring and visualizing the candidates in Steps (2) and (3) is a necessary follow-up step to support researchers and educators to check the candidates and select sensible common mistakes. Identifying candidates for common mistakes has so far been a time consuming process for CS education researchers, which required to go over data sets by hand. We provide algorithms that support Steps (1) – (3) from above, implement them, and thereby reduce the required effort considerably. The main technical challenge is with respect to Step (1). While in (Neider et al., 2025) a suitable specification language for tree transformations has been crafted and an algorithmic approach to identify transformations from data via a SAT solver was presented, our initial experiments show that this approach does not scale to large educational data sets. Yet, typical such data looks very structured and it is not very hard – though time consuming – for humans to find reasonable bug fixing transformations. This motivates our approach to use large language models (LLMs) to find candidate transformations (see Section 3 for details). We then employ the resulting tool-supported workflow on educational data sets for logical modelling: (a) On a data set for propositional logic with 6106 pairs of correct and incorrect formalizations, our workflow discovers 248 clusters of bug fixing transformations that can help to identify common mistakes. These clusters explain 84.4484.44% of the pairs in total, whereas common mistakes identified in previous work (Schmellenkamp et al., 2023) explain 71.5771.57% of the pairs. Our approach exclusively explains 15.0315.03% of the pairs, while 2.162.16% of the pairs are explained exclusively by previous work. When only considering clusters explaining at least 0.50.5% of the pairs, there are 21 clusters which still explain 66.3466.34% of pairs; with 4.64.6% explained exclusively. (b) On data sets for modal logic with 12482 pairs of correct and incorrect formalizations, our workflow yields clusters of bug fixing transformations that explain 79.3979.39%. When only considering clusters explaining at least 0.50.5% of the pairs, there are 38 clusters for modal logic which explain 40.3640.36%. For computation tree logic (CTL) with 7210 pairs, 35.8935.89% of the pairs are explained, and 19.7819.78% of the pairs are explained by 16 clusters which together explain 0.50.5% of the pairs each. 2. Related Work Research on mistakes is conducted for several formalisms. Early work focused on propositional logic (Almstrum, 1999; Herman et al., 2012), with later refinements by Schmellenkamp et al. (Schmellenkamp et al., 2023), who distinguish linguistic from logical operators to explain discrepancies in earlier findings. Analyses have also been conducted among others for regular expressions (Okuboyejo et al., 2025) and context-free grammars (Pillay, 2010; Schmellenkamp et al., 2024). A common representation of such mistakes uses bug fixing transformations that describe how incorrect attempts can be systematically corrected. In theoretical domains, this idea has been applied to feedback generation for propositional logic in tutoring systems (Geck et al., 2018) and extended by (Schmellenkamp et al., 2023). It has since been generalized to other formalisms, including context-free grammars (Schmellenkamp et al., 2025), demonstrating applicability beyond tree-structured representations. Related ideas also appear in work on regular expressions (Okuboyejo et al., 2025), where feedback is derived from systematic differences between incorrect and correct solutions. The view that student errors can be explained by systematic rules has a long tradition in intelligent tutoring systems. Brown and Burton (Brown and Burton, 1978) introduced diagnostic models of procedural bugs in arithmetic, and Sleeman (Sleeman, 1983) studied how such rules can be inferred for computer-aided instruction. Our notion of mistake candidates as transformations follows this tradition by representing errors as rule-like explanations for families of incorrect formalizations. Repair-based approaches synthesize transformations from incorrect to correct artifacts, for example in programming education (Singh et al., 2013; Gulwani, 2014; Ahmed et al., 2018; Rivers and Koedinger, 2017; Xu and Chee, 2003). More recent work explores large language models for automated feedback (Silva and Costa, 2025; Scholz et al., 2026), showing their potential while also highlighting the need for validation due to possible unreliability or misalignment with instructional goals. We adopt the repair-based perspective while incorporating external algorithmic verification. 3. A Workflow for Finding Common Mistakes data setFinding Bug Fixing Transformations(A∧(C→B),A∧(B→C)),(A (C→ B),\,A (B→ C)),(¬U→(S∨T),(S∨T)→¬U),( U→(S T),(S T)→ U),(F→S,S→F),(F→ S,\,S→ F),⋮ (A↔C,A→C)(A C,\,A→ C)data set(F→S,S→F),(F→ S,\,S→ F),(A∧(C→B),A∧(B→C)),(A (C→ B),\,A (B→ C)),… (¬U→(S∨T),(S∨T)→¬U),( U→(S T),(S T)→ U),… (A↔C,A→C)(A C,\,A→ C)… ⋮ batchesLLMPromptLLMPromptLLMPrompt⋮ → 2Y_2Y1Y_1 ↝ → 1Y_1Y2Y_2 , ↔ 2Y_2Y1Y_1 ↝ → 2Y_2Y1Y_1 , ⋮ set of transformations remaining data set withunexplained pairsapply toinput data setterminationcriterionsatisfied?output: set of collectedtransformationsyesnorepeatClustering↝ ↝ ↝ ↝ ↝ ↝ ↝ ↝ ↝ clusters table: Figure 1. Illustration of the workflow for finding bug fixing transformations, clustering them, and visualizing the clusters. In this section we describe our tool-supported workflow (see Figure 1) that allows to (1) identify candidates for common mistakes by finding bug fixing transformations that explain many student mistakes in large educational data sets, (2) cluster candidates according to similarities, and (3) visualize resulting clusters for instructors and CS education researchers. Step (1) uses an iterative process to generate candidates via an LLM and validates them algorithmically (see Section 3.1). For Step (2), we compute a correlation graph between candidate transformations (see Section 3.2). The workflow is applicable to various data sets. It can be used, for example, on educational data sets for modelling with logical formulas (propositional formulas, modal formulas, temporal formulas, …), regular expressions, mathematical expressions etc. Another use case is the application to multiple data sets for the same formalism to discover more specific mistakes. As an example, a partitioned data set for propositional modelling into smaller data sets according to linguistic operators occurring in natural language statements has been presented by Schmellenkamp et al. (Schmellenkamp et al., 2023). Applying our workflow to each of these smaller data sets results in candidates for common mistakes for each linguistic operator. 3.1. Finding Bug Fixing Transformations The goal of the first step of our workflow is, given a data set containing pairs of incorrect and correct formalizations, to find transformations that explain (frequent) structural differences between the correct and incorrect formalizations. More formally, the input is a data set D which contains pairs (t,t∗)(t,t^*) of syntax trees t and t∗t^* representing incorrect and correct formalizations. The goal is to identifiy a small set T of bug fixing transformations that explain the difference between as many pairs in D as possible. Here, roughly speaking, a bug fixing transformation is of the form σ↝σ∗σ σ^* for two tree patterns σ and σ∗σ^*. Such a transformation explains a pair (t,t∗)(t,t^*) if the pattern σ can be found in t and rearranging t according to the shape of σ∗σ^* yields the tree t∗t^* (see Examples 1.1 and 1.2 as well as (Neider et al., 2025) for details). Unfortunately, finding a small set of bug fixing transformations that explains a large data set is NP-hard (Neider et al., 2025) and SAT-solving based approaches do not scale well. Our algorithmic approach (see Algorithm 1 for pseudo code) is to generate candidates for bug fixing transformations with an LLM, validate those candidates algorithmically, and collect transformations that explain a δ-fraction of the initial data set in the output set T. This procedure is iterated until no new transformation has been found for k iterations. In our experiments we used δ=0.01δ=0.01 and k=10k=10, see Section 4 for details. Algorithm 1 Finding bug fixing transformations 0: A set D of pairs (t,t∗)(t,t^*) of syntax trees 0: A set T of bugfixing transformations 1: ^:= D:=D 2: :=∅T:= 3: while termination criterion is not fulfilled do 4: ℬ1,…,ℬb:=B_1,…,B_b:= randomly split D into batches of size s 5: for all batches ℬiB_i do 6: prompt LLM to find transformations 7: add those transformations to T which explain more than a δ-fraction of D 8: end for 9: ^:= D:= pairs in D not explained by any transformation in T 10: end while 11: return T We provide some details. In each iteration, the data set at hand is split into equally sized randomized batches of size s (in our experiments, we use s∼50s 50), to accommodate limits of used LLMs. Each of the batches is put into a prompt that also contains a brief description of the transformation language, a few sample specifications for special cases, and a description of the task to find transformations. The prompt that was used can be found in the (anonymously published) supplementary material (Authors, 2026). Via this prompt, the LLM provides a list of transformations for each one of the batches. The number of desired transformations for each batch is configurable (in our experiments, we use ⌊0.2⋅s⌋ 0.2· s ). For each transformation found by the LLM, the algorithm tests which fraction of pairs (t,t∗)(t,t^*) it can explains, i.e. pairs for which t can be transformed into t∗t^* by applying the transformation. If a transformation explains more than a δ-fraction of the data, it is added to the output T. 3.2. Clustering Bug Fixing Transformations The goal of the second step of the workflow is to structure the list of bug fixing transformations resulting from the first step for CS education researchers and educators. The idea is to cluster transformations according to “similarity” and to sort those clusters by the number of explained data points. The idea is that transformations in the list may explain similar kinds of mistakes or one transformation may explain all mistakes also explained by another transformation. As an example, consider the transformations ρ1 _1: ↔ Y2 Y1 ↝ ¬ ↔ Y2 Y1 to48.36pt to31.84pt 24.17993pt -24.83304pt to0.0pt @begingroup@_scopebegin=1 @begingroup@stroke=#000000 @begingroup@fill=#000000 @setlinewidth @begingroup@stroke-width=0.4pt @inpgf@ignorespaces @begingroup@_scopebegin=1 @closescope to0.0pt @begingroup@_scopebegin=1 @begingroup@_scopebegin=1 @inpgf@ignorespaces @begingroup@_scopebegin=1 @transformcm1.00.00.01.0-24.17993pt-24.83304pt @begingroup@transform=matrix(1.0 0.0 0.0 1.0 -33.46 -34.36) @hbox61 @closescope @closescope @closescope to0.0pt @inpgf@ignorespaces @inpgf@ignorespaces @discardpath @closescope @closescope to48.36pt to52.47pt 24.17993pt -44.83307pt to0.0pt @begingroup@_scopebegin=1 @begingroup@stroke=#000000 @begingroup@fill=#000000 @setlinewidth @begingroup@stroke-width=0.4pt @inpgf@ignorespaces @begingroup@_scopebegin=1 @closescope to0.0pt @begingroup@_scopebegin=1 @begingroup@_scopebegin=1 @inpgf@ignorespaces @begingroup@_scopebegin=1 @transformcm1.00.00.01.0-24.17993pt-44.83307pt @begingroup@transform=matrix(1.0 0.0 0.0 1.0 -33.46 -62.04) @hbox61 @closescope @closescope @closescope to0.0pt @inpgf@ignorespaces @inpgf@ignorespaces @discardpath @closescope @closescope and ρ2 _2: Y1 ↝ ¬ Y1 to19.18pt to15pt 9.58997pt -4.83301pt to0.0pt @begingroup@_scopebegin=1 @begingroup@stroke=#000000 @begingroup@fill=#000000 @setlinewidth @begingroup@stroke-width=0.4pt @inpgf@ignorespaces @begingroup@_scopebegin=1 @closescope to0.0pt @begingroup@_scopebegin=1 @begingroup@_scopebegin=1 @inpgf@ignorespaces @begingroup@_scopebegin=1 @transformcm1.00.00.01.0-9.58997pt-4.83301pt @begingroup@transform=matrix(1.0 0.0 0.0 1.0 -13.27 -6.69) @hbox61 @closescope @closescope @closescope to0.0pt @inpgf@ignorespaces @inpgf@ignorespaces @discardpath @closescope @closescope to19.18pt to32.47pt 9.58997pt -24.83304pt to0.0pt @begingroup@_scopebegin=1 @begingroup@stroke=#000000 @begingroup@fill=#000000 @setlinewidth @begingroup@stroke-width=0.4pt @inpgf@ignorespaces @begingroup@_scopebegin=1 @closescope to0.0pt @begingroup@_scopebegin=1 @begingroup@_scopebegin=1 @inpgf@ignorespaces @begingroup@_scopebegin=1 @transformcm1.00.00.01.0-9.58997pt-24.83304pt @begingroup@transform=matrix(1.0 0.0 0.0 1.0 -13.27 -34.36) @hbox61 @closescope @closescope @closescope to0.0pt @inpgf@ignorespaces @inpgf@ignorespaces @discardpath @closescope @closescope . Both explain mistakes where a negation ¬ has been forgotten, but the first one is more specific: it only explains pairs in which the negation is missing in front of a bi-implication ↔ . The first may explain mistakes that are specific when modelling natural language statements that involve negations and equivalences, while the second can explain natural language statements with negations more broadly. Our algorithmic approach for finding similar transformations is to compute, for each pair ρ1 _1 and ρ2 _2 of transformations, the fraction of data points explained by ρ1 _1 that are also explained by ρ2 _2. More precisely, denote by Eρ()E_ρ(D) the set of pairs in D that are explained by ρ. We compute a correlation graph G_D for the transformations found for data set D that has a node for each transformation found in Step (1). For each pair ρ1 _1 and ρ2 _2 of transformations, the graph has an edge (ρ1,ρ2)( _1, _2) of weight |Eρ1()∩Eρ2()||Eρ2()| |E_ _1(D)∩ E_ _2(D)||E_ _2(D)|. Thus, the weight of (ρ1,ρ2)( _1, _2) is the fraction of the data points explained by ρ2 _2 which are also explained by ρ1 _1. In particular, a value of 11 means ρ1 _1 explains all pairs of D explained by ρ2 _2 (and possibly more) and a value of 00 means that it explains none. A cluster within a correlation graph is a set of nodes that are connected by a path consisting of edges of non-zero weight. Consider the following illustrative toy example of a correlation graph for a small hand-chosen data set. Example 3.1. Consider the following five transformations ρ1 _1: → 2Y_2Y1Y_1 ↝ → 1Y_1Y2Y_2 , ρ2 _2: ∧ → 3Y_3Y2Y_2Y1Y_1 ↝ ∧ → 2Y_2Y3Y_3Y1Y_1 , ρ3 _3: ¬ → 2Y_2Y1Y_1 ↝ ¬ → 1Y_1Y2Y_2 , ρ4 _4: ∧ → 4Y_4Y3Y_3∨ 2Y_2Y1Y_1 ↝ ∧ → 3Y_3Y4Y_4∨ 2Y_2Y1Y_1 , ρ5 _5: ∧ →¬ 3Y_3Y2Y_2Y1Y_1 ↝ ∧ → 2Y_2¬ 3Y_3Y1Y_1 and data set S consisting of the following (incorrect, correct)-pairs: t1 t_1 =(A→B,B→A), =(A→ B,B→ A), t2 t_2 =(¬A→B,B→¬A), =( A→ B,B→ A), t3 t_3 =((A∨¬D)∧(B→C),(A∨¬D)∧(C→B)), =((A D) (B→ C),(A D) (C→ B)), t4 t_4 =(¬((A∨B)→(C→D)),¬((C→D)→(A∨B))), =( ((A B)→(C→ D)), ((C→ D)→(A B))), t5 t_5 =((A∨B)∧(C→D),(A∨B)∧(D→C)), =((A B) (C→ D),(A B) (D→ C)), t6 t_6 =(A∧(B→¬C),A∧(¬C→B)) =(A (B→ C),A ( C→ B)) We first compute the sets Eρi()E_ _i(S) of pairs explained by each transformation ρi _i: Eρ1() E_ _1(S) =t1,t2,t3,t4,t5,t6, =\t_1,t_2,t_3,t_4,t_5,t_6\, Eρ2() E_ _2(S) =t3,t5,t6, =\t_3,t_5,t_6\, Eρ3() E_ _3(S) =t4, =\t_4\, Eρ4() E_ _4(S) =t3,t5, =\t_3,t_5\, Eρ5() E_ _5(S) =t6. =\t_6\. The resulting correlation graph is depicted below. The edges are labelled with their weight, i.e. the fraction of pairs explained by the target transformation that are also explained by the source transformation. Self-loops, edges with weight 00, and “transitive edges” (ρ1,ρ4),(ρ4,ρ1),(ρ1,ρ5),(ρ5,ρ1)( _1, _4),( _4, _1),( _1, _5),( _5, _1) are omitted for clarity. ρ1 _1ρ2 _2ρ3 _3ρ4 _4ρ5 _51112 121116 161123 231113 13 As the correlation graph indicates, ρ1,…,ρ5 _1,…, _5 form a cluster. ∎ We use correlation graphs to provide visualizations of how bug fixing transformations found in Step (1) relate to each other. In our experiments, all correlation graphs can be partitioned into clusters of a very simple shape: (a) single-transformation clusters consisting of a single transformation that only explains data points that no other transformation explains; (b) clusters with equivalent transformations consisting of transformations that all explain the same data points; and (c) hierarchical clusters whose transformations can be arranged in a tree, such that if a transformation explains data points ′⊆D D then each of its children explains only data points ′⊆′D D . In particular, clusters of type (b) and (c) are helpful for CS education researchers to identify transformations representative for common mistakes and to distinguish “high-level” from “low-level” mistakes. 4. Evaluation In this section we employ our tool-supported workflow exemplarily on educational data sets for logical modelling. In all experiments we use the workflow to find transformations, evaluate how well they cover data, and present a selection of transformations that explain large fractions of the data. Detailed tables on all experiments can be found in the supplementary material (Authors, 2026). In a first set of experiments we use our workflow on a data set for modelling in propositional logic that has been used by Schmellenkamp et al. (Schmellenkamp et al., 2023) to identify common mistakes by hand. Here we apply our workflow to a partition of the data set according to linguistic operators used in natural language statements as well as to the full data set. The objective is to see whether our workflow works as well as the by-hand-approach used in previous work. Then, in a second set of experiments, we apply our workflow to data sets for modelling with modal logic and computation tree logic (CTL). Here the objective is to see, exemplarily, whether the workflow scales to other formalisms. We first describe the experimental setup and then the results for the experiments sketched above. For finding bug fixing transformations in Step (1) of our workflow, we use the GPT-OSS-120B model (OpenAI, 2025). Initial experiments showed that this model is powerful enough, but small enough to be locally deployable. As parameters we choose a batch size of 50, due to the token limitations of the model. In all experiments, the prompt asks for transformations that explain at least 20% of the pairs in a batch. For the propositional data set grouped by linguistic operators, found transformations additionally need to explain δ=1δ=1% of all data points. The iterative process is terminated if no new transformation is chosen for 10 iterations. 4.1. Results for propositional logic The propositional data set from (Schmellenkamp et al., 2023) contains 61066106 pairs with 15721572 of them being distinct. This data set comes with a partition into 3434 subdata sets for different linguistic operators. The median and average sizes of the subdata sets are 65.565.5 and 177.8177.8, respectively. Results for linguistic operator data sets Across the subdata sets, the found transformations explain at least as many pairs as the hand-picked mistakes in a substantial fraction of cases. For >64>64% of the lingustic operator data sets, our workflow finds bug fixing transformations transformations that explain more data points than the mistakes identified in (Schmellenkamp et al., 2023). For >14%>14\% of the subdata sets, the transformations explain exactly as many pairs as the hand-picked mistakes. Results for the full propositional data set Table 1. Exemplary excerpt of the table of hierarchical bug-fixing transformation clusters that cover most of the pairs explained by the common mistake that a disjunction was erroneously used instead of a conjunction (as identified in (Schmellenkamp et al., 2023)). For each transformation, a simple representative example is provided. For the mistake as a whole, each transformation, and the entire cluster, the number # and distinct number #dst of pairs are shown. The common mistake occurrs in 5.475.47% of all pairs in the full data set (3.883.88% distinct). Of these, the complete bug fixing transformation cluster found by our workflow explains 330330 (98.898.8%). The fraction of the 334334 pairs each transformation explains is also shown (columns % and %dst, respectively). A table with all bug fixing transformation clusters found by our workflow is presented in the (anonymously published) supplementary material (Authors, 2026) . Hand-picked mistake / transformations # % #dst %dst example of (incorrect, correct) formula pairs Mistake: disjunction instead of conjunction 334 5.47% 61 3.88% Transformations combined 330 98.80% 58 95.08% ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 201 60.18% 23 37.70% ¬(A∧B∧C), (A B C), ¬A∧¬B∧¬C A B C ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 153 45.81% 16 26.23% ¬(A∧B), (A B), ¬A∧¬B A B ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 150 44.91% 15 24.59% ¬(A∧B)→C, (A B)→ C, (¬A∧¬B)→C( A B)→ C Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 128 38.32% 34 55.74% A∨B∨C,A B C, A∧B∧CA B C Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 118 35.33% 29 47.54% A∨B,A B, A∧BA B ⌈ == (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 35 10.48% 9 14.75% (¬A∨¬B)→C,( A B)→ C, (¬A∧¬B)→C( A B)→ C ⌊ == ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 35 10.48% 9 14.75% (¬A∨¬B),( A B), (¬A∧¬B)( A B) (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 17 5.09% 6 9.84% (A∨B)→¬C,(A B)→ C, (A∧B)→¬C(A B)→ C Table 2. Overview of the data sets, number of clusters found by our workflow, and the percentage of pairs explained by clusters for the propositional logic (PL), modal logic (PL) and computation tree logic (CTL) data sets. For each data set, we provide the number of (incorrect, correct) formula pairs, modelling contexts (i.e. different assignments), and statements to be modelled. PL ML CTL # total formula pairs 61066106 1248212482 72107210 # modelling contexts 1111 66 66 # statements to be modelled 5858 2828 2020 # total clusters 248 1585 271 % total explained 84.4484.44% 79.3979.39% 35.8935.89% # clusters explaining ≥0.1≥ 0.1% 78 132 62 % explained by clusters explaining ≥0.1≥ 0.1% 76.0676.06% 56.0056.00% 29.7629.76% # clusters explaining ≥0.5≥ 0.5% 21 38 16 % explained by clusters explaining ≥0.5≥ 0.5% 66.3466.34% 40.3640.36% 19.7819.78% # clusters explaining ≥1≥ 1% 15 17 8 % explained by clusters explaining ≥1≥ 1% 62.4862.48% 28.2628.26% 13.8613.86% We conducted two different experiments. First, we compared hand-picked mistakes to transformations found by our workflow as follows: For each hand-picked mistake, we identified all transformations that explain at least one pair that is explained by the hand-picked mistake and clustered them as described in Section 3.2. As an example, Table 1 shows a hand-picked mistake that a disjunction was erroneously used instead of a conjunction, and the transformations corresponding to it. This particular hand-picked mistake occurred in 334 pairs (column #), which is 5.47% of the whole data set. Of these, 330 (98.80% of 334) were explained by bug fixing transformations. Across the whole data set, the bug fixing transformations found by our workflow explain 5156 of the pairs (84.4484.44%), whereas the hand-picked mistakes only explain 4370 of the pairs (71.5771.57%). 918 pairs (15.0315.03%) are exclusively explained by the transformations, i.e. no hand-picked mistake explains any of these pairs; 132 pairs (2.162.16%) exclusively by the hand-picked mistakes. For instance, the following bug fixing transformations exclusively explain pairs that have not been explained by common mistakes in previous work ρxor-nand _xor-nand: ∨ ∧ ¬ 1Y_1Y2Y_2∧ ¬ 2Y_2Y1Y_1 ↝ ¬ ∧ 2Y_2Y1Y_1 , and ρat-least-2 _at-least-2: ∨ 3Y_3Y2Y_2Y1Y_1 ↝ ∨ ∧ 3Y_3Y2Y_2∧ 3Y_3Y1Y_1∧ 2Y_2Y1Y_1 . The transformation ρxor-nand _xor-nand represents the common mistake of using an exclusive or, expressed using a disjunction of conjunctions, instead of a negated conjunction which explains 114 pairs (6.576.57% of the pairs unexplained by the hand-picked mistakes). While a similar hand-picked mistake was found in (Schmellenkamp et al., 2023), theirs only considers the case in which the exclusive or is expressed using a bi-implication, and thus does not explain the pairs explained by ρxor-nand _xor-nand. The transformation ρat-least-2 _at-least-2, which represents the common mistake of only using a disjunction to express that at least two literals are true, explains 28 pairs (1.611.61% of the pairs unexplained by the hand-picked mistakes). 4.2. Results for Modal Logic and CTL The data set for modal logic contains 1248212482 pairs with 39513951 of them being distinct and is also from (Schmellenkamp et al., 2023). The data set for CTL contains 72107210 pairs with 26952695 distinct pairs and was collected by us using an interactive learning tool in two iterations of an introductory logic course (summer 2025 and 2026). The results for the modal logic and CTL data sets are summarized in Table 2. For modal logic, the transformations found by our workflow explain 79.3979.39% of the pairs in the data set, which is comparable to the propositional logic case. Examples of transformations are ρ1mlρ^ml_1: □ 1Y_1 ↝ ◇ 1Y_1 , ρ2mlρ^ml_2: Y1Y_1 ↝ □ 1Y_1 , and ρ3mlρ^ml_3: ∨ 2Y_2Y1Y_1 ↝ ¬ ↔ 2Y_2Y1Y_1 , which explain 2.12.1%, 1.431.43%, and 3.373.37% of the data. While ρ1mlρ^ml_1 and ρ2mlρ^ml_2 change or add the modal operators ◇ and □ , ρ3modalρ^modal_3 was also found for the propositional logic data set. It represents the common mistake of modelling an “exclusive or” as an “or”. For CTL, the transformations found by our workflow explain 35.8935.89% of the pairs with the two transformations that explain the largest fractions of the data set being ρ1ctlρ^ctl_1: Y1Y_1 ↝ AGY1Y_1 , and ρ2ctlρ^ctl_2: AXY1Y_1 ↝ AGY1Y_1 explaining 2.982.98% and 2.482.48%, respectively. Determining Usefulness of Transformations To exemplarily determine the usefulness of clusters of transformations found by our workflow, a CS educator inspected all clusters explaining at least 0.50.5% of the pairs in each of the three data sets for propositional logic, modal logic, and CTL (see also Table 2). The focus was on whether the “main transformation”, i.e. the transformation forming the root of the cluster tree, is sufficient to provide targeted feedback, or if sub-transformations, those lower in the cluster’s hierarchy, would be required for this. In propositional logic, 19 clusters had main transformations suitable for feedback, though at least 4 required sub-transformations for more targeted feedback. In CTL, all 17 clusters had useful main transformations, with at least 6 requiring sub-transformations for sufficiently specific feedback. In modal logic, the main transformation of 18 clusters was suitable for feedback, but at least 7 required sub-transformations. In 16 clusters, the main transformations were too general to identify specific mistakes directly; for 5 of these, frequent sub-transformations revealed mistakes. 5. Discussion and Conclusion We presented a tool-supported workflow for identifying candidates for common mistakes in modelling with mathematical formalisms as bug fixing transformations, clustering them, and presenting them to educators and CS education researchers. Our experiments show that the workflow recovers many known propositional logic mistakes, finds additional ones, and can also be applied to other formalisms, such as modal logic and CTL. Beyond modelling, the workflow is likely also applicable to tasks in which students transform logical formulas into normal forms. A difference in that setting is that one does not immediately have (incorrect, correct) pairs. Instead, one has an incorrect formula, a previous correct formula, and the equivalence transformation that was applied incorrectly. A suitable pair can then be constructed by applying the intended equivalence transformation to the previous correct formula, yielding the correct formula for that step. Overall, the results suggest that transformation-based mistake candidates can help scale the discovery of common mistakes in education settings. Future work includes applying the workflow to diverse data sets from different domains, and studying how the resulting candidates can be integrated into feedback systems of interactive learning tools. Acknowledgements. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 448468041. References Ahmed et al. (2018) Umair Z. Ahmed, Pawan Kumar, Amey Karkare, Purushottam Kar, and Sumit Gulwani. 2018. Compilation error repair: for the student programs, from the student programs. 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Start of prompt: Instruction Find structural differences between pairs of propositional logic formulas and express them by transformations of a transformation language. A transformation of our transformation language consists of two tree patterns: • body: the pattern that matches a subtree in the input tree (left side of the transformation). • head: the pattern that replaces the matched subtree (right side of the transformation). • Transformations are written in the format: body —> head Patterns are trees that follow the following rules: • propositional: Inner nodes are labeled by the operators of propositional logic: “or”, “and”, “impl”, “not”, “eq”. modal: Inner nodes are labeled by the operators of modal logic: “or”, “and”, “impl”, “not”, “eq”, “box” (for □ ), “dia” (for ◇ ). CTL: Inner nodes are labeled by the operators of computation tree logic: “or”, “and”, “impl”, “not”, “eq”, “ax”, “ex”, “af”, “ef”, “ag”, “eg”, “au”, “eu”. • They are written as: operator[child1 child2 …] with children separated by spaces. • Leaf nodes are labeled by tree variables, which are placeholders for subtrees. Write them as Y1, Y2, … • Variadic patterns: “and” and “or” may have arbitrary arity. Use Y1 .. Yn to denote an ordered sequence of two or more child subtrees. Example: and[Y1 .. Yn] matches and[A B], and[A B C], and[A B C D], etc.; or[Y1 .. Yn] matches or[A B], or[A B C], or[A B C D], etc. • The sequence Y1 .. Yn must be preserved unchanged: do not reorder, duplicate, or split it. Do not remove or add single elements. • Use Y1 .. Yn only as the complete child list of an and/or node. Example: and[Y1 .. Yn] • Every tree variable that appears in the head must also appear in the body. • Propositional variables of the formulas may not appear in the transformations. Use only tree variables and the operators as node labels. Matching: • A match for the body may occur anywhere in the tree, not only at the root. • Matching is injective: every body-node is mapped to a unique node in the input tree. • If tree variables appear multiple times in the same pattern, the occurrences have to be matched by isomorphic subtrees. Application: When a match is found, the corresponding subtree is replaced by the head, with variables substituted by the subtrees/labels found in the match. Your Task: Find <n_transformations> transformation(s) that can transform as many of the formula pairs as possible in one step. Return the answer exclusively in the following JSON format. Write nothing outside this JSON. Pay attention to correct quotation marks, no comments, no headings. Replace TRANSFORMATION by the respective transformation. ⬇ "transformations": [ "name": "Transformation_1", "transformation": "TRANSFORMATION" ] Here is the dataset of formula pairs: ⬇ Input: <error_formula_1> Target: <correct_formula_1> Input: <error_formula_2> Target: <correct_formula_2> ⋮ Appendix B Detailed Evaluation Data B.1. Propositional Logic Data Set Grouped by Linguistic Operator The hand-picked mistakes are from (Schmellenkamp et al., 2023). Table 3. Hand-picked errors and transformations for linguistic operator(s) AND_AND_NONE_OF Hand-picked mistake / Transformations # % #dst %dst Unexplained by ALL hand errors 48 100.00% 26 100.00% Transformations combined 13 27.08% 12 46.15% T1: Y1∧Y2∧¬(Y3∧Y4)Y_1 Y_2 (Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 4 8.33% 3 11.54% T2: (Y1∧Y2)↔¬(Y3∧Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% T3: (Y1∧Y2)→(¬Y3∧¬Y4) (Y_1 Y_2 )→ ( Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% T4: (Y1∧Y2)↔(¬Y3∧¬Y4) (Y_1 Y_2 ) ( Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% T5: (Y1∧Y2∧¬Y3)∨(Y1∧Y2∧¬Y4) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% T6: (¬Y1∧¬Y2)→(Y3∧Y4) ( Y_1 Y_2 )→ (Y_3 Y_4 ) ↝ Y3∧Y4∧¬Y1∧¬Y2Y_3 Y_4 Y_1 Y_2 1 2.08% 1 3.85% T7: (Y1∧Y2)∨(¬Y3∧¬Y4) (Y_1 Y_2 ) ( Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% T8: Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 ↝ Y3∧Y1∧¬Y2∧¬Y4Y_3 Y_1 Y_2 Y_4 1 2.08% 1 3.85% T9: Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 ↝ Y1∧Y3∧¬Y4∧¬Y2Y_1 Y_3 Y_4 Y_2 1 2.08% 1 3.85% T10: Y1∧Y2∧¬(Y3∧Y4)Y_1 Y_2 (Y_3 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 2.08% 1 3.85% Whole file 48 100.00% 26 100.00% ANY hand error explained 0 0.00% 0 0.00% ANY transformation explained 13 27.08% 12 46.15% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 13 27.08% 12 46.15% Table 4. Hand-picked errors and transformations for linguistic operator(s) AND_AND Hand-picked mistake / Transformations # % #dst %dst BUGGY_ADD_OPERAND_TO_CONJUNCTION 19 65.52% 4 30.77% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 2 6.90% 2 15.38% Transformations combined 2 100.00% 2 100.00% T1: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 1 50.00% 1 50.00% T4: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∧Y1∧Y2Y_3 Y_1 Y_2 1 50.00% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 2 6.90% 1 7.69% Transformations combined 2 100.00% 1 100.00% T5: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1∧Y2∧Y3Y_1 Y_2 Y_3 2 100.00% 1 100.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 1 3.45% 1 7.69% Transformations combined 1 100.00% 1 100.00% T6: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1∧Y2∧Y3Y_1 Y_2 Y_3 1 100.00% 1 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 1 3.45% 1 7.69% Transformations combined 1 100.00% 1 100.00% T3: ¬Y1∨…∨¬Yn Y_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 1 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 1 3.45% 1 7.69% Transformations combined 1 100.00% 1 100.00% T2: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 1 100.00% 1 100.00% Unexplained by ALL hand errors 3 10.34% 3 23.08% Transformations combined 0 0.00% 0 0.00% Whole file 29 100.00% 13 100.00% ANY hand error explained 26 89.66% 10 76.92% ANY transformation explained 7 24.14% 6 46.15% Only explained by hand error 19 65.52% 4 30.77% Only explained by transformation 0 0.00% 0 0.00% Table 5. Hand-picked errors and transformations for linguistic operator(s) AND_IF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 12 8.89% 1 1.69% Transformations combined 12 100.00% 1 100.00% T2: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 12 100.00% 1 100.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 10 7.41% 3 5.08% Transformations combined 8 80.00% 1 33.33% T4: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 8 80.00% 1 33.33% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 9 6.67% 1 1.69% Transformations combined 9 100.00% 1 100.00% T3: (Y1↔Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 9 100.00% 1 100.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 7 5.19% 1 1.69% Transformations combined 7 100.00% 1 100.00% ⌈ == T5: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 7 100.00% 1 100.00% ⌊ == T6: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 7 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_CONJUNCTION 1 0.74% 1 1.69% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 90 66.67% 46 77.97% Transformations combined 47 52.22% 11 23.91% T1: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 22 24.44% 2 4.35% T7: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 3.33% 1 2.17% T8: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 3.33% 1 2.17% T9: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 3.33% 1 2.17% T10: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 3.33% 1 2.17% T11: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 3 3.33% 1 2.17% T13: Y1→¬(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 3.33% 1 2.17% T14: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y3→Y2)∧Y1 (Y_3→ Y_2 ) Y_1 3 3.33% 1 2.17% T12: ¬Y1→(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 2.22% 1 2.17% T15: Y1→¬(¬Y2→Y3)Y_1→ ( Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 2.22% 1 2.17% Whole file 135 100.00% 59 100.00% ANY hand error explained 45 33.33% 13 22.03% ANY transformation explained 83 61.48% 15 25.42% Only explained by hand error 9 6.67% 9 15.25% Only explained by transformation 47 34.81% 11 18.64% Table 6. Hand-picked errors and transformations for linguistic operator(s) AND_NOT_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 1 100.00% 1 100.00% Transformations combined 1 100.00% 1 100.00% T1: Y1↔Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 0 0.00% 0 0.00% Transformations combined 0 0.00% 0 0.00% Whole file 1 100.00% 1 100.00% ANY hand error explained 1 100.00% 1 100.00% ANY transformation explained 1 100.00% 1 100.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 0 0.00% 0 0.00% Table 7. Hand-picked errors and transformations for linguistic operator(s) AND_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 4 80.00% 1 50.00% Transformations combined 4 100.00% 1 100.00% T1: Y1∨¬Y2Y_1 Y_2 ↝ Y1∧¬Y2Y_1 Y_2 4 100.00% 1 100.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 1 20.00% 1 50.00% Transformations combined 1 100.00% 1 100.00% T2: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 0 0.00% 0 0.00% Transformations combined 0 0.00% 0 0.00% Whole file 5 100.00% 2 100.00% ANY hand error explained 5 100.00% 2 100.00% ANY transformation explained 5 100.00% 2 100.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 0 0.00% 0 0.00% Table 8. Hand-picked errors and transformations for linguistic operator(s) AND Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 50 78.12% 6 40.00% Transformations combined 50 100.00% 6 100.00% ⌈ == T1: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 50 100.00% 6 100.00% ⌊ == T2: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 50 100.00% 6 100.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 7 10.94% 3 20.00% Transformations combined 7 100.00% 3 100.00% T3: Y1→Y2Y_1→ Y_2 ↝ Y2∧Y1Y_2 Y_1 6 85.71% 2 66.67% T5: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 1 14.29% 1 33.33% BUGGY_ADD_OPERAND_TO_CONJUNCTION 2 3.12% 2 13.33% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 2 3.12% 1 6.67% Transformations combined 2 100.00% 1 100.00% T4: Y1↔Y2Y_1 Y_2 ↝ Y2∧Y1Y_2 Y_1 2 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 1 1.56% 1 6.67% Transformations combined 1 100.00% 1 100.00% T6: Y1∧¬Y2Y_1 Y_2 ↝ Y2∧Y1Y_2 Y_1 1 100.00% 1 100.00% Unexplained by ALL hand errors 2 3.12% 2 13.33% Transformations combined 0 0.00% 0 0.00% Whole file 64 100.00% 15 100.00% ANY hand error explained 62 96.88% 13 86.67% ANY transformation explained 60 93.75% 11 73.33% Only explained by hand error 2 3.12% 2 13.33% Only explained by transformation 0 0.00% 0 0.00% Table 9. Hand-picked errors and transformations for linguistic operator(s) AT_LEAST_NEUTRAL Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_NAND_BY_DISJUNCTION 2 40.00% 1 25.00% Transformations combined 2 100.00% 1 100.00% T1: ¬(Y1∧Y2∧Y3∧Y4) (Y_1 Y_2 Y_3 Y_4 ) ↝ Y1∨Y2∨Y3∨Y4Y_1 Y_2 Y_3 Y_4 2 100.00% 1 100.00% BUGGY_ADD_OPERAND_TO_DISJUNCTION 1 20.00% 1 25.00% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 2 40.00% 2 50.00% Transformations combined 2 100.00% 2 100.00% T2: (Y1∧¬Y2∧¬Y3∧¬Y4)∨(Y2∧¬Y1∧¬Y3∧¬Y4)∨(Y3∧¬Y1∧¬Y2∧¬Y4)∨(Y4∧¬Y1∧¬Y2∧¬Y3) (Y_1 Y_2 Y_3 Y_4 ) (Y_2 Y_1 Y_3 Y_4 ) (Y_3 Y_1 Y_2 Y_4 ) (Y_4 Y_1 Y_2 Y_3 ) ↝ Y1∨Y2∨Y3∨Y4Y_1 Y_2 Y_3 Y_4 1 50.00% 1 50.00% T3: (Y1↔¬(Y2∨Y3∨Y4))∨(Y2↔¬(Y1∨Y3∨Y4))∨(Y3↔¬(Y1∨Y2∨Y4))∨(Y4↔¬(Y1∨Y2∨Y3)) (Y_1 (Y_2 Y_3 Y_4 ) ) (Y_2 (Y_1 Y_3 Y_4 ) ) (Y_3 (Y_1 Y_2 Y_4 ) ) (Y_4 (Y_1 Y_2 Y_3 ) ) ↝ Y1∨Y2∨Y3∨Y4Y_1 Y_2 Y_3 Y_4 1 50.00% 1 50.00% Whole file 5 100.00% 4 100.00% ANY hand error explained 3 60.00% 2 50.00% ANY transformation explained 4 80.00% 3 75.00% Only explained by hand error 1 20.00% 1 25.00% Only explained by transformation 2 40.00% 2 50.00% Table 10. Hand-picked errors and transformations for linguistic operator(s) AT_LEAST Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 3 1.46% 2 1.61% Transformations combined 3 100.00% 2 100.00% T10: (Y1∧Y2)∨(Y1∧Y3)∨Y2∨Y3 (Y_1 Y_2 ) (Y_1 Y_3 ) Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 3 100.00% 2 100.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 2 0.97% 2 1.61% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_DISJUNCTION 2 0.97% 2 1.61% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 199 96.60% 118 95.16% Transformations combined 101 50.75% 30 25.42% T1: (Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2)∨(Y2∧Y3∧¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 31 15.58% 9 7.63% T2: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 28 14.07% 6 5.08% T3: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 10 5.03% 1 0.85% T5: (Y1∨Y2∨¬Y3)∧(Y1∨Y3∨¬Y2)∧(Y2∨Y3∨¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 7 3.52% 4 3.39% T4: (Y1∧Y2)∨Y3∨(Y1∧Y3)∨Y2∨(Y2∧Y3)∨Y1 (Y_1 Y_2 ) Y_3 (Y_1 Y_3 ) Y_2 (Y_2 Y_3 ) Y_1 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 7 3.52% 3 2.54% T6: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 6 3.02% 2 1.69% T7: ¬(¬Y1∧¬Y2∧¬Y3) ( Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 5 2.51% 2 1.69% T8: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 4 2.01% 1 0.85% T9: (Y1∧Y2)∨(Y1∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 3 1.51% 2 1.69% Whole file 206 100.00% 124 100.00% ANY hand error explained 7 3.40% 6 4.84% ANY transformation explained 104 50.49% 32 25.81% Only explained by hand error 4 1.94% 4 3.23% Only explained by transformation 101 49.03% 30 24.19% Table 11. Hand-picked errors and transformations for linguistic operator(s) EITHER_OR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_XOR 91 50.00% 2 6.25% Transformations combined 91 100.00% 2 100.00% T1: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 91 100.00% 2 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_XOR 21 11.54% 1 3.12% Transformations combined 21 100.00% 1 100.00% T2: Y1↔Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 21 100.00% 1 100.00% BUGGY_REPLACE_NAND_BY_XOR 12 6.59% 3 9.38% Transformations combined 11 91.67% 2 66.67% T3: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 9 75.00% 1 33.33% T15: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 16.67% 1 33.33% BUGGY_REPLACE_NOR_BY_XOR 10 5.49% 2 6.25% Transformations combined 10 100.00% 2 100.00% T4: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 60.00% 1 50.00% T9: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 40.00% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_XOR 6 3.30% 2 6.25% Transformations combined 6 100.00% 2 100.00% T8: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 3 50.00% 1 50.00% T10: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 50.00% 1 50.00% BUGGY_REPLACE_CONJUNCTION_BY_XOR 5 2.75% 1 3.12% Transformations combined 5 100.00% 1 100.00% T7: Y1∧Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 5 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 4 2.20% 2 6.25% Transformations combined 3 75.00% 1 50.00% T11: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 75.00% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_EQUIVALENCE 3 1.65% 2 6.25% Transformations combined 2 66.67% 1 50.00% T12: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 66.67% 1 50.00% BUGGY_REPLACE_NAND_BY_EQUIVALENCE 1 0.55% 1 3.12% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NOR_BY_EQUIVALENCE 1 0.55% 1 3.12% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 28 15.38% 15 46.88% Transformations combined 19 67.86% 6 40.00% T5: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 21.43% 1 6.67% T6: Y1→¬Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 5 17.86% 1 6.67% T14: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 14.29% 1 6.67% T13: (Y1∨¬Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 7.14% 2 13.33% T8: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 2 7.14% 1 6.67% Whole file 182 100.00% 32 100.00% ANY hand error explained 154 84.62% 17 53.12% ANY transformation explained 168 92.31% 18 56.25% Only explained by hand error 5 2.75% 5 15.62% Only explained by transformation 19 10.44% 6 18.75% Table 12. Hand-picked errors and transformations for linguistic operator(s) IF_AND_NEUTRAL Hand-picked mistake / Transformations # % #dst %dst BUGGY_REMOVE_NEGATION 9 37.50% 3 21.43% Transformations combined 9 100.00% 3 100.00% T4: Y1→¬Y2Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 9 100.00% 3 100.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 4 16.67% 2 14.29% Transformations combined 4 100.00% 2 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 4 100.00% 2 100.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 2 8.33% 1 7.14% Transformations combined 2 100.00% 1 100.00% T3: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 2 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_NAND 1 4.17% 1 7.14% Transformations combined 1 100.00% 1 100.00% T2: ¬Y1→Y2 Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 4.17% 1 7.14% Transformations combined 1 100.00% 1 100.00% T5: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 7 29.17% 6 42.86% Transformations combined 3 42.86% 2 33.33% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 3 42.86% 2 33.33% Whole file 24 100.00% 14 100.00% ANY hand error explained 17 70.83% 8 57.14% ANY transformation explained 20 83.33% 10 71.43% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 3 12.50% 2 14.29% Table 13. Hand-picked errors and transformations for linguistic operator(s) IF_AND_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_ADD_NEGATION 24 33.80% 6 15.00% Transformations combined 24 100.00% 6 100.00% T1: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 24 100.00% 6 100.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 12 16.90% 5 12.50% Transformations combined 12 100.00% 5 100.00% T2: ¬Y1→Y2 Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 12 100.00% 5 100.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 9 12.68% 5 12.50% Transformations combined 9 100.00% 5 100.00% ⌈ == T3: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 9 100.00% 5 100.00% ⌊ == T18: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 9 100.00% 5 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 5 7.04% 3 7.50% Transformations combined 5 100.00% 3 100.00% T4: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 5 100.00% 3 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 2 2.82% 2 5.00% Transformations combined 2 100.00% 2 100.00% T7: ¬Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 50.00% 1 50.00% T16: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 50.00% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 1.41% 1 2.50% Transformations combined 1 100.00% 1 100.00% T11: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 1 1.41% 1 2.50% Transformations combined 1 100.00% 1 100.00% T9: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 100.00% 1 100.00% Unexplained by ALL hand errors 17 23.94% 17 42.50% Transformations combined 13 76.47% 13 76.47% T8: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 3 17.65% 3 17.65% T5: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 2 11.76% 2 11.76% T6: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 2 11.76% 2 11.76% T10: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 5.88% 1 5.88% T12: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 5.88% 1 5.88% T13: Y1∧Y2∧¬Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 5.88% 1 5.88% T14: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1→¬Y2Y_1→ Y_2 1 5.88% 1 5.88% T15: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 5.88% 1 5.88% T17: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 5.88% 1 5.88% Whole file 71 100.00% 40 100.00% ANY hand error explained 54 76.06% 23 57.50% ANY transformation explained 67 94.37% 36 90.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 13 18.31% 13 32.50% Table 14. Hand-picked errors and transformations for linguistic operator(s) IF_AND_ONLY_IF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_EQUIVALENCE 628 88.20% 39 52.00% Transformations combined 626 99.68% 38 97.44% T1: Y1→Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 344 54.78% 20 51.28% T2: Y1→Y2Y_1→ Y_2 ↝ Y1↔Y2Y_1 Y_2 282 44.90% 18 46.15% BUGGY_REPLACE_CONJUNCTION_BY_EQUIVALENCE 35 4.92% 10 13.33% Transformations combined 35 100.00% 10 100.00% ⌈ == T3: Y1∧Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 18 51.43% 4 40.00% ⌊ == T4: Y1∧…∧YnY_1 … Y_n ↝ Y1↔Y2Y_1 Y_2 18 51.43% 4 40.00% ⌈ == T5: Y1∧Y2Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 17 48.57% 6 60.00% ⌊ == T6: Y1∧…∧YnY_1 … Y_n ↝ Y2↔Y1Y_2 Y_1 17 48.57% 6 60.00% BUGGY_ADD_EQUIVALENCE 9 1.26% 3 4.00% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 8 1.12% 7 9.33% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_EQUIVALENCE 2 0.28% 2 2.67% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_IMPLICATION_BY_XOR 1 0.14% 1 1.33% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 29 4.07% 13 17.33% Transformations combined 18 62.07% 4 30.77% T1: Y1→Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 9 31.03% 2 15.38% T2: Y1→Y2Y_1→ Y_2 ↝ Y1↔Y2Y_1 Y_2 9 31.03% 2 15.38% Whole file 712 100.00% 75 100.00% ANY hand error explained 683 95.93% 62 82.67% ANY transformation explained 679 95.37% 52 69.33% Only explained by hand error 22 3.09% 14 18.67% Only explained by transformation 18 2.53% 4 5.33% Table 15. Hand-picked errors and transformations for linguistic operator(s) IF_AND Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 6 25.00% 3 17.65% Transformations combined 6 100.00% 3 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 6 100.00% 3 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 2 8.33% 2 11.76% Transformations combined 2 100.00% 2 100.00% T2: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 2 100.00% 2 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 4.17% 1 5.88% Transformations combined 1 100.00% 1 100.00% T3: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 4.17% 1 5.88% Transformations combined 1 100.00% 1 100.00% T5: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 14 58.33% 10 58.82% Transformations combined 7 50.00% 6 60.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 3 21.43% 2 20.00% T7: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ (Y2∧Y3)→Y1 (Y_2 Y_3 )→ Y_1 2 14.29% 2 20.00% T4: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y3∧Y2)→Y1 (Y_3 Y_2 )→ Y_1 1 7.14% 1 10.00% T6: (Y1→Y2)∧(Y1→Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ (Y1∧Y3)→Y2 (Y_1 Y_3 )→ Y_2 1 7.14% 1 10.00% Whole file 24 100.00% 17 100.00% ANY hand error explained 10 41.67% 7 41.18% ANY transformation explained 17 70.83% 13 76.47% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 7 29.17% 6 35.29% Table 16. Hand-picked errors and transformations for linguistic operator(s) IF_IF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 40 29.63% 2 4.00% Transformations combined 40 100.00% 2 100.00% T1: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 40 100.00% 2 100.00% T16: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 13 32.50% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 10 7.41% 2 4.00% Transformations combined 9 90.00% 1 50.00% ⌈ == T8: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 9 90.00% 1 50.00% ⌊ == T17: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 9 90.00% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 3 2.22% 2 4.00% Transformations combined 3 100.00% 2 100.00% T6: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 3 100.00% 2 100.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 1 0.74% 1 2.00% Transformations combined 1 100.00% 1 100.00% T1: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 1 100.00% 1 100.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 1 0.74% 1 2.00% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 1 0.74% 1 2.00% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 79 58.52% 41 82.00% Transformations combined 50 63.29% 12 29.27% T2: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 16 20.25% 1 2.44% T3: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 5 6.33% 1 2.44% T4: (Y1↔Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 5 6.33% 1 2.44% T5: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 4 5.06% 1 2.44% T13: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 4 5.06% 1 2.44% T9: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 3 3.80% 1 2.44% T10: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 3 3.80% 1 2.44% T7: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 2 2.53% 1 2.44% T11: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 2 2.53% 1 2.44% T12: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ Y1→(Y3→Y2)Y_1→ (Y_3→ Y_2 ) 2 2.53% 1 2.44% T14: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ Y2→(Y3→Y1)Y_2→ (Y_3→ Y_1 ) 2 2.53% 1 2.44% T15: (Y1→Y2)∧(Y3→Y3) (Y_1→ Y_2 ) (Y_3→ Y_3 ) ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 2 2.53% 1 2.44% Whole file 135 100.00% 50 100.00% ANY hand error explained 56 41.48% 9 18.00% ANY transformation explained 103 76.30% 18 36.00% Only explained by hand error 3 2.22% 3 6.00% Only explained by transformation 50 37.04% 12 24.00% Table 17. Hand-picked errors and transformations for linguistic operator(s) IF_NEITHER_NOR_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 73 20.05% 3 3.16% Transformations combined 73 100.00% 3 100.00% ⌈ == T1: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 65 89.04% 2 66.67% || == T2: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 65 89.04% 2 66.67% || == T3: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 65 89.04% 2 66.67% ⌊ == T28: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 65 89.04% 2 66.67% T20: (¬Y1∨¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 8 10.96% 1 33.33% BUGGY_ADD_NEGATION 61 16.76% 4 4.21% Transformations combined 58 95.08% 2 50.00% ⌈ == T4: (¬Y1∧…∧¬Yn)→Y3 ( Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→¬Y3 ( Y_1 … Y_n )→ Y_3 43 70.49% 1 25.00% ⌊ == T5: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 43 70.49% 1 25.00% ⌈ == T8: ¬(Y1∨…∨Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→¬Y3 ( Y_1 … Y_n )→ Y_3 15 24.59% 1 25.00% ⌊ == T9: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 15 24.59% 1 25.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 28 7.69% 3 3.16% Transformations combined 28 100.00% 3 100.00% T6: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 21 75.00% 2 66.67% T13: ¬Y1→¬(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 7 25.00% 1 33.33% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 10 2.75% 2 2.11% Transformations combined 8 80.00% 1 50.00% T19: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 8 80.00% 1 50.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 8 2.20% 2 2.11% Transformations combined 8 100.00% 2 100.00% ⌈ == T23: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 50.00% 1 50.00% ⌊ == T32: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 50.00% 1 50.00% T27: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 4 50.00% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 7 1.92% 2 2.11% Transformations combined 6 85.71% 1 50.00% T15: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 6 85.71% 1 50.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 6 1.65% 1 1.05% Transformations combined 6 100.00% 1 100.00% ⌈ == T14: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 6 100.00% 1 100.00% ⌊ == T21: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 6 100.00% 1 100.00% BUGGY_REPLACE_XOR_BY_NOR 5 1.37% 1 1.05% Transformations combined 5 100.00% 1 100.00% ⌈ == T25: ¬(Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 5 100.00% 1 100.00% || == T29: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 5 100.00% 1 100.00% ⌊ == T31: ¬(Y1↔Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 5 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 2 0.55% 2 2.11% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 0.27% 1 1.05% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 1 0.27% 1 1.05% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 162 44.51% 73 76.84% Transformations combined 73 45.06% 10 13.70% T7: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 18 11.11% 1 1.37% T18: ¬Y1→¬(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 13 8.02% 1 1.37% T10: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 9 5.56% 1 1.37% ⌈ == T11: (Y1∨…∨Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→¬Y3 ( Y_1 … Y_n )→ Y_3 7 4.32% 1 1.37% ⌊ == T12: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 7 4.32% 1 1.37% T24: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 5 3.09% 1 1.37% T30: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 5 3.09% 1 1.37% T16: ¬(Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 2.47% 1 1.37% T17: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 2.47% 1 1.37% T22: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 2.47% 1 1.37% T26: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 4 2.47% 1 1.37% Whole file 364 100.00% 95 100.00% ANY hand error explained 202 55.49% 22 23.16% ANY transformation explained 265 72.80% 24 25.26% Only explained by hand error 10 2.75% 8 8.42% Only explained by transformation 73 20.05% 10 10.53% Table 18. Hand-picked errors and transformations for linguistic operator(s) IF_NEITHER_NOR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 37 45.12% 2 6.25% Transformations combined 37 100.00% 2 100.00% T1: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 28 75.68% 1 50.00% T2: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 9 24.32% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 5 6.10% 2 6.25% Transformations combined 5 100.00% 2 100.00% T4: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 4 80.00% 1 50.00% T14: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 1 20.00% 1 50.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 4 4.88% 1 3.12% Transformations combined 4 100.00% 1 100.00% T3: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 3 3.66% 2 6.25% Transformations combined 3 100.00% 2 100.00% T6: (¬Y1∧¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 66.67% 1 50.00% T12: ¬(Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 33.33% 1 50.00% BUGGY_REPLACE_XOR_BY_NOR 3 3.66% 1 3.12% Transformations combined 3 100.00% 1 100.00% T5: ¬(Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 3 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_NOR 2 2.44% 1 3.12% Transformations combined 2 100.00% 1 100.00% T15: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 100.00% 1 100.00% BUGGY_ADD_CONCLUSION_FOR_IMPLICATION 1 1.22% 1 3.12% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_NEGATION 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T28: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 100.00% 1 100.00% BUGGY_MOVE_PARENTHESIS2 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T22: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 1 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T25: ¬(Y1∨¬Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 1 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T9: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T24: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 1 100.00% 1 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 1 1.22% 1 3.12% Transformations combined 1 100.00% 1 100.00% T8: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 100.00% 1 100.00% Unexplained by ALL hand errors 21 25.61% 16 50.00% Transformations combined 18 85.71% 13 81.25% T10: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 14.29% 1 6.25% T7: ¬(Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 9.52% 1 6.25% T11: (Y1↔¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 9.52% 1 6.25% T17: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 9.52% 1 6.25% T13: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% T16: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 1 4.76% 1 6.25% T18: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% T19: (¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% T20: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% T21: (Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 1 4.76% 1 6.25% T23: (¬Y1↔Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% T26: Y1∧¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 1 4.76% 1 6.25% T27: ¬(Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 4.76% 1 6.25% Whole file 82 100.00% 32 100.00% ANY hand error explained 61 74.39% 16 50.00% ANY transformation explained 78 95.12% 28 87.50% Only explained by hand error 1 1.22% 1 3.12% Only explained by transformation 18 21.95% 13 40.62% Table 19. Hand-picked errors and transformations for linguistic operator(s) IF_NOT_AND Hand-picked mistake / Transformations # % #dst %dst BUGGY_ADD_NEGATION 16 39.02% 2 12.50% Transformations combined 16 100.00% 2 100.00% T1: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y2∧¬Y1)→Y3 (Y_2 Y_1 )→ Y_3 15 93.75% 1 50.00% T11: Y1∨¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y3∧¬Y2)→Y1 (Y_3 Y_2 )→ Y_1 1 6.25% 1 50.00% BUGGY_REMOVE_NEGATION 6 14.63% 2 12.50% Transformations combined 6 100.00% 2 100.00% T2: (¬Y1∧Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 5 83.33% 1 50.00% T7: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ Y1∧¬Y2Y_1 Y_2 1 16.67% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 4 9.76% 2 12.50% Transformations combined 4 100.00% 2 100.00% T3: Y1→(Y2∧¬Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧¬Y3)→Y1 (Y_2 Y_3 )→ Y_1 4 100.00% 2 100.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 2 4.88% 1 6.25% Transformations combined 2 100.00% 1 100.00% T4: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 2 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 2.44% 1 6.25% Transformations combined 1 100.00% 1 100.00% T13: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 12 29.27% 8 50.00% Transformations combined 9 75.00% 6 75.00% T5: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ Y2∧¬Y1Y_2 Y_1 2 16.67% 1 12.50% T6: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y2∧¬Y1)→Y3 (Y_2 Y_1 )→ Y_3 2 16.67% 1 12.50% T10: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (Y3∧¬Y2)→Y1 (Y_3 Y_2 )→ Y_1 2 16.67% 1 12.50% T8: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y3∧¬Y2)→Y1 (Y_3 Y_2 )→ Y_1 1 8.33% 1 12.50% T9: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y3∧¬Y1)→Y2 (Y_3 Y_1 )→ Y_2 1 8.33% 1 12.50% T12: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y3∧¬Y1)→Y2 (Y_3 Y_1 )→ Y_2 1 8.33% 1 12.50% Whole file 41 100.00% 16 100.00% ANY hand error explained 29 70.73% 8 50.00% ANY transformation explained 38 92.68% 14 87.50% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 9 21.95% 6 37.50% Table 20. Hand-picked errors and transformations for linguistic operator(s) IF_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 137 47.24% 1 4.35% Transformations combined 137 100.00% 1 100.00% T1: ¬Y1→Y2 Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 137 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 54 18.62% 2 8.70% Transformations combined 54 100.00% 2 100.00% T2: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 49 90.74% 1 50.00% T8: Y1↔¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 5 9.26% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 20 6.90% 2 8.70% Transformations combined 20 100.00% 2 100.00% T5: Y1↔¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 15 75.00% 1 50.00% T9: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 5 25.00% 1 50.00% BUGGY_ADD_NEGATION 20 6.90% 1 4.35% Transformations combined 20 100.00% 1 100.00% T4: Y1→Y2Y_1→ Y_2 ↝ Y1→¬Y2Y_1→ Y_2 20 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 14 4.83% 1 4.35% Transformations combined 14 100.00% 1 100.00% T3: Y1∧¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 14 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 10 3.45% 1 4.35% Transformations combined 10 100.00% 1 100.00% T6: Y1→Y2Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 10 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 8 2.76% 1 4.35% Transformations combined 8 100.00% 1 100.00% T3: Y1∧¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 8 100.00% 1 100.00% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 4 1.38% 1 4.35% Transformations combined 4 100.00% 1 100.00% T7: Y1∨¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 4 100.00% 1 100.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 2 0.69% 1 4.35% Transformations combined 2 100.00% 1 100.00% T7: Y1∨¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 2 100.00% 1 100.00% BUGGY_EXPLICIFY_IMPLICATION_1 1 0.34% 1 4.35% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NOR_BY_REVERSED_IMPLICATION 1 0.34% 1 4.35% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 19 6.55% 10 43.48% Transformations combined 10 52.63% 2 20.00% T11: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→¬Y2Y_1→ Y_2 7 36.84% 1 10.00% T10: Y1↔Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 3 15.79% 1 10.00% Whole file 290 100.00% 23 100.00% ANY hand error explained 271 93.45% 13 56.52% ANY transformation explained 279 96.21% 13 56.52% Only explained by hand error 2 0.69% 2 8.70% Only explained by transformation 10 3.45% 2 8.70% Table 21. Hand-picked errors and transformations for linguistic operator(s) IF_OR_NEUTRAL Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 6 17.65% 2 9.09% Transformations combined 6 100.00% 2 100.00% T1: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 6 100.00% 2 100.00% BUGGY_REMOVE_NEGATION 5 14.71% 2 9.09% Transformations combined 5 100.00% 2 100.00% T2: Y1→(Y2∨¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 4 80.00% 1 50.00% T5: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 1 20.00% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 4 11.76% 1 4.55% Transformations combined 4 100.00% 1 100.00% T3: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 4 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_DISJUNCTION 3 8.82% 2 9.09% Transformations combined 3 100.00% 2 100.00% T4: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 66.67% 1 50.00% T12: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 33.33% 1 50.00% BUGGY_REPLACE_NAND_BY_DISJUNCTION 2 5.88% 2 9.09% Transformations combined 2 100.00% 2 100.00% T8: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1∨Y2Y_1 Y_2 1 50.00% 1 50.00% T13: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 50.00% 1 50.00% BUGGY_REMOVE_FIRST_OPERAND_FROM_CONJUNCTION 1 2.94% 1 4.55% Transformations combined 1 100.00% 1 100.00% T9: (Y1∨Y2)∧¬(Y1∧Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ Y1∨Y2Y_1 Y_2 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 2.94% 1 4.55% Transformations combined 1 100.00% 1 100.00% T7: Y1↔(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 1 2.94% 1 4.55% Transformations combined 1 100.00% 1 100.00% T10: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 1 100.00% 1 100.00% Unexplained by ALL hand errors 11 32.35% 10 45.45% Transformations combined 7 63.64% 7 70.00% T6: ¬Y1→(Y2∨¬Y3) Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T11: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T14: ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T15: Y1↔(¬Y2∧¬Y3)Y_1 ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T16: Y1↔(¬Y2∨¬Y3)Y_1 ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T17: Y1↔((Y2∨Y3)∧¬(Y2∧Y3))Y_1 ( (Y_2 Y_3 ) (Y_2 Y_3 ) ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% T18: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 9.09% 1 10.00% Whole file 34 100.00% 22 100.00% ANY hand error explained 23 67.65% 12 54.55% ANY transformation explained 30 88.24% 19 86.36% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 7 20.59% 7 31.82% Table 22. Hand-picked errors and transformations for linguistic operator(s) IF_OR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 18 52.94% 4 23.53% Transformations combined 18 100.00% 4 100.00% ⌈ == T1: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 18 100.00% 4 100.00% ⌊ == T9: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 18 100.00% 4 100.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 3 8.82% 2 11.76% Transformations combined 3 100.00% 2 100.00% T3: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 3 100.00% 2 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 3 8.82% 2 11.76% Transformations combined 3 100.00% 2 100.00% T2: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 100.00% 2 100.00% BUGGY_PULL_NEGATION_DISJUNCTION 1 2.94% 1 5.88% Transformations combined 1 100.00% 1 100.00% T6: (¬Y1∨¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 2.94% 1 5.88% Transformations combined 1 100.00% 1 100.00% T7: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 2.94% 1 5.88% Transformations combined 1 100.00% 1 100.00% T8: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 7 20.59% 6 35.29% Transformations combined 2 28.57% 2 33.33% T4: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 14.29% 1 16.67% T5: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 14.29% 1 16.67% Whole file 34 100.00% 17 100.00% ANY hand error explained 27 79.41% 11 64.71% ANY transformation explained 29 85.29% 13 76.47% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 2 5.88% 2 11.76% Table 23. Hand-picked errors and transformations for linguistic operator(s) IF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 61 58.65% 4 19.05% Transformations combined 61 100.00% 4 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 61 100.00% 4 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 20 19.23% 4 19.05% Transformations combined 20 100.00% 4 100.00% T2: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 20 100.00% 4 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 10 9.62% 4 19.05% Transformations combined 10 100.00% 4 100.00% T4: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 6 60.00% 1 25.00% T3: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 4 40.00% 3 75.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 3 2.88% 2 9.52% Transformations combined 3 100.00% 2 100.00% T3: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 3 100.00% 2 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 3 2.88% 1 4.76% Transformations combined 3 100.00% 1 100.00% T5: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 3 100.00% 1 100.00% BUGGY_REMOVE_NEGATION 1 0.96% 1 4.76% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 1 0.96% 1 4.76% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 1 0.96% 1 4.76% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 1 0.96% 1 4.76% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_IMPLICATION 1 0.96% 1 4.76% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 2 1.92% 1 4.76% Transformations combined 0 0.00% 0 0.00% Whole file 104 100.00% 21 100.00% ANY hand error explained 102 98.08% 20 95.24% ANY transformation explained 97 93.27% 15 71.43% Only explained by hand error 5 4.81% 5 23.81% Only explained by transformation 0 0.00% 0 0.00% Table 24. Hand-picked errors and transformations for linguistic operator(s) NEITHER_NOR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 25 37.31% 7 23.33% Transformations combined 25 100.00% 7 100.00% T1: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 14 56.00% 2 28.57% ⌈ == T2: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 7 28.00% 2 28.57% ⌊ == T7: ¬Y1∨…∨¬Yn Y_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 7 28.00% 2 28.57% T11: ¬Y1∨¬Y2∨¬Y3 Y_1 Y_2 Y_3 ↝ ¬Y1∧¬Y3∧¬Y2 Y_1 Y_3 Y_2 2 8.00% 1 14.29% ⌈ == T4: ¬Y1∨¬Y2∨¬Y3 Y_1 Y_2 Y_3 ↝ ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 1 4.00% 1 14.29% ⌊ == T9: Y1∨…∨Yn∨Y3Y_1 … Y_n Y_3 ↝ Y1∧…∧Yn∧Y3Y_1 … Y_n Y_3 1 4.00% 1 14.29% T14: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y1∧Y2∧Y3Y_1 Y_2 Y_3 1 4.00% 1 14.29% BUGGY_ADD_OPERAND_TO_DISJUNCTION 4 5.97% 2 6.67% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 3 4.48% 1 3.33% Transformations combined 3 100.00% 1 100.00% T3: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 3 100.00% 1 100.00% BUGGY_ADD_NEGATION 2 2.99% 2 6.67% Transformations combined 2 100.00% 2 100.00% T10: Y1∧¬Y2∧¬Y3Y_1 Y_2 Y_3 ↝ ¬Y2∧¬Y3∧¬Y1 Y_2 Y_3 Y_1 1 50.00% 1 50.00% T12: Y1∧¬Y2∧¬Y3Y_1 Y_2 Y_3 ↝ ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 1 50.00% 1 50.00% BUGGY_REMOVE_NEGATION 1 1.49% 1 3.33% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 1 1.49% 1 3.33% Transformations combined 1 100.00% 1 100.00% T6: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 100.00% 1 100.00% Unexplained by ALL hand errors 31 46.27% 16 53.33% Transformations combined 5 16.13% 5 31.25% T5: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y2∧¬Y3∧¬Y1 Y_2 Y_3 Y_1 1 3.23% 1 6.25% T8: Y1↔(Y2↔Y3)Y_1 (Y_2 Y_3 ) ↝ Y3∧Y2∧Y1Y_3 Y_2 Y_1 1 3.23% 1 6.25% T13: (Y1↔¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ ¬Y2∧¬Y1∧¬Y3 Y_2 Y_1 Y_3 1 3.23% 1 6.25% T15: ¬(Y1∧Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ ¬Y3∧¬Y1∧¬Y2 Y_3 Y_1 Y_2 1 3.23% 1 6.25% T16: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ ¬Y1∧¬Y3∧¬Y2 Y_1 Y_3 Y_2 1 3.23% 1 6.25% Whole file 67 100.00% 30 100.00% ANY hand error explained 36 53.73% 14 46.67% ANY transformation explained 36 53.73% 16 53.33% Only explained by hand error 5 7.46% 3 10.00% Only explained by transformation 5 7.46% 5 16.67% Table 25. Hand-picked errors and transformations for linguistic operator(s) NEUTRAL Hand-picked mistake / Transformations # % #dst %dst BUGGY_REMOVE_NEGATION 52 100.00% 2 100.00% Transformations combined 52 100.00% 2 100.00% T1: ¬Y1 Y_1 ↝ Y1Y_1 52 100.00% 2 100.00% Unexplained by ALL hand errors 0 0.00% 0 0.00% Transformations combined 0 0.00% 0 0.00% Whole file 52 100.00% 2 100.00% ANY hand error explained 52 100.00% 2 100.00% ANY transformation explained 52 100.00% 2 100.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 0 0.00% 0 0.00% Table 26. Hand-picked errors and transformations for linguistic operator(s) NONE_OF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 36 78.26% 7 46.67% Transformations combined 36 100.00% 7 100.00% T1: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 34 94.44% 5 71.43% T7: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 2 5.56% 2 28.57% BUGGY_REPLACE_NOR_BY_CONJUNCTION 4 8.70% 2 13.33% Transformations combined 4 100.00% 2 100.00% T2: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 4 100.00% 2 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 2 4.35% 2 13.33% Transformations combined 2 100.00% 2 100.00% T3: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 50.00% 1 50.00% T6: ¬(¬Y1∧…∧¬Yn) ( Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 50.00% 1 50.00% Unexplained by ALL hand errors 4 8.70% 4 26.67% Transformations combined 2 50.00% 2 50.00% T4: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ ¬Y3∧¬Y1∧¬Y2 Y_3 Y_1 Y_2 1 25.00% 1 25.00% T5: ¬(Y1∧Y2)∧¬Y3 (Y_1 Y_2 ) Y_3 ↝ ¬Y3∧¬Y1∧¬Y2 Y_3 Y_1 Y_2 1 25.00% 1 25.00% Whole file 46 100.00% 15 100.00% ANY hand error explained 42 91.30% 11 73.33% ANY transformation explained 44 95.65% 13 86.67% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 2 4.35% 2 13.33% Table 27. Hand-picked errors and transformations for linguistic operator(s) NOT_ALL_OF Hand-picked mistake / Transformations # % #dst %dst BUGGY_PULL_NEGATION_CONJUNCTION 67 12.48% 13 7.78% Transformations combined 67 100.00% 13 100.00% ⌈ == T3: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 61 91.04% 12 92.31% ⌊ == T4: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 61 91.04% 12 92.31% T17: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 6 8.96% 1 7.69% BUGGY_REPLACE_XOR_BY_NAND 44 8.19% 5 2.99% Transformations combined 43 97.73% 4 80.00% T7: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 24 54.55% 2 40.00% T11: ¬Y1↔Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 19 43.18% 2 40.00% BUGGY_REPLACE_DISJUNCTION_BY_NAND 39 7.26% 8 4.79% Transformations combined 35 89.74% 6 75.00% ⌈ == T5: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 35 89.74% 6 75.00% ⌊ == T6: Y1∨…∨YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 35 89.74% 6 75.00% BUGGY_REPLACE_NOR_BY_NAND 26 4.84% 7 4.19% Transformations combined 22 84.62% 6 85.71% ⌈ == T8: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 84.62% 6 85.71% ⌊ == T9: ¬(Y1∨…∨Yn) (Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 22 84.62% 6 85.71% BUGGY_REPLACE_IMPLICATION_BY_NAND 18 3.35% 5 2.99% Transformations combined 15 83.33% 3 60.00% T15: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 8 44.44% 2 40.00% T21: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 7 38.89% 1 20.00% BUGGY_REPLACE_CONJUNCTION_BY_NAND 14 2.61% 4 2.40% Transformations combined 13 92.86% 3 75.00% ⌈ == T12: Y1∧Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 13 92.86% 3 75.00% ⌊ == T24: Y1∧…∧YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 13 92.86% 3 75.00% BUGGY_REPLACE_EQUIVALENCE_BY_NAND 11 2.05% 5 2.99% Transformations combined 10 90.91% 4 80.00% T13: Y1↔Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 10 90.91% 4 80.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 5 0.93% 4 2.40% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_DISJUNCTION 4 0.74% 3 1.80% Transformations combined 0 0.00% 0 0.00% BUGGY_MOVE_PARENTHESIS1 4 0.74% 2 1.20% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_NEGATION 4 0.74% 1 0.60% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 1 0.19% 1 0.60% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 1 0.19% 1 0.60% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_DISJUNCTION 1 0.19% 1 0.60% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 298 55.49% 107 64.07% Transformations combined 245 82.21% 62 57.94% T1: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 114 38.26% 20 18.69% T2: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 66 22.15% 6 5.61% T10: (Y1∨¬Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 7.38% 7 6.54% T23: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 15 5.03% 12 11.21% ⌈ == T19: (Y1∨Y2)∧¬(Y1∧Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 2.01% 4 3.74% ⌊ == T20: Y1∧¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ ¬(Y2∧Y3) (Y_2 Y_3 ) 6 2.01% 4 3.74% T14: (Y1∧Y2)∨(Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 9 3.02% 6 5.61% T16: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 7 2.35% 3 2.80% T18: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 2.01% 4 3.74% T22: Y1∧¬Y2∧Y2∧¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 2.01% 4 3.74% Whole file 537 100.00% 167 100.00% ANY hand error explained 239 44.51% 60 35.93% ANY transformation explained 450 83.80% 101 60.48% Only explained by hand error 34 6.33% 21 12.57% Only explained by transformation 245 45.62% 62 37.13% Table 28. Hand-picked errors and transformations for linguistic operator(s) NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_ADD_NEGATION 1 100.00% 1 100.00% Transformations combined 1 100.00% 1 100.00% T1: Y1Y_1 ↝ ¬Y1 Y_1 1 100.00% 1 100.00% Unexplained by ALL hand errors 0 0.00% 0 0.00% Transformations combined 0 0.00% 0 0.00% Whole file 1 100.00% 1 100.00% ANY hand error explained 1 100.00% 1 100.00% ANY transformation explained 1 100.00% 1 100.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 0 0.00% 0 0.00% Table 29. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF_AND Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 446 50.06% 5 5.75% Transformations combined 443 99.33% 3 60.00% ⌈ == T1: (Y1∧…∧Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ Y3→(Y1∧…∧Yn)Y_3→ (Y_1 … Y_n ) 443 99.33% 3 60.00% || == T2: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 443 99.33% 3 60.00% ⌊ == T3: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 443 99.33% 3 60.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 202 22.67% 4 4.60% Transformations combined 201 99.50% 3 75.00% ⌈ == T4: (Y1∧…∧Yn)↔Y3 (Y_1 … Y_n ) Y_3 ↝ Y3→(Y1∧…∧Yn)Y_3→ (Y_1 … Y_n ) 201 99.50% 3 75.00% || == T5: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 201 99.50% 3 75.00% ⌊ == T6: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 201 99.50% 3 75.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 18 2.02% 3 3.45% Transformations combined 18 100.00% 3 100.00% ⌈ == T7: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) 18 100.00% 3 100.00% || == T8: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 18 100.00% 3 100.00% ⌊ == T9: Y3↔(Y1∧Y2)Y_3 (Y_1 Y_2 ) ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 18 100.00% 3 100.00% BUGGY_ADD_PREMISE_FOR_IMPLICATION 12 1.35% 2 2.30% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 10 1.12% 2 2.30% Transformations combined 10 100.00% 2 100.00% T10: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 10 100.00% 2 100.00% BUGGY_REPLACE_CONJUNCTION_BY_NAND 5 0.56% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_NEGATION 4 0.45% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 4 0.45% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 3 0.34% 2 2.30% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_REVERSED_IMPLICATION 3 0.34% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_OPERAND_TO_CONJUNCTION 2 0.22% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 2 0.22% 1 1.15% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 1 0.11% 1 1.15% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 179 20.09% 62 71.26% Transformations combined 9 5.03% 1 1.61% ⌈ == T11: (Y1∧…∧Yn)↔¬Y3 (Y_1 … Y_n ) Y_3 ↝ Y3→(Y1∧…∧Yn)Y_3→ (Y_1 … Y_n ) 9 5.03% 1 1.61% ⌊ == T12: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 9 5.03% 1 1.61% Whole file 891 100.00% 87 100.00% ANY hand error explained 712 79.91% 25 28.74% ANY transformation explained 681 76.43% 12 13.79% Only explained by hand error 40 4.49% 14 16.09% Only explained by transformation 9 1.01% 1 1.15% Table 30. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF_AT_LEAST Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 277 45.26% 20 10.10% Transformations combined 274 98.92% 18 90.00% T3: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 239 86.28% 4 20.00% T7: (Y1∨Y2∨Y3)→Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ Y4→(Y1∨Y2∨Y3)Y_4→ (Y_1 Y_2 Y_3 ) 35 12.64% 14 70.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 33 5.39% 4 2.02% Transformations combined 33 100.00% 4 100.00% T1: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 33 100.00% 4 100.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 29 4.74% 17 8.59% Transformations combined 23 79.31% 12 70.59% T6: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 23 79.31% 12 70.59% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 29 4.74% 6 3.03% Transformations combined 29 100.00% 6 100.00% T4: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 29 100.00% 6 100.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 12 1.96% 3 1.52% Transformations combined 11 91.67% 2 66.67% T5: Y1∧…∧YnY_1 … Y_n ↝ Y1∨…∨YnY_1 … Y_n 11 91.67% 2 66.67% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 8 1.31% 4 2.02% Transformations combined 6 75.00% 2 50.00% T6: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 6 75.00% 2 50.00% BUGGY_REPLACE_XOR_BY_DISJUNCTION 6 0.98% 3 1.52% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_DISJUNCTION 5 0.82% 2 1.01% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_DISJUNCTION 4 0.65% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 3 0.49% 3 1.52% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_OPERAND_TO_DISJUNCTION 2 0.33% 2 1.01% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_NOR 2 0.33% 2 1.01% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_NEGATION 2 0.33% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_PREMISE_FOR_IMPLICATION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_MOVE_PARENTHESIS2 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_FIRST_OPERAND_FROM_CONJUNCTION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_FIRST_OPERAND_FROM_DISJUNCTION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_LATER_OPERAND_FROM_DISJUNCTION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NOR_BY_DISJUNCTION 1 0.16% 1 0.51% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 193 31.54% 123 62.12% Transformations combined 10 5.18% 1 0.81% T2: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 10 5.18% 1 0.81% Whole file 612 100.00% 198 100.00% ANY hand error explained 419 68.46% 75 37.88% ANY transformation explained 386 63.07% 45 22.73% Only explained by hand error 43 7.03% 31 15.66% Only explained by transformation 10 1.63% 1 0.51% Table 31. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF_NEITHER_NOR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 138 28.34% 33 15.21% Transformations combined 138 100.00% 33 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 117 84.78% 20 60.61% T4: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 21 15.22% 13 39.39% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 47 9.65% 17 7.83% Transformations combined 47 100.00% 17 100.00% ⌈ == T2: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 29 61.70% 10 58.82% ⌊ == T3: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 29 61.70% 10 58.82% T14: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 18 38.30% 7 41.18% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 25 5.13% 15 6.91% Transformations combined 25 100.00% 15 100.00% T7: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 19 76.00% 9 60.00% T17: Y1↔¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 6 24.00% 6 40.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 21 4.31% 7 3.23% Transformations combined 21 100.00% 7 100.00% ⌈ == T5: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 21 100.00% 7 100.00% ⌊ == T6: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 21 100.00% 7 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 17 3.49% 8 3.69% Transformations combined 17 100.00% 8 100.00% ⌈ == T8: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 17 100.00% 8 100.00% ⌊ == T10: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 17 100.00% 8 100.00% BUGGY_ADD_NEGATION 9 1.85% 5 2.30% Transformations combined 9 100.00% 5 100.00% T18: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 5 55.56% 3 60.00% T16: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 44.44% 2 40.00% BUGGY_REMOVE_NEGATION 6 1.23% 4 1.84% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 4 0.82% 4 1.84% Transformations combined 0 0.00% 0 0.00% BUGGY_MOVE_PARENTHESIS2 3 0.62% 2 0.92% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 2 0.41% 2 0.92% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 2 0.41% 2 0.92% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_EQUIVALENCE_BY_NOR 2 0.41% 2 0.92% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_FIRST_FROM_EQUIVALENCE 1 0.21% 1 0.46% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_NAND 1 0.21% 1 0.46% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 1 0.21% 1 0.46% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_NOR 1 0.21% 1 0.46% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 207 42.51% 112 51.61% Transformations combined 132 63.77% 46 41.07% T11: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 40 19.32% 14 12.50% T12: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 19 9.18% 7 6.25% T9: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 17 8.21% 7 6.25% ⌈ == T2: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 15 7.25% 2 1.79% ⌊ == T3: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 15 7.25% 2 1.79% T4: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 14 6.76% 2 1.79% T15: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 13 6.28% 6 5.36% T13: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 9 4.35% 6 5.36% T16: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 5 2.42% 2 1.79% Whole file 487 100.00% 217 100.00% ANY hand error explained 280 57.49% 105 48.39% ANY transformation explained 389 79.88% 131 60.37% Only explained by hand error 23 4.72% 20 9.22% Only explained by transformation 132 27.10% 46 21.20% Table 32. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF_NOT_AND_NOT_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 19 32.76% 2 11.11% Transformations combined 19 100.00% 2 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 11 57.89% 1 50.00% T7: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 42.11% 1 50.00% BUGGY_ADD_NEGATION 3 5.17% 2 11.11% Transformations combined 3 100.00% 2 100.00% T10: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 2 66.67% 1 50.00% T16: Y1→Y2Y_1→ Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 1 33.33% 1 50.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 3 5.17% 1 5.56% Transformations combined 3 100.00% 1 100.00% T3: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 3 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_CONJUNCTION 2 3.45% 1 5.56% Transformations combined 2 100.00% 1 100.00% T4: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 2 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 1 1.72% 1 5.56% Transformations combined 1 100.00% 1 100.00% T2: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 1 1.72% 1 5.56% Transformations combined 1 100.00% 1 100.00% T12: ¬(Y1∨Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 1 100.00% 1 100.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 1 1.72% 1 5.56% Transformations combined 1 100.00% 1 100.00% T5: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 100.00% 1 100.00% Unexplained by ALL hand errors 28 48.28% 9 50.00% Transformations combined 27 96.43% 8 88.89% T6: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 28.57% 1 11.11% T8: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 7 25.00% 1 11.11% T9: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 4 14.29% 1 11.11% T11: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 2 7.14% 1 11.11% T14: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 2 7.14% 1 11.11% T15: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 2 7.14% 1 11.11% T13: ¬Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 1 3.57% 1 11.11% T17: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 1 3.57% 1 11.11% Whole file 58 100.00% 18 100.00% ANY hand error explained 30 51.72% 9 50.00% ANY transformation explained 57 98.28% 17 94.44% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 27 46.55% 8 44.44% Table 33. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF_NOT_OR_NOT_NOT Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 50 30.12% 10 12.05% Transformations combined 50 100.00% 10 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 44 88.00% 7 70.00% T11: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 6 12.00% 3 30.00% BUGGY_ADD_NEGATION 21 12.65% 10 12.05% Transformations combined 21 100.00% 10 100.00% T2: Y1→Y2Y_1→ Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 16 76.19% 6 60.00% T16: Y1∨Y2Y_1 Y_2 ↝ Y2∨¬Y1Y_2 Y_1 3 14.29% 2 20.00% T14: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 2 9.52% 2 20.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 14 8.43% 4 4.82% Transformations combined 13 92.86% 3 75.00% T6: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 13 92.86% 3 75.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 12 7.23% 6 7.23% Transformations combined 12 100.00% 6 100.00% T3: ¬(Y1∨…∨Yn) (Y_1 … Y_n ) ↝ ¬Y1∨…∨¬Yn Y_1 … Y_n 8 66.67% 4 66.67% ⌈ == T4: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬Y1∨¬Y2 Y_1 Y_2 4 33.33% 2 33.33% ⌊ == T5: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬Y1∨…∨¬Yn Y_1 … Y_n 4 33.33% 2 33.33% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 10 6.02% 5 6.02% Transformations combined 9 90.00% 4 80.00% T7: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 9 90.00% 4 80.00% BUGGY_REPLACE_NOR_BY_DISJUNCTION 10 6.02% 5 6.02% Transformations combined 10 100.00% 5 100.00% T10: Y1→Y2Y_1→ Y_2 ↝ ¬Y2→Y1 Y_2→ Y_1 10 100.00% 5 100.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 3 1.81% 2 2.41% Transformations combined 3 100.00% 2 100.00% T9: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 100.00% 2 100.00% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 2 1.20% 2 2.41% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 1 0.60% 1 1.20% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_DISJUNCTION 1 0.60% 1 1.20% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 42 25.30% 37 44.58% Transformations combined 13 30.95% 9 24.32% T12: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 5 11.90% 4 10.81% T8: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 7.14% 2 5.41% T13: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 3 7.14% 2 5.41% T15: ((Y1∧¬Y2)∨(Y2∧¬Y1))→Y3 ( (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 2 4.76% 1 2.70% Whole file 166 100.00% 83 100.00% ANY hand error explained 124 74.70% 46 55.42% ANY transformation explained 131 78.92% 49 59.04% Only explained by hand error 6 3.61% 6 7.23% Only explained by transformation 13 7.83% 9 10.84% Table 34. Hand-picked errors and transformations for linguistic operator(s) ONLY_IF Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 164 35.12% 1 3.70% Transformations combined 164 100.00% 1 100.00% T1: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 164 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 156 33.40% 2 7.41% Transformations combined 152 97.44% 1 50.00% T2: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 152 97.44% 1 50.00% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 97 20.77% 3 11.11% Transformations combined 93 95.88% 1 33.33% T3: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 93 95.88% 1 33.33% BUGGY_REPLACE_XOR_BY_REVERSED_IMPLICATION 14 3.00% 3 11.11% Transformations combined 13 92.86% 2 66.67% T5: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 8 57.14% 1 33.33% T8: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 5 35.71% 1 33.33% BUGGY_REPLACE_XOR_BY_IMPLICATION 7 1.50% 2 7.41% Transformations combined 6 85.71% 1 50.00% T6: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 6 85.71% 1 50.00% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 4 0.86% 1 3.70% Transformations combined 4 100.00% 1 100.00% ⌈ == T7: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 4 100.00% 1 100.00% ⌊ == T9: Y2∧Y1Y_2 Y_1 ↝ Y1→Y2Y_1→ Y_2 4 100.00% 1 100.00% BUGGY_ADD_NEGATION 1 0.21% 1 3.70% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_NEGATION 1 0.21% 1 3.70% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 1 0.21% 1 3.70% Transformations combined 1 100.00% 1 100.00% ⌈ == T7: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 1 100.00% 1 100.00% ⌊ == T9: Y2∧Y1Y_2 Y_1 ↝ Y1→Y2Y_1→ Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 22 4.71% 12 44.44% Transformations combined 10 45.45% 1 8.33% T4: Y1↔¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 10 45.45% 1 8.33% Whole file 467 100.00% 27 100.00% ANY hand error explained 445 95.29% 15 55.56% ANY transformation explained 443 94.86% 9 33.33% Only explained by hand error 12 2.57% 7 25.93% Only explained by transformation 10 2.14% 1 3.70% Table 35. Hand-picked errors and transformations for linguistic operator(s) OR_AND_OR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 5 13.89% 1 4.55% Transformations combined 5 100.00% 1 100.00% T1: (Y1∨Y2)↔(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y3∨Y4)∧(Y1∨Y2) (Y_3 Y_4 ) (Y_1 Y_2 ) 5 100.00% 1 100.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 4 11.11% 1 4.55% Transformations combined 4 100.00% 1 100.00% T7: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y1∧(Y2∨Y3)Y_1 (Y_2 Y_3 ) 4 100.00% 1 100.00% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 3 8.33% 1 4.55% Transformations combined 3 100.00% 1 100.00% T4: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 3 100.00% 1 100.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 1 2.78% 1 4.55% Transformations combined 1 100.00% 1 100.00% T5: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 1 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_DISJUNCTION 1 2.78% 1 4.55% Transformations combined 1 100.00% 1 100.00% T9: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ Y1∨Y2Y_1 Y_2 1 100.00% 1 100.00% Unexplained by ALL hand errors 22 61.11% 17 77.27% Transformations combined 20 90.91% 15 88.24% T2: ¬(Y1↔Y2)∧¬(Y3↔Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 5 22.73% 1 5.88% T8: Y1∧Y2∧Y3∧Y4Y_1 Y_2 Y_3 Y_4 ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 2 9.09% 1 5.88% T3: (Y1∨¬Y2)↔(Y3∨¬Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y4∨Y3)∧(Y2∨Y1) (Y_4 Y_3 ) (Y_2 Y_1 ) 1 4.55% 1 5.88% T6: (Y1∧Y2)↔(Y3∧Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T10: ((Y1∧¬Y2)∨(Y2∧¬Y1))∧((Y3∧¬Y4)∨(Y4∧¬Y3)) ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ( (Y_3 Y_4 ) (Y_4 Y_3 ) ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T11: (Y1∧Y2)→(Y3∧Y4) (Y_1 Y_2 )→ (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T12: (Y1∨¬Y2)↔(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y3∨Y4)∧(Y1∨Y2) (Y_3 Y_4 ) (Y_1 Y_2 ) 1 4.55% 1 5.88% T13: ¬(Y1↔Y2)∧¬(Y3∧Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T14: (Y1∨Y2)∧(Y3∨Y4)∧¬(Y1∧Y2)∧¬(Y3∧Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T15: ¬(Y1↔Y2)∨¬(Y3↔Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y2∨Y1)∧(Y3∨Y4) (Y_2 Y_1 ) (Y_3 Y_4 ) 1 4.55% 1 5.88% T16: Y1∨¬Y2∨Y3∨¬Y4Y_1 Y_2 Y_3 Y_4 ↝ (Y1∨Y2)∧(Y4∨Y3) (Y_1 Y_2 ) (Y_4 Y_3 ) 1 4.55% 1 5.88% T17: (Y1∨¬Y2)∧(Y3∨¬Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y4∨Y3) (Y_1 Y_2 ) (Y_4 Y_3 ) 1 4.55% 1 5.88% T18: (Y1↔¬Y2)∨(Y3↔¬Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y4∨Y3) (Y_1 Y_2 ) (Y_4 Y_3 ) 1 4.55% 1 5.88% T19: (Y1↔¬Y2)∧(Y3↔¬Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y4∨Y3)∧(Y2∨Y1) (Y_4 Y_3 ) (Y_2 Y_1 ) 1 4.55% 1 5.88% T20: (Y1↔¬Y2)↔(Y3↔¬Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y4∨Y3)∧(Y1∨Y2) (Y_4 Y_3 ) (Y_1 Y_2 ) 1 4.55% 1 5.88% Whole file 36 100.00% 22 100.00% ANY hand error explained 14 38.89% 5 22.73% ANY transformation explained 34 94.44% 20 90.91% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 20 55.56% 15 68.18% Table 36. Hand-picked errors and transformations for linguistic operator(s) OR Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 30 83.33% 5 62.50% Transformations combined 30 100.00% 5 100.00% T3: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y1∨Y3∨Y2Y_1 Y_3 Y_2 15 50.00% 1 20.00% T4: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∨Y1∨Y2Y_3 Y_1 Y_2 9 30.00% 2 40.00% T1: Y1∧…∧YnY_1 … Y_n ↝ Y1∨…∨YnY_1 … Y_n 5 16.67% 1 20.00% T2: Y1∧…∧YnY_1 … Y_n ↝ Y1∨…∨YnY_1 … Y_n 1 3.33% 1 20.00% BUGGY_REPLACE_IMPLICATION_BY_DISJUNCTION 4 11.11% 1 12.50% Transformations combined 4 100.00% 1 100.00% T5: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1∨Y2∨Y3Y_1 Y_2 Y_3 4 100.00% 1 100.00% Unexplained by ALL hand errors 2 5.56% 2 25.00% Transformations combined 2 100.00% 2 100.00% T6: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y2∨Y1∨Y3Y_2 Y_1 Y_3 1 50.00% 1 50.00% T7: Y1↔¬Y2Y_1 Y_2 ↝ Y2∨Y1Y_2 Y_1 1 50.00% 1 50.00% Whole file 36 100.00% 8 100.00% ANY hand error explained 34 94.44% 6 75.00% ANY transformation explained 36 100.00% 8 100.00% Only explained by hand error 0 0.00% 0 0.00% Only explained by transformation 2 5.56% 2 25.00% B.2. Full Propositional Logic Data Set The hand-picked mistakes are from (Schmellenkamp et al., 2023). Table 37. Hand-picked errors and transformations for the ungrouped propositional data set. Hand-picked mistake / Transformations # % #dst %dst BUGGY_REPLACE_IMPLICATION_BY_REVERSED_IMPLICATION 1418 23.22% 105 6.68% Transformations combined 1414 99.72% 102 97.14% T169: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 1343 94.71% 80 76.19% T184: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→Y1 (Y_2 Y_3 )→ Y_1 172 12.13% 37 35.24% T210: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 55 3.88% 17 16.19% T293: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 0.56% 1 0.95% T280: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 6 0.42% 3 2.86% T382: Y1∨¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) 2 0.14% 1 0.95% BUGGY_REPLACE_IMPLICATION_BY_EQUIVALENCE 663 10.86% 45 2.86% Transformations combined 660 99.55% 43 95.56% T168: Y1→Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 360 54.30% 22 48.89% T167: Y1→Y2Y_1→ Y_2 ↝ Y1↔Y2Y_1 Y_2 298 44.95% 20 44.44% T255: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 0.30% 1 2.22% BUGGY_REPLACE_EQUIVALENCE_BY_REVERSED_IMPLICATION 446 7.30% 45 2.86% Transformations combined 444 99.55% 43 95.56% T94: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 426 95.52% 31 68.89% T120: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 201 45.07% 3 6.67% T140: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 56 12.56% 3 6.67% T164: (¬Y1∨¬Y2)↔¬Y3 ( Y_1 Y_2 ) Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 13 2.91% 3 6.67% T133: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.22% 1 2.22% T113: Y1↔¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 7 1.57% 7 15.56% T106: Y1↔¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 6 1.35% 2 4.44% T143: ¬Y1↔¬Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 3 0.67% 1 2.22% T151: ¬(¬Y1)↔Y2 ( Y_1 ) Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.22% 1 2.22% T157: ¬(¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.22% 1 2.22% BUGGY_REPLACE_DISJUNCTION_BY_CONJUNCTION 334 5.47% 61 3.88% Transformations combined 330 98.80% 58 95.08% T318: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 201 60.18% 23 37.70% T323: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 153 45.81% 16 26.23% T274: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 150 44.91% 15 24.59% T362: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 128 38.32% 34 55.74% T367: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 118 35.33% 29 47.54% ⌈ == T313: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 35 10.48% 9 14.75% ⌊ == T428: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 35 10.48% 9 14.75% T303: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 17 5.09% 6 9.84% T424: ¬Y1∨…∨¬Yn Y_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 44 13.17% 13 21.31% ⌈ == T313: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 35 10.48% 9 14.75% ⌊ == T428: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 35 10.48% 9 14.75% T87: (¬Y1∨¬Y2)∧¬Y3 ( Y_1 Y_2 ) Y_3 ↝ ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 1 0.30% 1 1.64% BUGGY_REPLACE_EQUIVALENCE_BY_IMPLICATION 293 4.80% 37 2.35% Transformations combined 288 98.29% 35 94.59% T92: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 278 94.88% 30 81.08% T121: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 14 4.78% 6 16.22% T138: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 5 1.71% 1 2.70% T153: ¬(Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 1.37% 3 8.11% T155: ¬(Y1∨Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.68% 1 2.70% T218: Y1→((Y2∧Y3)∨(¬Y2∧¬Y3))Y_1→ ( (Y_2 Y_3 ) ( Y_2 Y_3 ) ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.34% 1 2.70% BUGGY_ADD_NEGATION 183 3.00% 41 2.61% Transformations combined 160 87.43% 34 82.93% T1: Y1Y_1 ↝ ¬Y1 Y_1 126 68.85% 24 58.54% T225: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 67 36.61% 7 17.07% T171: Y1→Y2Y_1→ Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 17 9.29% 7 17.07% T291: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 15 8.20% 1 2.44% T233: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 7 3.83% 4 9.76% T272: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 4 2.19% 1 2.44% T378: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 4 2.19% 1 2.44% T204: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 2 1.09% 2 4.88% T212: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 2 1.09% 1 2.44% BUGGY_REMOVE_NEGATION 112 1.83% 35 2.23% Transformations combined 107 95.54% 30 85.71% T317: ¬Y1 Y_1 ↝ Y1Y_1 84 75.00% 19 54.29% T198: Y1→¬Y2Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 12 10.71% 5 14.29% T104: Y1↔¬Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 5 4.46% 4 11.43% T61: ¬Y1∧¬Y2 Y_1 Y_2 ↝ Y1∧¬Y2Y_1 Y_2 5 4.46% 1 2.86% T251: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 2 1.79% 2 5.71% T135: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 1 0.89% 1 2.86% T348: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.89% 1 2.86% T170: Y1→Y2Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 10 8.93% 1 2.86% T292: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 3 2.68% 2 5.71% T146: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 2.68% 1 2.86% T136: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 1 0.89% 1 2.86% T147: ¬Y1↔¬(¬Y2) Y_1 ( Y_2 ) ↝ Y1↔Y2Y_1 Y_2 1 0.89% 1 2.86% T205: Y1→¬(Y2∧¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y3∨Y2)Y_1→ (Y_3 Y_2 ) 1 0.89% 1 2.86% T261: ¬Y1→¬(Y2∧¬Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y3∨¬Y2) Y_1→ ( Y_3 Y_2 ) 1 0.89% 1 2.86% T281: ¬(Y1∧Y2)→¬(¬Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.89% 1 2.86% T289: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.89% 1 2.86% T327: ¬(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 0.89% 1 2.86% BUGGY_REPLACE_CONJUNCTION_BY_IMPLICATION 94 1.54% 31 1.97% Transformations combined 89 94.68% 26 83.87% T16: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 69 73.40% 19 61.29% T15: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 18 19.15% 6 19.35% T19: Y1∧¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 8 8.51% 1 3.23% T40: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 1.06% 1 3.23% T402: (Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_2 ) (Y_3 Y_2 ) ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 2 2.13% 1 3.23% BUGGY_REPLACE_DISJUNCTION_BY_XOR 91 1.49% 2 0.13% Transformations combined 91 100.00% 2 100.00% T374: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 91 100.00% 2 100.00% BUGGY_REPLACE_CONJUNCTION_BY_DISJUNCTION 70 1.15% 22 1.40% Transformations combined 70 100.00% 22 100.00% T4: Y1∧…∧YnY_1 … Y_n ↝ Y1∨…∨YnY_1 … Y_n 37 52.86% 14 63.64% T181: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 24 34.29% 8 36.36% T58: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬Y1∨…∨¬Yn Y_1 … Y_n 4 5.71% 2 9.09% T73: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y1∨Y3∨Y2Y_1 Y_3 Y_2 15 21.43% 1 4.55% T392: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∨Y1∨Y2Y_3 Y_1 Y_2 9 12.86% 2 9.09% T263: ¬Y1→¬(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 8 11.43% 4 18.18% T20: Y1∧¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 1 1.43% 1 4.55% BUGGY_PULL_NEGATION_CONJUNCTION 67 1.10% 13 0.83% Transformations combined 67 100.00% 13 100.00% T57: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 67 100.00% 13 100.00% T63: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 61 91.04% 12 92.31% BUGGY_REPLACE_CONJUNCTION_BY_REVERSED_IMPLICATION 48 0.79% 18 1.15% Transformations combined 46 95.83% 16 88.89% T16: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 28 58.33% 11 61.11% T30: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 10 20.83% 2 11.11% T15: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 16 33.33% 3 16.67% T19: Y1∧¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 14 29.17% 1 5.56% T40: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 4.17% 2 11.11% T26: Y1∧¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 4.17% 2 11.11% BUGGY_REPLACE_NOR_BY_CONJUNCTION 47 0.77% 19 1.21% Transformations combined 47 100.00% 19 100.00% T2: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 40 85.11% 13 68.42% T226: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 31 65.96% 9 47.37% T56: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 6 12.77% 5 26.32% T331: ¬(¬Y1∧…∧¬Yn) ( Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 5 10.64% 4 21.05% T215: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 2.13% 1 5.26% BUGGY_REPLACE_XOR_BY_NAND 44 0.72% 5 0.32% Transformations combined 44 100.00% 5 100.00% ⌈ == T88: Y1↔Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 24 54.55% 2 40.00% ⌊ == T337: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 24 54.55% 2 40.00% T141: ¬Y1↔Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 19 43.18% 2 40.00% T89: Y1↔Y2Y_1 Y_2 ↝ Y2∧Y1Y_2 Y_1 1 2.27% 1 20.00% BUGGY_REPLACE_DISJUNCTION_BY_NAND 39 0.64% 8 0.51% Transformations combined 39 100.00% 8 100.00% T364: Y1∨…∨YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 39 100.00% 8 100.00% T373: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 35 89.74% 6 75.00% BUGGY_REPLACE_NAND_BY_CONJUNCTION 36 0.59% 19 1.21% Transformations combined 35 97.22% 18 94.74% T363: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 25 69.44% 13 68.42% ⌈ == T297: (Y1∨…∨Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→Y3 ( Y_1 … Y_n )→ Y_3 22 61.11% 10 52.63% ⌊ == T301: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 22 61.11% 10 52.63% T305: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 11.11% 1 5.26% ⌈ == T170: Y1→Y2Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 9 25.00% 4 21.05% ⌊ == T185: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 9 25.00% 4 21.05% ⌈ == T317: ¬Y1 Y_1 ↝ Y1Y_1 1 2.78% 1 5.26% ⌊ == T330: ¬(¬Y1∧…∧¬Yn) ( Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 2.78% 1 5.26% BUGGY_REPLACE_CONJUNCTION_BY_EQUIVALENCE 35 0.57% 10 0.64% Transformations combined 35 100.00% 10 100.00% T12: Y1∧Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 18 51.43% 4 40.00% T13: Y1∧Y2Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 17 48.57% 6 60.00% BUGGY_REPLACE_NOR_BY_NAND 26 0.43% 7 0.45% Transformations combined 26 100.00% 7 100.00% ⌈ == T355: ¬(Y1∨…∨Yn) (Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 26 100.00% 7 100.00% ⌊ == T362: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 26 100.00% 7 100.00% ⌈ == T357: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 84.62% 6 85.71% ⌊ == T367: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 22 84.62% 6 85.71% BUGGY_ADD_OPERAND_TO_CONJUNCTION 23 0.38% 7 0.45% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_IMPLICATION_BY_CONJUNCTION 21 0.34% 10 0.64% Transformations combined 20 95.24% 9 90.00% T166: Y1→Y2Y_1→ Y_2 ↝ Y2∧Y1Y_2 Y_1 14 66.67% 3 30.00% T165: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 5 23.81% 5 50.00% T246: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 1 4.76% 1 10.00% T351: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 4.76% 1 10.00% T262: ¬Y1→¬(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 4.76% 1 10.00% BUGGY_REPLACE_CONJUNCTION_BY_NAND 21 0.34% 7 0.45% Transformations combined 19 90.48% 5 71.43% ⌈ == T1: Y1Y_1 ↝ ¬Y1 Y_1 14 66.67% 4 57.14% ⌊ == T3: Y1∧…∧YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 14 66.67% 4 57.14% T229: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 5 23.81% 1 14.29% BUGGY_REPLACE_EQUIVALENCE_BY_XOR 21 0.34% 1 0.06% Transformations combined 21 100.00% 1 100.00% T1: Y1Y_1 ↝ ¬Y1 Y_1 21 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_CONJUNCTION 18 0.29% 11 0.70% Transformations combined 16 88.89% 10 90.91% T89: Y1↔Y2Y_1 Y_2 ↝ Y2∧Y1Y_2 Y_1 9 50.00% 4 36.36% T88: Y1↔Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 6 33.33% 5 45.45% T191: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) 2 11.11% 1 9.09% T339: ¬(Y1↔¬Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 1 5.56% 1 9.09% BUGGY_REPLACE_IMPLICATION_BY_NAND 18 0.29% 5 0.32% Transformations combined 18 100.00% 5 100.00% T174: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 8 44.44% 2 40.00% T379: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 7 38.89% 1 20.00% T175: Y1→Y2Y_1→ Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 11.11% 1 20.00% T260: ¬Y1→¬Y2 Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 5.56% 1 20.00% BUGGY_REPLACE_XOR_BY_REVERSED_IMPLICATION 17 0.28% 4 0.25% Transformations combined 17 100.00% 4 100.00% T139: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 8 47.06% 2 50.00% T336: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 8 47.06% 1 25.00% T343: ¬(¬Y1↔¬Y2) ( Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 5.88% 1 25.00% BUGGY_REPLACE_NOR_BY_DISJUNCTION 15 0.25% 9 0.57% Transformations combined 14 93.33% 8 88.89% T172: Y1→Y2Y_1→ Y_2 ↝ ¬Y2→Y1 Y_2→ Y_1 10 66.67% 5 55.56% T317: ¬Y1 Y_1 ↝ Y1Y_1 4 26.67% 3 33.33% ⌈ == T198: Y1→¬Y2Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 3 20.00% 2 22.22% ⌊ == T209: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 3 20.00% 2 22.22% T81: (Y1∨Y2)∧¬(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 6.67% 1 11.11% BUGGY_ADD_PREMISE_FOR_IMPLICATION 13 0.21% 3 0.19% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_DISJUNCTION 12 0.20% 8 0.51% Transformations combined 9 75.00% 6 75.00% T219: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 4 33.33% 2 25.00% ⌈ == T201: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 3 25.00% 2 25.00% || == T319: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ Y1∨…∨YnY_1 … Y_n 3 25.00% 2 25.00% ⌊ == T325: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1∨Y2Y_1 Y_2 3 25.00% 2 25.00% T265: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 1 8.33% 1 12.50% T430: ¬(Y1∧Y2)∨¬(Y1∧Y3)∨¬(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 8.33% 1 12.50% BUGGY_REPLACE_DISJUNCTION_BY_REVERSED_IMPLICATION 12 0.20% 6 0.38% Transformations combined 11 91.67% 5 83.33% T371: Y1∨Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 7 58.33% 4 66.67% T432: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 16.67% 2 33.33% T369: Y1∨Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 4 33.33% 1 16.67% BUGGY_REPLACE_NAND_BY_XOR 12 0.20% 3 0.19% Transformations combined 12 100.00% 3 100.00% ⌈ == T12: Y1∧Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 9 75.00% 1 33.33% ⌊ == T324: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 9 75.00% 1 33.33% T429: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 16.67% 1 33.33% T13: Y1∧Y2Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 1 8.33% 1 33.33% BUGGY_REPLACE_EQUIVALENCE_BY_NAND 11 0.18% 5 0.32% Transformations combined 10 90.91% 4 80.00% T97: Y1↔Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 10 90.91% 4 80.00% BUGGY_REPLACE_NOR_BY_XOR 10 0.16% 2 0.13% Transformations combined 10 100.00% 2 100.00% ⌈ == T358: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 60.00% 1 50.00% ⌊ == T368: Y1∨Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 6 60.00% 1 50.00% T64: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 40.00% 1 50.00% BUGGY_ADD_EQUIVALENCE 9 0.15% 3 0.19% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_NOR 9 0.15% 3 0.19% Transformations combined 9 100.00% 3 100.00% T334: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 9 100.00% 3 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_DISJUNCTION 8 0.13% 4 0.25% Transformations combined 7 87.50% 3 75.00% T192: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 4 50.00% 1 25.00% T145: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 3 37.50% 2 50.00% BUGGY_REPLACE_XOR_BY_IMPLICATION 8 0.13% 3 0.19% Transformations combined 8 100.00% 3 100.00% T335: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 6 75.00% 1 33.33% T137: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 2 25.00% 2 66.67% BUGGY_REPLACE_DISJUNCTION_BY_IMPLICATION 7 0.11% 6 0.38% Transformations combined 6 85.71% 5 83.33% T371: Y1∨Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 3 42.86% 3 50.00% T71: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 1 14.29% 1 16.67% T418: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 14.29% 1 16.67% T369: Y1∨Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 3 42.86% 2 33.33% BUGGY_ADD_OPERAND_TO_DISJUNCTION 7 0.11% 5 0.32% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_XOR_BY_DISJUNCTION 7 0.11% 4 0.25% Transformations combined 6 85.71% 3 75.00% T206: Y1→¬(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y3∨Y2)Y_1→ (Y_3 Y_2 ) 5 71.43% 2 50.00% T344: ¬(¬Y1↔¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 14.29% 1 25.00% BUGGY_REPLACE_IMPLICATION_BY_XOR 7 0.11% 3 0.19% Transformations combined 7 100.00% 3 100.00% T176: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 42.86% 1 33.33% T381: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 3 42.86% 1 33.33% T347: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2↔Y1Y_2 Y_1 1 14.29% 1 33.33% BUGGY_MOVE_PARENTHESIS2 5 0.08% 4 0.25% Transformations combined 4 80.00% 3 75.00% T306: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 3 60.00% 2 50.00% T214: Y1→¬(Y2∨¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 20.00% 1 25.00% BUGGY_REPLACE_CONJUNCTION_BY_XOR 5 0.08% 1 0.06% Transformations combined 5 100.00% 1 100.00% T17: Y1∧Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 5 100.00% 1 100.00% BUGGY_REPLACE_EQUIVALENCE_BY_NOR 4 0.07% 3 0.19% Transformations combined 2 50.00% 2 66.67% T243: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 2 50.00% 2 66.67% BUGGY_MOVE_PARENTHESIS1 4 0.07% 2 0.13% Transformations combined 4 100.00% 2 100.00% T23: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 3 75.00% 1 50.00% T359: ¬(Y1∨¬Y2) (Y_1 Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 25.00% 1 50.00% BUGGY_REPLACE_IMPLICATION_BY_DISJUNCTION 4 0.07% 1 0.06% Transformations combined 4 100.00% 1 100.00% T217: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1∨Y2∨Y3Y_1 Y_2 Y_3 4 100.00% 1 100.00% BUGGY_REMOVE_FIRST_OPERAND_FROM_CONJUNCTION 2 0.03% 2 0.13% Transformations combined 1 50.00% 1 50.00% T190: Y1→((Y2∨Y3)∧¬(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) (Y_2 Y_3 ) ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 50.00% 1 50.00% BUGGY_REPLACE_DISJUNCTION_BY_EQUIVALENCE 2 0.03% 2 0.13% Transformations combined 1 50.00% 1 50.00% T368: Y1∨Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 1 50.00% 1 50.00% BUGGY_REPLACE_DISJUNCTION_BY_NOR 2 0.03% 2 0.13% Transformations combined 0 0.00% 0 0.00% BUGGY_ADD_CONCLUSION_FOR_IMPLICATION 1 0.02% 1 0.06% Transformations combined 0 0.00% 0 0.00% BUGGY_EXPLICIFY_IMPLICATION_1 1 0.02% 1 0.06% Transformations combined 1 100.00% 1 100.00% T372: Y1∨Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 100.00% 1 100.00% BUGGY_PULL_NEGATION_DISJUNCTION 1 0.02% 1 0.06% Transformations combined 1 100.00% 1 100.00% T314: (¬Y1∨¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 100.00% 1 100.00% BUGGY_REMOVE_FIRST_FROM_EQUIVALENCE 1 0.02% 1 0.06% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_FIRST_OPERAND_FROM_DISJUNCTION 1 0.02% 1 0.06% Transformations combined 0 0.00% 0 0.00% BUGGY_REMOVE_LATER_OPERAND_FROM_DISJUNCTION 1 0.02% 1 0.06% Transformations combined 0 0.00% 0 0.00% BUGGY_REPLACE_NAND_BY_EQUIVALENCE 1 0.02% 1 0.06% Transformations combined 1 100.00% 1 100.00% T361: ¬(¬Y1∨¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 1 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_EQUIVALENCE 1 0.02% 1 0.06% Transformations combined 1 100.00% 1 100.00% T333: ¬(¬Y1∧¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 1 100.00% 1 100.00% BUGGY_REPLACE_NOR_BY_REVERSED_IMPLICATION 1 0.02% 1 0.06% Transformations combined 1 100.00% 1 100.00% T350: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2→¬Y1Y_2→ Y_1 1 100.00% 1 100.00% BUGGY_REPLACE_XOR_BY_CONJUNCTION 1 0.02% 1 0.06% Transformations combined 0 0.00% 0 0.00% Unexplained by ALL hand errors 1736 28.43% 910 57.89% Transformations combined 918 52.88% 366 40.22% T407: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 114 6.57% 20 2.20% T202: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 70 4.03% 16 1.76% T107: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 66 3.80% 6 0.66% T390: (Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2)∨(Y2∧Y3∧¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 31 1.79% 9 0.99% T365: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 28 1.61% 6 0.66% T86: (Y1∨¬Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 1.27% 7 0.77% T222: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 22 1.27% 2 0.22% T105: Y1↔¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 21 1.21% 4 0.44% T124: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 9 0.52% 1 0.11% T144: ¬Y1↔¬Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.06% 1 0.11% T220: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 20 1.15% 9 0.99% T186: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 20 1.15% 8 0.88% ⌈ == T271: ¬(Y1∧…∧Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→¬Y3 ( Y_1 … Y_n )→ Y_3 18 1.04% 1 0.11% ⌊ == T275: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 18 1.04% 1 0.11% T249: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 16 0.92% 1 0.11% T216: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 14 0.81% 7 0.77% T224: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 14 0.81% 4 0.44% T239: (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 3 0.17% 2 0.22% T111: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 12 0.69% 7 0.77% T393: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 10 0.58% 1 0.11% T398: (Y1∧Y2)∨(Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 9 0.52% 6 0.66% T227: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 9 0.52% 1 0.11% T228: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 0.46% 1 0.11% T70: (Y1∨Y2∨¬Y3)∧(Y1∨Y3∨¬Y2)∧(Y2∨Y3∨¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 7 0.40% 4 0.44% T22: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 7 0.40% 3 0.33% ⌈ == T149: ¬(Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 7 0.40% 3 0.33% ⌊ == T150: ¬(Y2∧Y3)↔Y1 (Y_2 Y_3 ) Y_1 ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 7 0.40% 3 0.33% T188: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 7 0.40% 1 0.11% T252: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→¬Y2Y_1→ Y_2 7 0.40% 1 0.11% T38: Y1∧¬Y2∧Y2∧¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.35% 4 0.44% ⌈ == T68: (Y1∨…∨Yn)∧¬(Y1∧…∧Yn) (Y_1 … Y_n ) (Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 6 0.35% 4 0.44% ⌊ == T79: (Y1∨Y2)∧¬(Y1∧Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.35% 4 0.44% T437: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.35% 4 0.44% T300: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 6 0.35% 3 0.33% T308: ((Y1∧Y2)∨(Y1∧¬Y2)∨(Y2∧¬Y1))→Y3 ( (Y_1 Y_2 ) (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 6 0.35% 3 0.33% T8: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 6 0.35% 2 0.22% T5: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y2→(Y1∧Y3)Y_2→ (Y_1 Y_3 ) 6 0.35% 1 0.11% T380: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 0.35% 1 0.11% T84: (Y1∨Y2)∧(¬Y1∨¬Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 5 0.29% 4 0.44% T277: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 5 0.29% 4 0.44% T332: ¬(¬Y1∧¬Y2∧¬Y3) ( Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 5 0.29% 2 0.22% T42: (Y1↔Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 5 0.29% 1 0.11% T99: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 5 0.29% 1 0.11% T199: Y1→¬Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 5 0.29% 1 0.11% T211: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 5 0.29% 1 0.11% T264: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 4 0.23% 4 0.44% T93: Y1↔Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 4 0.23% 3 0.33% T309: ((Y1∧¬Y2)∨(Y2∧¬Y1))→Y3 ( (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 4 0.23% 3 0.33% T95: Y1↔Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 4 0.23% 2 0.22% T24: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 0.23% 1 0.11% T122: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 0.23% 1 0.11% T182: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 4 0.23% 1 0.11% T203: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 4 0.23% 1 0.11% T223: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 4 0.23% 1 0.11% T240: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 4 0.23% 1 0.11% T241: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 4 0.23% 1 0.11% T279: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 4 0.23% 1 0.11% T115: Y1↔(¬Y2∨¬Y3)Y_1 ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.17% 3 0.33% T258: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.17% 3 0.33% T142: ¬Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.17% 2 0.22% T299: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 3 0.17% 2 0.22% T307: ((Y1∧Y2)∨Y1∨Y2)→Y3 ( (Y_1 Y_2 ) Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 0.17% 2 0.22% T397: (Y1∧Y2)∨(Y1∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 3 0.17% 2 0.22% T408: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1∨Y2Y_1 Y_2 3 0.17% 2 0.22% T31: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 3 0.17% 1 0.11% T46: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 3 0.17% 1 0.11% T59: ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y3)→¬Y2 ( Y_1 Y_3 )→ Y_2 3 0.17% 1 0.11% T98: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 0.17% 1 0.11% T179: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 0.17% 1 0.11% T180: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y3→Y2)∧Y1 (Y_3→ Y_2 ) Y_1 3 0.17% 1 0.11% T242: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 0.17% 1 0.11% T247: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 3 0.17% 1 0.11% T248: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 0.17% 1 0.11% T417: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 0.17% 1 0.11% T18: Y1∧¬Y2∧¬Y3Y_1 Y_2 Y_3 ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.12% 2 0.22% T25: Y1∧¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.12% 2 0.22% T60: ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 2 0.12% 2 0.22% T77: (Y1∨Y2)∧¬Y1∧¬Y2 (Y_1 Y_2 ) Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 2 0.22% T100: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.12% 2 0.22% T108: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 0.12% 2 0.22% T114: Y1↔(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.12% 2 0.22% T163: (¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.12% 2 0.22% T230: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.12% 2 0.22% T234: (Y1∧¬Y2)→(Y2∧¬Y1) (Y_1 Y_2 )→ (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 2 0.22% T237: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 2 0.12% 2 0.22% T282: ¬(Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.12% 2 0.22% T302: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 2 0.12% 2 0.22% T304: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.12% 2 0.22% T409: (Y1∧¬Y2)∨Y1∨Y2∨(Y2∧¬Y1) (Y_1 Y_2 ) Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 2 0.22% T21: Y1∧¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 2 0.12% 1 0.11% T34: Y1∧Y2∧Y3∧Y4Y_1 Y_2 Y_3 Y_4 ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 2 0.12% 1 0.11% T52: (Y1→¬Y2)∧(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 1 0.11% T55: (¬Y1→Y2)∧(¬Y2→Y1) ( Y_1→ Y_2 ) ( Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 1 0.11% T69: (Y1∨Y2∨Y3)∧(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 2 0.12% 1 0.11% T159: (Y1∨Y2∨Y3)↔Y4 (Y_1 Y_2 Y_3 ) Y_4 ↝ Y1→(Y2∨Y3∨Y4)Y_1→ (Y_2 Y_3 Y_4 ) 2 0.12% 1 0.11% T161: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.12% 1 0.11% T183: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 2 0.12% 1 0.11% T189: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (Y3∧¬Y2)→Y1 (Y_3 Y_2 )→ Y_1 2 0.12% 1 0.11% T193: Y1→(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.12% 1 0.11% T194: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ Y2→(Y3→Y1)Y_2→ (Y_3→ Y_1 ) 2 0.12% 1 0.11% T207: Y1→¬(¬Y2→Y3)Y_1→ ( Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 0.12% 1 0.11% T254: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 0.12% 1 0.11% T259: ¬Y1→(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 0.12% 1 0.11% T273: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.12% 1 0.11% T345: ¬((Y1∨Y2)↔Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.12% 1 0.11% T349: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2→Y1Y_2→ Y_1 2 0.12% 1 0.11% T360: ¬((Y1∧¬Y2)∨(Y2∧¬Y1)) ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 1 0.11% T381: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 2 0.12% 1 0.11% T413: (Y1↔Y2)∨(Y1↔Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.12% 1 0.11% T422: (¬Y1→Y2)∨(¬Y2→Y1) ( Y_1→ Y_2 ) ( Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.12% 1 0.11% T6: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 1 0.06% 1 0.11% T7: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.06% 1 0.11% T10: Y1∧Y2∧¬Y3Y_1 Y_2 Y_3 ↝ (Y3∧Y1)∨(Y3∧Y2)∨(Y1∧Y2) (Y_3 Y_1 ) (Y_3 Y_2 ) (Y_1 Y_2 ) 1 0.06% 1 0.11% T11: Y1∧Y2∧¬(Y3∧Y4)∧¬(Y5∧Y6)Y_1 Y_2 (Y_3 Y_4 ) (Y_5 Y_6 ) ↝ Y1∧Y2Y_1 Y_2 1 0.06% 1 0.11% ⌈ == T20: Y1∧¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.06% 1 0.11% ⌊ == T62: ¬Y1∧¬Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.06% 1 0.11% T27: Y1∧¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.06% 1 0.11% T35: Y1∧Y2∧Y3∧¬Y2Y_1 Y_2 Y_3 Y_2 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T37: Y1∧Y2∧(Y1∨Y2)Y_1 Y_2 (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T39: Y1∧¬Y2∧(Y2∨¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T41: (Y1↔Y2)∧Y1 (Y_1 Y_2 ) Y_1 ↝ Y2→Y1Y_2→ Y_1 1 0.06% 1 0.11% T43: (Y1↔¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 1 0.06% 1 0.11% T44: (Y1↔¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T47: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y2→(Y1→Y3)Y_2→ (Y_1→ Y_3 ) 1 0.06% 1 0.11% T48: (Y1→Y2)∧(Y1→Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ (Y1∧Y3)→Y2 (Y_1 Y_3 )→ Y_2 1 0.06% 1 0.11% T49: (Y1→Y2)∧(Y2→Y3) (Y_1→ Y_2 ) (Y_2→ Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.06% 1 0.11% T50: (Y1→Y3)∧(Y2→Y3) (Y_1→ Y_3 ) (Y_2→ Y_3 ) ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T51: (Y1→¬Y2)∧(Y1→¬Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 1 0.06% 1 0.11% T53: (Y1→¬Y2)∧(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 0.06% 1 0.11% T54: (Y1→¬Y2)∧¬Y3 (Y_1→ Y_2 ) Y_3 ↝ (¬Y3∧¬Y2)→Y1 ( Y_3 Y_2 )→ Y_1 1 0.06% 1 0.11% T65: ¬(Y1∧Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∧¬Y1∧¬Y2Y_3 Y_1 Y_2 1 0.06% 1 0.11% T78: (Y1∨Y2)∧¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y3∧Y1)∨(Y3∧Y2)∨(Y1∧Y2) (Y_3 Y_1 ) (Y_3 Y_2 ) (Y_1 Y_2 ) 1 0.06% 1 0.11% T80: (Y1∨Y2)∧¬(Y1∨Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T82: (Y1∨Y2)∧(Y2∨Y3) (Y_1 Y_2 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T83: (Y1∨Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T85: (Y1∨¬Y1)∧(Y2∨¬Y2) (Y_1 Y_1 ) (Y_2 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T96: Y1↔Y2Y_1 Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 1 0.06% 1 0.11% T101: Y1↔(Y2∧¬Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y3∧¬Y2)→Y1 ( Y_3 Y_2 )→ Y_1 1 0.06% 1 0.11% T109: Y1↔¬Y2Y_1 Y_2 ↝ Y2∨Y1Y_2 Y_1 1 0.06% 1 0.11% T110: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y3→Y2)∧Y1 (Y_3→ Y_2 ) Y_1 1 0.06% 1 0.11% T112: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 1 0.06% 1 0.11% T119: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.06% 1 0.11% T123: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.06% 1 0.11% T125: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.06% 1 0.11% T126: (Y1∧¬Y2)↔Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.06% 1 0.11% T127: (Y1∧¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T128: (Y1∧¬Y2)↔(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T129: (Y1∧¬Y2)↔(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T130: (Y1↔Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.06% 1 0.11% T131: (Y1↔Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 1 0.06% 1 0.11% T132: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.06% 1 0.11% T134: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 1 0.06% 1 0.11% T156: ¬(Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T160: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T162: (Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 1 0.06% 1 0.11% T178: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.06% 1 0.11% T195: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 1 0.06% 1 0.11% T196: Y1→(¬Y2→Y3)Y_1→ ( Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.06% 1 0.11% T197: Y1→¬Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 1 0.06% 1 0.11% T200: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.06% 1 0.11% T214: Y1→¬(Y2∨¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 0.06% 1 0.11% T221: (Y1∧Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ Y2→Y1Y_2→ Y_1 1 0.06% 1 0.11% T231: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T232: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∨Y1)Y_3→ (Y_2 Y_1 ) 1 0.06% 1 0.11% T235: (Y1∧¬Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T238: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T244: (¬Y1↔¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.06% 1 0.11% T245: (¬Y1↔¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T250: (Y1→¬Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.06% 1 0.11% T253: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T257: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y3∧¬Y1)→Y2 (Y_3 Y_1 )→ Y_2 1 0.06% 1 0.11% T266: ¬Y1→(Y2∨¬Y3) Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 0.06% 1 0.11% T278: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.06% 1 0.11% T283: ¬(Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∨Y1)Y_3→ (Y_2 Y_1 ) 1 0.06% 1 0.11% T288: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T298: (Y1∨Y2∨Y3)→Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ Y2→(Y1∨Y4∨Y3)Y_2→ (Y_1 Y_4 Y_3 ) 1 0.06% 1 0.11% T306: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.06% 1 0.11% T310: ((Y1↔Y2)∨(Y1∧Y2))→Y3 ( (Y_1 Y_2 ) (Y_1 Y_2 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T311: ((Y1↔Y2)∨Y1∨Y2)→Y3 ( (Y_1 Y_2 ) Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T316: (Y1∨¬Y2∨Y2∨¬Y1)→Y3 (Y_1 Y_2 Y_2 Y_1 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T321: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T322: ¬(Y1∧Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ ¬Y3∧¬Y1∧¬Y2 Y_3 Y_1 Y_2 1 0.06% 1 0.11% T328: ¬(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T329: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T340: ¬(Y1↔¬Y2) (Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.06% 1 0.11% T341: ¬(Y1↔¬(Y2∧Y3)) (Y_1 (Y_2 Y_3 ) ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.06% 1 0.11% T342: ¬(¬Y1↔Y2) ( Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 1 0.06% 1 0.11% T346: ¬((Y1∨Y2)↔Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 1 0.06% 1 0.11% T352: ¬(Y1→¬Y2) (Y_1→ Y_2 ) ↝ Y2↔Y1Y_2 Y_1 1 0.06% 1 0.11% T366: Y1∨Y2∨¬Y1∨¬Y2Y_1 Y_2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T370: Y1∨Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 1 0.06% 1 0.11% T377: Y1∨¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.06% 1 0.11% T385: (Y1∧Y2∧Y3)∨(Y1∧Y2∧Y3)∨(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T386: (Y1∧Y2∧Y3)∨(Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T387: (Y1∧Y2∧Y3)∨(Y3∧¬Y1∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_3 Y_1 Y_2 ) ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T388: (Y1∧Y2∧¬Y3)∨(Y1∧Y2∧¬Y4) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 0.06% 1 0.11% T389: (Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2)∨(Y2∧Y3∧¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) 1 0.06% 1 0.11% T395: (Y1∧Y2)∨(Y1∧Y2∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_2 Y_3 ) (Y_2 Y_3 ) ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 1 0.06% 1 0.11% T396: (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) 1 0.06% 1 0.11% T400: (Y1∧Y2)∨(Y1∧¬Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T401: (Y1∧Y2)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T403: (Y1∧Y2)∨(¬Y1∧¬Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T404: (Y1∧Y2)∨(Y2↔¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T405: (Y1∧Y2)∨¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T410: (Y2∧Y1)∨Y3 (Y_2 Y_1 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.06% 1 0.11% T412: (Y1↔Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 1 0.06% 1 0.11% T414: (Y1↔Y2)∨(Y3↔Y1)∨(Y3↔Y2) (Y_1 Y_2 ) (Y_3 Y_1 ) (Y_3 Y_2 ) ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.06% 1 0.11% T415: (Y1↔Y2)∨(Y3↔Y1) (Y_1 Y_2 ) (Y_3 Y_1 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.06% 1 0.11% T419: (Y1→Y2)∨(Y2→Y1) (Y_1→ Y_2 ) (Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T420: (Y1→¬Y2)∨(Y2→¬Y1) (Y_1→ Y_2 ) (Y_2→ Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T421: (Y1→¬Y2)∨(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T423: ((Y1∨Y2)→Y3)∨Y1∨Y2 ( (Y_1 Y_2 )→ Y_3 ) Y_1 Y_2 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% T427: ¬Y1∨¬Y2∨¬Y3 Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T434: Y1∨Y2∨Y1∨Y3Y_1 Y_2 Y_1 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.06% 1 0.11% T436: Y1∨¬Y2∨(Y2∧¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T438: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.06% 1 0.11% T439: ¬Y1∨¬Y2∨Y3 Y_1 Y_2 Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.06% 1 0.11% Whole data set 6106 100.00% 1572 100.00% ANY hand error explained 4370 71.57% 662 42.11% ANY transformation explained 5156 84.44% 955 60.75% Only explained by hand error 132 2.16% 73 4.64% Only explained by transformation 918 15.03% 366 23.28% B.3. Propositional Logic: Hierarchical Clustering of Transformations Table 38. Transformation hierarchy clusters Transformations # % #dst %dst Whole data set 6106 100.00% 1572 100.00% ANY transformation explained 5156 84.44% 955 60.75% Cluster 1 T169: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 1343 21.99% 80 5.09% T184: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→Y1 (Y_2 Y_3 )→ Y_1 172 2.82% 37 2.35% Cluster 2 T94: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 426 6.98% 31 1.97% T120: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 201 3.29% 3 0.19% T140: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 56 0.92% 3 0.19% T164: (¬Y1∨¬Y2)↔¬Y3 ( Y_1 Y_2 ) Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 13 0.21% 3 0.19% T133: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.02% 1 0.06% Cluster 3 T168: Y1→Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 360 5.90% 22 1.40% Cluster 4 T167: Y1→Y2Y_1→ Y_2 ↝ Y1↔Y2Y_1 Y_2 298 4.88% 20 1.27% Cluster 5 T92: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 278 4.55% 30 1.91% T121: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 14 0.23% 6 0.38% Cluster 6 T318: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 201 3.29% 23 1.46% T323: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 153 2.51% 16 1.02% T274: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 150 2.46% 15 0.95% Cluster 7 T1: Y1Y_1 ↝ ¬Y1 Y_1 161 2.64% 29 1.84% T225: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 67 1.10% 7 0.45% T171: Y1→Y2Y_1→ Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 17 0.28% 7 0.45% T3: Y1∧…∧YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 14 0.23% 4 0.25% Cluster 8 T362: Y1∨…∨YnY_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 154 2.52% 41 2.61% T367: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 140 2.29% 35 2.23% ⌈ == T313: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 35 0.57% 9 0.57% ⌊ == T428: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 35 0.57% 9 0.57% T357: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 0.36% 6 0.38% T303: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 17 0.28% 6 0.38% T424: ¬Y1∨…∨¬Yn Y_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 44 0.72% 13 0.83% ⌈ == T313: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 35 0.57% 9 0.57% ⌊ == T428: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬Y1∧¬Y2 Y_1 Y_2 35 0.57% 9 0.57% T355: ¬(Y1∨…∨Yn) (Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 26 0.43% 7 0.45% T357: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 0.36% 6 0.38% Cluster 9 T407: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 114 1.87% 20 1.27% Cluster 10 T16: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 97 1.59% 30 1.91% T30: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 10 0.16% 2 0.13% Cluster 11 T374: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 91 1.49% 2 0.13% Cluster 12 T317: ¬Y1 Y_1 ↝ Y1Y_1 89 1.46% 23 1.46% T198: Y1→¬Y2Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 15 0.25% 7 0.45% T209: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 3 0.05% 2 0.13% T104: Y1↔¬Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 5 0.08% 4 0.25% T61: ¬Y1∧¬Y2 Y_1 Y_2 ↝ Y1∧¬Y2Y_1 Y_2 5 0.08% 1 0.06% T251: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 2 0.03% 2 0.13% T81: (Y1∨Y2)∧¬(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 1 0.02% 1 0.06% T135: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 1 0.02% 1 0.06% T330: ¬(¬Y1∧…∧¬Yn) ( Y_1 … Y_n ) ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 1 0.02% 1 0.06% T348: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.02% 1 0.06% Cluster 13 T202: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 70 1.15% 16 1.02% Cluster 14 T57: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 67 1.10% 13 0.83% T63: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 61 1.00% 12 0.76% Cluster 15 T107: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 66 1.08% 6 0.38% Cluster 16 T210: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 55 0.90% 17 1.08% Cluster 17 T2: Y1∧…∧YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 40 0.66% 13 0.83% T226: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 31 0.51% 9 0.57% Cluster 18 T364: Y1∨…∨YnY_1 … Y_n ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 39 0.64% 8 0.51% T373: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 35 0.57% 6 0.38% Cluster 19 T4: Y1∧…∧YnY_1 … Y_n ↝ Y1∨…∨YnY_1 … Y_n 37 0.61% 14 0.89% T181: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 24 0.39% 8 0.51% T58: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ ¬Y1∨…∨¬Yn Y_1 … Y_n 4 0.07% 2 0.13% Cluster 20 T15: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 34 0.56% 9 0.57% T19: Y1∧¬Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 22 0.36% 2 0.13% T40: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 3 0.05% 3 0.19% Cluster 21 T390: (Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2)∨(Y2∧Y3∧¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 31 0.51% 9 0.57% Cluster 22 T88: Y1↔Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 30 0.49% 7 0.45% T337: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 24 0.39% 2 0.13% T191: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 23 T365: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 28 0.46% 6 0.38% Cluster 24 T12: Y1∧Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 27 0.44% 5 0.32% T324: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 9 0.15% 1 0.06% Cluster 25 T363: Y1∨…∨YnY_1 … Y_n ↝ ¬Y1∧…∧¬Yn Y_1 … Y_n 25 0.41% 13 0.83% ⌈ == T297: (Y1∨…∨Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→Y3 ( Y_1 … Y_n )→ Y_3 22 0.36% 10 0.64% ⌊ == T301: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 22 0.36% 10 0.64% T305: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 0.07% 1 0.06% Cluster 26 T86: (Y1∨¬Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 22 0.36% 7 0.45% Cluster 27 T222: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 22 0.36% 2 0.13% Cluster 28 T105: Y1↔¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 21 0.34% 4 0.25% T124: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 9 0.15% 1 0.06% T144: ¬Y1↔¬Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 29 T220: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 20 0.33% 9 0.57% Cluster 30 T186: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 20 0.33% 8 0.51% Cluster 31 T170: Y1→Y2Y_1→ Y_2 ↝ Y2→¬Y1Y_2→ Y_1 19 0.31% 5 0.32% T185: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 9 0.15% 4 0.25% Cluster 32 T141: ¬Y1↔Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 19 0.31% 2 0.13% Cluster 33 T13: Y1∧Y2Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 18 0.29% 7 0.45% Cluster 34 ⌈ == T271: ¬(Y1∧…∧Yn)→Y3 (Y_1 … Y_n )→ Y_3 ↝ (¬Y1∧…∧¬Yn)→¬Y3 ( Y_1 … Y_n )→ Y_3 18 0.29% 1 0.06% ⌊ == T275: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 18 0.29% 1 0.06% Cluster 35 T249: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 16 0.26% 1 0.06% Cluster 36 T73: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y1∨Y3∨Y2Y_1 Y_3 Y_2 15 0.25% 1 0.06% Cluster 37 T291: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 15 0.25% 1 0.06% Cluster 38 T216: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 14 0.23% 7 0.45% Cluster 39 T224: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 14 0.23% 4 0.25% T239: (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 3 0.05% 2 0.13% Cluster 40 T166: Y1→Y2Y_1→ Y_2 ↝ Y2∧Y1Y_2 Y_1 14 0.23% 3 0.19% Cluster 41 T111: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 12 0.20% 7 0.45% Cluster 42 T371: Y1∨Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 10 0.16% 7 0.45% T432: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.03% 2 0.13% T71: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 1 0.02% 1 0.06% T418: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.02% 1 0.06% Cluster 43 T89: Y1↔Y2Y_1 Y_2 ↝ Y2∧Y1Y_2 Y_1 10 0.16% 5 0.32% Cluster 44 T172: Y1→Y2Y_1→ Y_2 ↝ ¬Y2→Y1 Y_2→ Y_1 10 0.16% 5 0.32% Cluster 45 T97: Y1↔Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 10 0.16% 4 0.25% Cluster 46 T393: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 10 0.16% 1 0.06% Cluster 47 T398: (Y1∧Y2)∨(Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 9 0.15% 6 0.38% Cluster 48 T334: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 9 0.15% 3 0.19% Cluster 49 T392: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∨Y1∨Y2Y_3 Y_1 Y_2 9 0.15% 2 0.13% Cluster 50 T227: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 9 0.15% 1 0.06% Cluster 51 T263: ¬Y1→¬(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 8 0.13% 4 0.25% Cluster 52 T139: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 8 0.13% 2 0.13% Cluster 53 T174: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 8 0.13% 2 0.13% Cluster 54 T228: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 0.13% 1 0.06% Cluster 55 T293: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 8 0.13% 1 0.06% Cluster 56 T336: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 8 0.13% 1 0.06% Cluster 57 T113: Y1↔¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 7 0.11% 7 0.45% Cluster 58 T70: (Y1∨Y2∨¬Y3)∧(Y1∨Y3∨¬Y2)∧(Y2∨Y3∨¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 7 0.11% 4 0.25% Cluster 59 T233: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 7 0.11% 4 0.25% Cluster 60 T22: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 7 0.11% 3 0.19% Cluster 61 ⌈ == T149: ¬(Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 7 0.11% 3 0.19% ⌊ == T150: ¬(Y2∧Y3)↔Y1 (Y_2 Y_3 ) Y_1 ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 7 0.11% 3 0.19% Cluster 62 T369: Y1∨Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 7 0.11% 3 0.19% Cluster 63 T368: Y1∨Y2Y_1 Y_2 ↝ Y1↔Y2Y_1 Y_2 7 0.11% 2 0.13% T358: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 0.10% 1 0.06% Cluster 64 T188: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 7 0.11% 1 0.06% Cluster 65 T252: ¬Y1→Y2 Y_1→ Y_2 ↝ Y1→¬Y2Y_1→ Y_2 7 0.11% 1 0.06% Cluster 66 T379: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 7 0.11% 1 0.06% Cluster 67 T56: ¬Y1∧…∧¬Yn Y_1 … Y_n ↝ Y1∧…∧YnY_1 … Y_n 6 0.10% 5 0.32% T331: ¬(¬Y1∧…∧¬Yn) ( Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 5 0.08% 4 0.25% Cluster 68 T38: Y1∧¬Y2∧Y2∧¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.10% 4 0.25% Cluster 69 ⌈ == T68: (Y1∨…∨Yn)∧¬(Y1∧…∧Yn) (Y_1 … Y_n ) (Y_1 … Y_n ) ↝ ¬(Y1∧…∧Yn) (Y_1 … Y_n ) 6 0.10% 4 0.25% ⌊ == T79: (Y1∨Y2)∧¬(Y1∧Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.10% 4 0.25% Cluster 70 T437: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 6 0.10% 4 0.25% Cluster 71 T280: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 6 0.10% 3 0.19% Cluster 72 T300: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 6 0.10% 3 0.19% Cluster 73 T308: ((Y1∧Y2)∨(Y1∧¬Y2)∨(Y2∧¬Y1))→Y3 ( (Y_1 Y_2 ) (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 6 0.10% 3 0.19% Cluster 74 T8: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 6 0.10% 2 0.13% Cluster 75 T106: Y1↔¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 6 0.10% 2 0.13% Cluster 76 T5: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y2→(Y1∧Y3)Y_2→ (Y_1 Y_3 ) 6 0.10% 1 0.06% Cluster 77 T335: ¬(Y1↔Y2) (Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 6 0.10% 1 0.06% Cluster 78 T380: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 6 0.10% 1 0.06% Cluster 79 T165: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 5 0.08% 5 0.32% T246: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 1 0.02% 1 0.06% T351: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 80 T84: (Y1∨Y2)∧(¬Y1∨¬Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 5 0.08% 4 0.25% Cluster 81 T277: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 5 0.08% 4 0.25% Cluster 82 T206: Y1→¬(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y3∨Y2)Y_1→ (Y_3 Y_2 ) 5 0.08% 2 0.13% Cluster 83 T332: ¬(¬Y1∧¬Y2∧¬Y3) ( Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 5 0.08% 2 0.13% Cluster 84 T381: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 5 0.08% 2 0.13% Cluster 85 T17: Y1∧Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 5 0.08% 1 0.06% Cluster 86 T42: (Y1↔Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 5 0.08% 1 0.06% Cluster 87 T99: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 5 0.08% 1 0.06% Cluster 88 T138: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 5 0.08% 1 0.06% Cluster 89 T199: Y1→¬Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 5 0.08% 1 0.06% Cluster 90 T211: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 5 0.08% 1 0.06% Cluster 91 T229: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 5 0.08% 1 0.06% Cluster 92 T264: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 4 0.07% 4 0.25% Cluster 93 T93: Y1↔Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 4 0.07% 3 0.19% Cluster 94 T153: ¬(Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 0.07% 3 0.19% T155: ¬(Y1∨Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 1 0.06% Cluster 95 T306: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 4 0.07% 3 0.19% Cluster 96 T309: ((Y1∧¬Y2)∨(Y2∧¬Y1))→Y3 ( (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 4 0.07% 3 0.19% Cluster 97 T95: Y1↔Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 4 0.07% 2 0.13% Cluster 98 T219: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 4 0.07% 2 0.13% Cluster 99 T24: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 0.07% 1 0.06% Cluster 100 T64: ¬Y1∧¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 4 0.07% 1 0.06% Cluster 101 T122: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 4 0.07% 1 0.06% Cluster 102 T182: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 4 0.07% 1 0.06% Cluster 103 T192: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 4 0.07% 1 0.06% Cluster 104 T203: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 4 0.07% 1 0.06% Cluster 105 T217: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1∨Y2∨Y3Y_1 Y_2 Y_3 4 0.07% 1 0.06% Cluster 106 T223: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 4 0.07% 1 0.06% Cluster 107 T240: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 4 0.07% 1 0.06% Cluster 108 T241: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 4 0.07% 1 0.06% Cluster 109 T272: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 4 0.07% 1 0.06% Cluster 110 T279: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∧¬Y2) Y_3→ ( Y_1 Y_2 ) 4 0.07% 1 0.06% Cluster 111 T378: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 4 0.07% 1 0.06% Cluster 112 T115: Y1↔(¬Y2∨¬Y3)Y_1 ( Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.05% 3 0.19% Cluster 113 T258: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.05% 3 0.19% Cluster 114 T142: ¬Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 3 0.05% 2 0.13% Cluster 115 T145: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 3 0.05% 2 0.13% Cluster 116 ⌈ == T201: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 3 0.05% 2 0.13% || == T319: ¬(Y1∧…∧Yn) (Y_1 … Y_n ) ↝ Y1∨…∨YnY_1 … Y_n 3 0.05% 2 0.13% ⌊ == T325: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1∨Y2Y_1 Y_2 3 0.05% 2 0.13% Cluster 117 T292: ¬(Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 3 0.05% 2 0.13% Cluster 118 T299: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 3 0.05% 2 0.13% Cluster 119 T307: ((Y1∧Y2)∨Y1∨Y2)→Y3 ( (Y_1 Y_2 ) Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 0.05% 2 0.13% Cluster 120 T397: (Y1∧Y2)∨(Y1∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 3 0.05% 2 0.13% Cluster 121 T408: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1∨Y2Y_1 Y_2 3 0.05% 2 0.13% Cluster 122 T23: Y1∧¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 3 0.05% 1 0.06% Cluster 123 T31: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 3 0.05% 1 0.06% Cluster 124 T46: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 3 0.05% 1 0.06% Cluster 125 T59: ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 ↝ (¬Y1∧¬Y3)→¬Y2 ( Y_1 Y_3 )→ Y_2 3 0.05% 1 0.06% Cluster 126 T98: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 0.05% 1 0.06% Cluster 127 T143: ¬Y1↔¬Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 3 0.05% 1 0.06% Cluster 128 T146: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 0.05% 1 0.06% Cluster 129 T176: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 0.05% 1 0.06% Cluster 130 T179: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 0.05% 1 0.06% Cluster 131 T180: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y3→Y2)∧Y1 (Y_3→ Y_2 ) Y_1 3 0.05% 1 0.06% Cluster 132 T242: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 3 0.05% 1 0.06% Cluster 133 T247: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 3 0.05% 1 0.06% Cluster 134 T248: (Y1→Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 3 0.05% 1 0.06% Cluster 135 T417: (Y1→Y2)∨Y3 (Y_1→ Y_2 ) Y_3 ↝ (Y2→Y1)∧Y3 (Y_2→ Y_1 ) Y_3 3 0.05% 1 0.06% Cluster 136 T18: Y1∧¬Y2∧¬Y3Y_1 Y_2 Y_3 ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.03% 2 0.13% Cluster 137 T20: Y1∧¬Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 2 0.03% 2 0.13% T62: ¬Y1∧¬Y2 Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 138 T25: Y1∧¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.03% 2 0.13% Cluster 139 T26: Y1∧¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.03% 2 0.13% Cluster 140 T60: ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 2 0.03% 2 0.13% Cluster 141 T77: (Y1∨Y2)∧¬Y1∧¬Y2 (Y_1 Y_2 ) Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 142 T100: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 2 0.13% Cluster 143 T108: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 0.03% 2 0.13% Cluster 144 T114: Y1↔(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 2 0.03% 2 0.13% Cluster 145 T137: ¬Y1↔Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 2 0.03% 2 0.13% Cluster 146 T163: (¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 2 0.13% Cluster 147 T204: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 2 0.03% 2 0.13% Cluster 148 T214: Y1→¬(Y2∨¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 2 0.13% Cluster 149 T230: (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 2 0.13% Cluster 150 T234: (Y1∧¬Y2)→(Y2∧¬Y1) (Y_1 Y_2 )→ (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 151 T237: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 152 T243: (Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 2 0.03% 2 0.13% Cluster 153 T282: ¬(Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 154 T302: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 155 T304: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 2 0.13% Cluster 156 T409: (Y1∧¬Y2)∨Y1∨Y2∨(Y2∧¬Y1) (Y_1 Y_2 ) Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 2 0.13% Cluster 157 T21: Y1∧¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 2 0.03% 1 0.06% Cluster 158 T34: Y1∧Y2∧Y3∧Y4Y_1 Y_2 Y_3 Y_4 ↝ (Y1∨Y2)∧(Y3∨Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) 2 0.03% 1 0.06% Cluster 159 T52: (Y1→¬Y2)∧(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 160 T55: (¬Y1→Y2)∧(¬Y2→Y1) ( Y_1→ Y_2 ) ( Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 161 T69: (Y1∨Y2∨Y3)∧(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 162 T159: (Y1∨Y2∨Y3)↔Y4 (Y_1 Y_2 Y_3 ) Y_4 ↝ Y1→(Y2∨Y3∨Y4)Y_1→ (Y_2 Y_3 Y_4 ) 2 0.03% 1 0.06% Cluster 163 T161: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 1 0.06% Cluster 164 T175: Y1→Y2Y_1→ Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 0.03% 1 0.06% Cluster 165 T183: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 2 0.03% 1 0.06% Cluster 166 T189: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ (Y3∧¬Y2)→Y1 (Y_3 Y_2 )→ Y_1 2 0.03% 1 0.06% Cluster 167 T193: Y1→(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 168 T194: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ Y2→(Y3→Y1)Y_2→ (Y_3→ Y_1 ) 2 0.03% 1 0.06% Cluster 169 T207: Y1→¬(¬Y2→Y3)Y_1→ ( Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 0.03% 1 0.06% Cluster 170 T212: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 171 T254: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 2 0.03% 1 0.06% Cluster 172 T255: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 173 T259: ¬Y1→(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 2 0.03% 1 0.06% Cluster 174 T273: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 175 T345: ¬((Y1∨Y2)↔Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 2 0.03% 1 0.06% Cluster 176 T349: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2→Y1Y_2→ Y_1 2 0.03% 1 0.06% Cluster 177 T360: ¬((Y1∧¬Y2)∨(Y2∧¬Y1)) ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 178 T382: Y1∨¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 179 T402: (Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_2 ) (Y_3 Y_2 ) ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 2 0.03% 1 0.06% Cluster 180 T413: (Y1↔Y2)∨(Y1↔Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.03% 1 0.06% Cluster 181 T422: (¬Y1→Y2)∨(¬Y2→Y1) ( Y_1→ Y_2 ) ( Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 182 T429: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 0.03% 1 0.06% Cluster 183 T6: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 1 0.02% 1 0.06% Cluster 184 T7: Y1∧Y2∧Y3Y_1 Y_2 Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.02% 1 0.06% Cluster 185 T10: Y1∧Y2∧¬Y3Y_1 Y_2 Y_3 ↝ (Y3∧Y1)∨(Y3∧Y2)∨(Y1∧Y2) (Y_3 Y_1 ) (Y_3 Y_2 ) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 186 T11: Y1∧Y2∧¬(Y3∧Y4)∧¬(Y5∧Y6)Y_1 Y_2 (Y_3 Y_4 ) (Y_5 Y_6 ) ↝ Y1∧Y2Y_1 Y_2 1 0.02% 1 0.06% Cluster 187 T27: Y1∧¬(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.02% 1 0.06% Cluster 188 T35: Y1∧Y2∧Y3∧¬Y2Y_1 Y_2 Y_3 Y_2 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 189 T37: Y1∧Y2∧(Y1∨Y2)Y_1 Y_2 (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 190 T39: Y1∧¬Y2∧(Y2∨¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 191 T41: (Y1↔Y2)∧Y1 (Y_1 Y_2 ) Y_1 ↝ Y2→Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 192 T43: (Y1↔¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 193 T44: (Y1↔¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 194 T47: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y2→(Y1→Y3)Y_2→ (Y_1→ Y_3 ) 1 0.02% 1 0.06% Cluster 195 T48: (Y1→Y2)∧(Y1→Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ (Y1∧Y3)→Y2 (Y_1 Y_3 )→ Y_2 1 0.02% 1 0.06% Cluster 196 T49: (Y1→Y2)∧(Y2→Y3) (Y_1→ Y_2 ) (Y_2→ Y_3 ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.02% 1 0.06% Cluster 197 T50: (Y1→Y3)∧(Y2→Y3) (Y_1→ Y_3 ) (Y_2→ Y_3 ) ↝ (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 198 T51: (Y1→¬Y2)∧(Y1→¬Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ (¬Y2∧¬Y3)→Y1 ( Y_2 Y_3 )→ Y_1 1 0.02% 1 0.06% Cluster 199 T53: (Y1→¬Y2)∧(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 200 T54: (Y1→¬Y2)∧¬Y3 (Y_1→ Y_2 ) Y_3 ↝ (¬Y3∧¬Y2)→Y1 ( Y_3 Y_2 )→ Y_1 1 0.02% 1 0.06% Cluster 201 T65: ¬(Y1∧Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3∧¬Y1∧¬Y2Y_3 Y_1 Y_2 1 0.02% 1 0.06% Cluster 202 T78: (Y1∨Y2)∧¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y3∧Y1)∨(Y3∧Y2)∨(Y1∧Y2) (Y_3 Y_1 ) (Y_3 Y_2 ) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 203 T80: (Y1∨Y2)∧¬(Y1∨Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 204 T82: (Y1∨Y2)∧(Y2∨Y3) (Y_1 Y_2 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 205 T83: (Y1∨Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 206 T85: (Y1∨¬Y1)∧(Y2∨¬Y2) (Y_1 Y_1 ) (Y_2 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 207 T87: (¬Y1∨¬Y2)∧¬Y3 ( Y_1 Y_2 ) Y_3 ↝ ¬Y1∧¬Y2∧¬Y3 Y_1 Y_2 Y_3 1 0.02% 1 0.06% Cluster 208 T96: Y1↔Y2Y_1 Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 1 0.02% 1 0.06% Cluster 209 T101: Y1↔(Y2∧¬Y3)Y_1 (Y_2 Y_3 ) ↝ (¬Y3∧¬Y2)→Y1 ( Y_3 Y_2 )→ Y_1 1 0.02% 1 0.06% Cluster 210 T109: Y1↔¬Y2Y_1 Y_2 ↝ Y2∨Y1Y_2 Y_1 1 0.02% 1 0.06% Cluster 211 T110: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ (Y3→Y2)∧Y1 (Y_3→ Y_2 ) Y_1 1 0.02% 1 0.06% Cluster 212 T112: Y1↔¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 213 T119: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.02% 1 0.06% Cluster 214 T123: (Y1∧Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.02% 1 0.06% Cluster 215 T125: (Y1∧Y2)↔¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.02% 1 0.06% Cluster 216 T126: (Y1∧¬Y2)↔Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 217 T127: (Y1∧¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 218 T128: (Y1∧¬Y2)↔(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 219 T129: (Y1∧¬Y2)↔(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 220 T130: (Y1↔Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.02% 1 0.06% Cluster 221 T131: (Y1↔Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y2∧Y1)Y_3→ (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 222 T132: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.02% 1 0.06% Cluster 223 T134: (Y1→Y2)↔Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 1 0.02% 1 0.06% Cluster 224 T136: ¬Y1↔Y2 Y_1 Y_2 ↝ Y2↔Y1Y_2 Y_1 1 0.02% 1 0.06% Cluster 225 T147: ¬Y1↔¬(¬Y2) Y_1 ( Y_2 ) ↝ Y1↔Y2Y_1 Y_2 1 0.02% 1 0.06% Cluster 226 T151: ¬(¬Y1)↔Y2 ( Y_1 ) Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 227 T156: ¬(Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 228 T157: ¬(¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 229 T160: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 230 T162: (Y1∨¬Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ (¬Y2∧¬Y1)→Y3 ( Y_2 Y_1 )→ Y_3 1 0.02% 1 0.06% Cluster 231 T178: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.02% 1 0.06% Cluster 232 T190: Y1→((Y2∨Y3)∧¬(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) (Y_2 Y_3 ) ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 233 T195: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ Y3→(Y2→Y1)Y_3→ (Y_2→ Y_1 ) 1 0.02% 1 0.06% Cluster 234 T196: Y1→(¬Y2→Y3)Y_1→ ( Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.02% 1 0.06% Cluster 235 T197: Y1→¬Y2Y_1→ Y_2 ↝ Y2↔Y1Y_2 Y_1 1 0.02% 1 0.06% Cluster 236 T200: Y1→¬(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.02% 1 0.06% Cluster 237 T205: Y1→¬(Y2∧¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y3∨Y2)Y_1→ (Y_3 Y_2 ) 1 0.02% 1 0.06% Cluster 238 T215: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ (Y2∧Y3)→¬Y1 (Y_2 Y_3 )→ Y_1 1 0.02% 1 0.06% Cluster 239 T218: Y1→((Y2∧Y3)∨(¬Y2∧¬Y3))Y_1→ ( (Y_2 Y_3 ) ( Y_2 Y_3 ) ) ↝ Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) 1 0.02% 1 0.06% Cluster 240 T221: (Y1∧Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ Y2→Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 241 T231: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 242 T232: (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∨Y1)Y_3→ (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 243 T235: (Y1∧¬Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 244 T238: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 245 T244: (¬Y1↔¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.02% 1 0.06% Cluster 246 T245: (¬Y1↔¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 247 T250: (Y1→¬Y2)→Y3 (Y_1→ Y_2 )→ Y_3 ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.02% 1 0.06% Cluster 248 T253: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 249 T257: ¬Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ (Y3∧¬Y1)→Y2 (Y_3 Y_1 )→ Y_2 1 0.02% 1 0.06% Cluster 250 T260: ¬Y1→¬Y2 Y_1→ Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 251 T261: ¬Y1→¬(Y2∧¬Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y3∨¬Y2) Y_1→ ( Y_3 Y_2 ) 1 0.02% 1 0.06% Cluster 252 T262: ¬Y1→¬(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ (Y2→Y3)∧Y1 (Y_2→ Y_3 ) Y_1 1 0.02% 1 0.06% Cluster 253 T265: ¬Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 254 T266: ¬Y1→(Y2∨¬Y3) Y_1→ (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 255 T278: ¬(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1→Y3)∧Y2 (Y_1→ Y_3 ) Y_2 1 0.02% 1 0.06% Cluster 256 T281: ¬(Y1∧Y2)→¬(¬Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 257 T283: ¬(Y1↔Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y2∨Y1)Y_3→ (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 258 T288: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 259 T289: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ (Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.02% 1 0.06% Cluster 260 T298: (Y1∨Y2∨Y3)→Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ Y2→(Y1∨Y4∨Y3)Y_2→ (Y_1 Y_4 Y_3 ) 1 0.02% 1 0.06% Cluster 261 T310: ((Y1↔Y2)∨(Y1∧Y2))→Y3 ( (Y_1 Y_2 ) (Y_1 Y_2 ) )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 262 T311: ((Y1↔Y2)∨Y1∨Y2)→Y3 ( (Y_1 Y_2 ) Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 263 T314: (¬Y1∨¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 264 T316: (Y1∨¬Y2∨Y2∨¬Y1)→Y3 (Y_1 Y_2 Y_2 Y_1 )→ Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 265 T321: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 266 T322: ¬(Y1∧Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ ¬Y3∧¬Y1∧¬Y2 Y_3 Y_1 Y_2 1 0.02% 1 0.06% Cluster 267 T327: ¬(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 268 T328: ¬(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 269 T329: ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 270 T333: ¬(¬Y1∧¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 271 T339: ¬(Y1↔¬Y2) (Y_1 Y_2 ) ↝ ¬Y1∧¬Y2 Y_1 Y_2 1 0.02% 1 0.06% Cluster 272 T340: ¬(Y1↔¬Y2) (Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.02% 1 0.06% Cluster 273 T341: ¬(Y1↔¬(Y2∧Y3)) (Y_1 (Y_2 Y_3 ) ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.02% 1 0.06% Cluster 274 T342: ¬(¬Y1↔Y2) ( Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 275 T343: ¬(¬Y1↔¬Y2) ( Y_1 Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.02% 1 0.06% Cluster 276 T344: ¬(¬Y1↔¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 277 T346: ¬((Y1∨Y2)↔Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ ¬Y3→(¬Y1∨¬Y2) Y_3→ ( Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 278 T347: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2↔Y1Y_2 Y_1 1 0.02% 1 0.06% Cluster 279 T350: ¬(Y1→Y2) (Y_1→ Y_2 ) ↝ Y2→¬Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 280 T352: ¬(Y1→¬Y2) (Y_1→ Y_2 ) ↝ Y2↔Y1Y_2 Y_1 1 0.02% 1 0.06% Cluster 281 T359: ¬(Y1∨¬Y2) (Y_1 Y_2 ) ↝ ¬(Y2∧Y1) (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 282 T361: ¬(¬Y1∨¬Y2) ( Y_1 Y_2 ) ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 1 0.02% 1 0.06% Cluster 283 T366: Y1∨Y2∨¬Y1∨¬Y2Y_1 Y_2 Y_1 Y_2 ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 284 T370: Y1∨Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 1 0.02% 1 0.06% Cluster 285 T372: Y1∨Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 286 T377: Y1∨¬Y2Y_1 Y_2 ↝ Y2→¬Y1Y_2→ Y_1 1 0.02% 1 0.06% Cluster 287 T385: (Y1∧Y2∧Y3)∨(Y1∧Y2∧Y3)∨(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 288 T386: (Y1∧Y2∧Y3)∨(Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 289 T387: (Y1∧Y2∧Y3)∨(Y3∧¬Y1∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_3 Y_1 Y_2 ) ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 290 T388: (Y1∧Y2∧¬Y3)∨(Y1∧Y2∧¬Y4) (Y_1 Y_2 Y_3 ) (Y_1 Y_2 Y_4 ) ↝ Y1∧Y2∧¬Y3∧¬Y4Y_1 Y_2 Y_3 Y_4 1 0.02% 1 0.06% Cluster 291 T389: (Y1∧Y2∧¬Y3)∨(Y1∧Y3∧¬Y2)∨(Y2∧Y3∧¬Y1) (Y_1 Y_2 Y_3 ) (Y_1 Y_3 Y_2 ) (Y_2 Y_3 Y_1 ) ↝ ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 292 T395: (Y1∧Y2)∨(Y1∧Y2∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_2 Y_3 ) (Y_2 Y_3 ) ↝ Y2→(Y1∨Y3)Y_2→ (Y_1 Y_3 ) 1 0.02% 1 0.06% Cluster 293 T396: (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ ¬(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 294 T400: (Y1∧Y2)∨(Y1∧¬Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 295 T401: (Y1∧Y2)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 296 T403: (Y1∧Y2)∨(¬Y1∧¬Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 297 T404: (Y1∧Y2)∨(Y2↔¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 298 T405: (Y1∧Y2)∨¬Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 299 T410: (Y2∧Y1)∨Y3 (Y_2 Y_1 ) Y_3 ↝ Y3→(Y1→Y2)Y_3→ (Y_1→ Y_2 ) 1 0.02% 1 0.06% Cluster 300 T412: (Y1↔Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 1 0.02% 1 0.06% Cluster 301 T414: (Y1↔Y2)∨(Y3↔Y1)∨(Y3↔Y2) (Y_1 Y_2 ) (Y_3 Y_1 ) (Y_3 Y_2 ) ↝ (Y1∧Y3)∨(Y1∧Y2)∨(Y3∧Y2) (Y_1 Y_3 ) (Y_1 Y_2 ) (Y_3 Y_2 ) 1 0.02% 1 0.06% Cluster 302 T415: (Y1↔Y2)∨(Y3↔Y1) (Y_1 Y_2 ) (Y_3 Y_1 ) ↝ (¬Y2∧¬Y3)→¬Y1 ( Y_2 Y_3 )→ Y_1 1 0.02% 1 0.06% Cluster 303 T419: (Y1→Y2)∨(Y2→Y1) (Y_1→ Y_2 ) (Y_2→ Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 304 T420: (Y1→¬Y2)∨(Y2→¬Y1) (Y_1→ Y_2 ) (Y_2→ Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 305 T421: (Y1→¬Y2)∨(¬Y1→Y2) (Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 306 T423: ((Y1∨Y2)→Y3)∨Y1∨Y2 ( (Y_1 Y_2 )→ Y_3 ) Y_1 Y_2 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 307 T427: ¬Y1∨¬Y2∨¬Y3 Y_1 Y_2 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 308 T430: ¬(Y1∧Y2)∨¬(Y1∧Y3)∨¬(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 309 T434: Y1∨Y2∨Y1∨Y3Y_1 Y_2 Y_1 Y_3 ↝ (Y1∧Y2)∨(Y1∧Y3)∨(Y2∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) (Y_2 Y_3 ) 1 0.02% 1 0.06% Cluster 310 T436: Y1∨¬Y2∨(Y2∧¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 311 T438: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.02% 1 0.06% Cluster 312 T439: ¬Y1∨¬Y2∨Y3 Y_1 Y_2 Y_3 ↝ Y3→(Y1∧Y2)Y_3→ (Y_1 Y_2 ) 1 0.02% 1 0.06% B.4. Modal Logic: Hierarchical Clustering of Transformations Table 39. Transformation hierarchy clusters Transformations # % #dst %dst Whole data set 12482 100.00% 3951 100.00% ANY transformation explained 9910 79.39% 2333 59.05% Cluster 1 T960: Y1→Y2Y_1→ Y_2 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 707 5.66% 162 4.10% T1035: Y1→◇(¬Y1)Y_1→ ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 32 0.26% 1 0.03% T1758: ◇(¬Y1)∨□(¬Y1) ( Y_1 ) ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 16 0.13% 1 0.03% T981: Y1→(¬Y1∧◇Y2)Y_1→ ( Y_1 Y_2 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 4 0.03% 2 0.05% T331: ¬Y1∧◇(¬Y1) Y_1 ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 3 0.02% 1 0.03% ⌈ == T530: □(□Y1) ( Y_1 ) ↝ ◇(◇Y1) ( Y_1 ) 4 0.03% 1 0.03% ⌊ == T545: □(□(¬Y1)) ( ( Y_1 ) ) ↝ ◇(◇(¬Y1)) ( ( Y_1 ) ) 4 0.03% 1 0.03% T1810: ¬Y1∨□(□(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 3 0.02% 1 0.03% T1423: ¬Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 2 0.02% 1 0.03% T987: Y1→□Y1Y_1→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T1104: Y1→(¬(◇Y1)∨◇(◇Y1))Y_1→ ( ( Y_1 ) ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 2 ⌈ == T1226: □Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 421 3.37% 1 0.03% ⌊ == T1587: Y1∨Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 421 3.37% 1 0.03% Cluster 3 T1708: □Y1∨Y2 Y_1 Y_2 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 290 2.32% 4 0.10% T1715: □Y1∨□(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 168 1.35% 1 0.03% T1717: □Y1∨□(◇Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 115 0.92% 1 0.03% T1709: □Y1∨□Y1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 6 0.05% 1 0.03% Cluster 4 T637: □(Y1∨Y2) (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 287 2.30% 12 0.30% T643: □(Y1∨◇Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 131 1.05% 1 0.03% T636: □(Y1∨Y2) (Y_1 Y_2 ) ↝ □Y1∧□Y2 Y_1 Y_2 130 1.04% 1 0.03% T649: □(Y1∨◇(◇Y2)) (Y_1 ( Y_2 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 6 0.05% 3 0.08% T646: □(Y1∨◇(◇Y1)) (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 4 0.03% 1 0.03% T641: □(Y1∨□(□Y1)) (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 5 0.04% 1 0.03% T642: □(Y1∨□(◇Y1)) (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 4 0.03% 1 0.03% T633: □(Y1∨Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% T651: □(Y1∨¬Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 5 T68: Y1∧◇Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 264 2.12% 14 0.35% T92: Y1∧◇(¬Y2)Y_1 ( Y_2 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 219 1.75% 4 0.10% T86: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 216 1.73% 2 0.05% T94: Y1∧◇(¬(◇Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T61: Y1∧◇Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 11 0.09% 1 0.03% T74: Y1∧◇(Y2∧¬Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 7 0.06% 2 0.05% T71: Y1∧◇(Y1∧¬Y1)Y_1 (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% T82: Y1∧◇(◇Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T72: Y1∧◇(Y1∧¬(◇Y1))Y_1 (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% T78: Y1∧◇(□(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% T96: Y1∧◇(Y1∨¬Y1)Y_1 (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 6 T446: □Y1 Y_1 ↝ ◇Y1 Y_1 262 2.10% 15 0.38% T1533: ¬(□Y1) ( Y_1 ) ↝ ¬(◇Y1) ( Y_1 ) 95 0.76% 3 0.08% T30: Y1∧□Y2Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 82 0.66% 2 0.05% T621: □(¬Y1) ( Y_1 ) ↝ ◇(¬Y1) ( Y_1 ) 45 0.36% 3 0.08% T529: □(□Y1) ( Y_1 ) ↝ □(◇Y1) ( Y_1 ) 15 0.12% 1 0.03% T639: □(Y1∨Y2) (Y_1 Y_2 ) ↝ ◇(Y1∨Y2) (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 7 T1152: □Y1→Y2 Y_1→ Y_2 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 238 1.91% 85 2.15% T1235: □Y1→(◇(¬Y2)∨◇(◇(¬Y2))) Y_1→ ( ( Y_2 ) ( ( Y_2 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 25 0.20% 2 0.05% T1176: □Y1→□Y2 Y_1→ Y_2 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 13 0.10% 7 0.18% T1201: □Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 11 0.09% 1 0.03% T1224: □Y1→(Y1∨◇Y1) Y_1→ (Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 10 0.08% 1 0.03% T1232: □Y1→(◇Y1∨◇(◇Y1)) Y_1→ ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 7 0.06% 1 0.03% T1210: □Y1→¬Y1 Y_1→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% T1157: □Y1→(Y1∧□Y1) Y_1→ (Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T1193: □Y1→◇Y1 Y_1→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T1205: □Y1→◇((Y2→¬Y1)∨¬Y1) Y_1→ ( (Y_2→ Y_1 ) Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T1237: □Y1→(¬Y1∨◇(□(¬Y1))) Y_1→ ( Y_1 ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 8 ⌈ == T18: Y1∧Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 217 1.74% 3 0.08% ⌊ == T67: Y1∧◇Y2Y_1 Y_2 ↝ Y1→◇Y2Y_1→ Y_2 217 1.74% 3 0.08% T86: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 216 1.73% 2 0.05% T142: Y1∧Y2∧◇(Y1∨Y2)Y_1 Y_2 (Y_1 Y_2 ) ↝ (Y1∧Y2)→◇(Y1∨Y2) (Y_1 Y_2 )→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 9 T1580: Y1∨Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 199 1.59% 6 0.15% T1715: □Y1∨□(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 168 1.35% 1 0.03% Cluster 10 T676: ◇Y1 Y_1 ↝ □Y1 Y_1 193 1.55% 16 0.40% T753: ◇(◇Y1) ( Y_1 ) ↝ □(◇Y1) ( Y_1 ) 22 0.18% 1 0.03% T1317: ◇Y1→Y2 Y_1→ Y_2 ↝ □Y1→Y2 Y_1→ Y_2 14 0.11% 4 0.10% T1364: ◇(Y1∧Y2)→(Y2∨◇Y3) (Y_1 Y_2 )→ (Y_2 Y_3 ) ↝ □(Y1∧Y2)→(Y2∨◇Y3) (Y_1 Y_2 )→ (Y_2 Y_3 ) 1 0.01% 1 0.03% T1552: ¬(◇Y1) ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 10 0.08% 1 0.03% T772: ◇(Y1→Y2) (Y_1→ Y_2 ) ↝ □(Y1→Y2) (Y_1→ Y_2 ) 2 0.02% 1 0.03% Cluster 11 T2: Y1Y_1 ↝ □Y1 Y_1 178 1.43% 9 0.23% ⌈ == T954: Y1→Y2Y_1→ Y_2 ↝ □(Y1→Y2) (Y_1→ Y_2 ) 20 0.16% 1 0.03% ⌊ == T1453: ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 20 0.16% 1 0.03% T677: ◇Y1 Y_1 ↝ □(◇Y1) ( Y_1 ) 11 0.09% 1 0.03% T1519: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 11 0.09% 1 0.03% T1518: ¬Y1 Y_1 ↝ ¬(□Y1) ( Y_1 ) 7 0.06% 1 0.03% T1079: Y1→(Y2∨Y1)Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 6 0.05% 2 0.05% T41: Y1∧□(□Y1)Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% T963: Y1→Y2Y_1→ Y_2 ↝ □Y1→Y2 Y_1→ Y_2 2 0.02% 1 0.03% Cluster 12 T1747: ◇(□Y1)∨□Y1 ( Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 163 1.31% 1 0.03% Cluster 13 T5: Y1Y_1 ↝ ¬Y1 Y_1 144 1.15% 15 0.38% T822: Y1↔Y2Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 56 0.45% 1 0.03% T680: ◇Y1 Y_1 ↝ ◇(¬Y1) ( Y_1 ) 28 0.22% 4 0.10% ⌈ == T65: Y1∧◇Y2Y_1 Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 18 0.14% 3 0.08% ⌊ == T684: ◇Y1 Y_1 ↝ ¬(◇Y1) ( Y_1 ) 18 0.14% 3 0.08% T459: □(Y1∧Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 10 0.08% 1 0.03% T1590: Y1∨□Y1Y_1 Y_1 ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 8 0.06% 1 0.03% Cluster 14 T640: □(Y1∨□Y2) (Y_1 Y_2 ) ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 139 1.11% 7 0.18% T636: □(Y1∨Y2) (Y_1 Y_2 ) ↝ □Y1∧□Y2 Y_1 Y_2 130 1.04% 1 0.03% T664: □(◇Y1∨□Y1) ( Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% T662: □(□Y1∨□Y1) ( Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 15 T3: Y1Y_1 ↝ ◇Y1 Y_1 138 1.11% 14 0.35% T109: Y1∧¬Y2Y_1 Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 53 0.42% 3 0.08% T1083: Y1→(Y2∨◇(◇Y2))Y_1→ (Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 30 0.24% 2 0.05% T15: Y1∧Y2Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 14 0.11% 1 0.03% T957: Y1→Y2Y_1→ Y_2 ↝ Y1→◇Y2Y_1→ Y_2 13 0.10% 3 0.08% ⌈ == T679: ◇Y1 Y_1 ↝ ◇(◇Y1) ( Y_1 ) 8 0.06% 2 0.05% ⌊ == T1732: ◇Y1∨◇Y1 Y_1 Y_1 ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 8 0.06% 2 0.05% T932: ¬Y1↔(Y1∧□Y2) Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 16 T113: Y1∧¬Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 131 1.05% 6 0.15% T123: Y1∧¬(◇Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 96 0.77% 1 0.03% T107: Y1∧¬Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 16 0.13% 1 0.03% T114: Y1∧¬(□Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 14 0.11% 1 0.03% T132: Y1∧¬(◇(◇Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% T131: Y1∧¬(◇(□Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 17 T793: ◇(¬Y1) ( Y_1 ) ↝ ¬(◇Y1) ( Y_1 ) 130 1.04% 3 0.08% Cluster 18 ⌈ == T1588: Y1∨Y2Y_1 Y_2 ↝ ◇Y1∨◇Y2 Y_1 Y_2 120 0.96% 2 0.05% ⌊ == T1604: Y1∨◇Y1Y_1 Y_1 ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 120 0.96% 2 0.05% Cluster 19 T204: ◇Y1∧□Y2 Y_1 Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 114 0.91% 11 0.28% T262: ◇(¬Y1)∧□Y2 ( Y_1 ) Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 93 0.75% 3 0.08% T259: ◇(¬Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 89 0.71% 1 0.03% T271: ◇(¬(◇Y1))∧□Y1 ( ( Y_1 ) ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% T201: ◇Y1∧□Y1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% T244: ◇(□(Y1→¬Y2))∧□Y2 ( (Y_1→ Y_2 ) ) Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 1 0.01% 1 0.03% T245: ◇(□(¬Y1))∧□Y1 ( ( Y_1 ) ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% T249: ◇(◇Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 20 T21: Y1∧Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 113 0.91% 7 0.18% T376: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 105 0.84% 4 0.10% Cluster 21 T1466: (Y1∨Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 108 0.87% 1 0.03% Cluster 22 T377: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(◇(¬Y3)∨◇(◇(¬Y3)))Y_3→ ( ( Y_3 ) ( ( Y_3 ) ) ) 106 0.85% 24 0.61% T439: (◇(¬Y1)∨□(◇(¬Y1)))∧Y1 ( ( Y_1 ) ( ( Y_1 ) ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% T421: (□(¬Y1)∨□(◇(¬Y1)))∧Y1 ( ( Y_1 ) ( ( Y_1 ) ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% T400: (Y1∨◇(◇Y1))∧Y1 (Y_1 ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T412: (□Y1∨□(□Y1))∧Y1 ( Y_1 ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T424: (◇Y1∨□(□Y1))∧Y1 ( Y_1 ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 23 T37: Y1∧□Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 97 0.78% 3 0.08% T259: ◇(¬Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 89 0.71% 1 0.03% T380: (Y1∨Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 8 0.06% 2 0.05% T440: (◇(¬Y1)∨◇(◇(¬Y1)))∧□Y1 ( ( Y_1 ) ( ( Y_1 ) ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 5 0.04% 1 0.03% Cluster 24 T961: Y1→Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 94 0.75% 9 0.23% T1378: ◇(¬Y1)→Y1 ( Y_1 )→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T1451: ¬(Y1↔Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 25 T444: □Y1 Y_1 ↝ Y1Y_1 86 0.69% 16 0.40% T1150: □Y1→Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 63 0.50% 3 0.08% T589: □(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→Y2Y_1→ Y_2 11 0.09% 4 0.10% T528: □(□Y1) ( Y_1 ) ↝ □Y1 Y_1 2 0.02% 2 0.05% T1088: Y1→(□Y2∨Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.02% 2 0.05% T729: ◇(□Y1) ( Y_1 ) ↝ ◇Y1 Y_1 2 0.02% 1 0.03% T1170: □Y1→□Y1 Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 2 0.02% 1 0.03% T627: □(¬(□Y1)) ( ( Y_1 ) ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 26 T32: Y1∧□Y2Y_1 Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 83 0.66% 20 0.51% T240: ◇(□Y1)∧□Y1 ( Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 35 0.28% 1 0.03% ⌈ == T17: Y1∧Y2Y_1 Y_2 ↝ □Y1∧□Y2 Y_1 Y_2 11 0.09% 1 0.03% ⌊ == T25: Y1∧□Y1Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 11 0.09% 1 0.03% T248: ◇(◇Y1)∧□Y1 ( Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 1 0.03% T351: ¬(□(◇Y1))∧□Y1 ( ( Y_1 ) ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% T393: (Y1∨◇Y1)∧□Y1 (Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 27 T953: Y1→Y2Y_1→ Y_2 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 79 0.63% 31 0.78% T1014: Y1→□(Y1∨Y2)Y_1→ (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 16 0.13% 3 0.08% T1076: Y1→(Y1∨□Y1)Y_1→ (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 4 0.03% 1 0.03% T1091: Y1→(◇Y1∨◇(◇Y1))Y_1→ ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 28 T689: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 79 0.63% 9 0.23% T704: ◇(Y1∧¬Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 23 0.18% 1 0.03% T694: ◇(Y1∧◇Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% T692: ◇(Y1∧□(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T703: ◇(Y1∧◇(Y1∨¬Y1)) (Y_1 (Y_1 Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 29 T20: Y1∧Y2Y_1 Y_2 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 77 0.62% 21 0.53% T87: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 9 0.07% 1 0.03% T43: Y1∧□(◇(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 4 0.03% 1 0.03% T79: Y1∧◇(□(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% T42: Y1∧□(□(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% T75: Y1∧◇(¬Y1∧◇(¬Y1))Y_1 ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% T76: Y1∧◇(□Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% T27: Y1∧□Y1Y_1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T45: Y1∧□(◇(¬Y1∨◇(¬Y1)))Y_1 ( ( Y_1 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T58: Y1∧□(◇(¬Y1)∨◇(¬Y1))Y_1 ( ( Y_1 ) ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T104: Y1∧◇(¬Y1∨◇Y1)Y_1 ( Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T124: Y1∧¬(◇Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 30 T312: ¬Y1∧□Y2 Y_1 Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 75 0.60% 9 0.23% T353: ¬(◇Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 50 0.40% 1 0.03% Cluster 31 T1583: Y1∨Y2Y_1 Y_2 ↝ Y2↔¬Y1Y_2 Y_1 75 0.60% 2 0.05% Cluster 32 T1248: □(¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 75 0.60% 1 0.03% Cluster 33 T1136: (¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 73 0.58% 1 0.03% Cluster 34 T445: □Y1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 72 0.58% 1 0.03% Cluster 35 T1531: ¬(□Y1) ( Y_1 ) ↝ □(¬Y1) ( Y_1 ) 67 0.54% 2 0.05% T1535: ¬(□(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 40 0.32% 1 0.03% T1630: Y1∨¬(□Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 27 0.22% 1 0.03% Cluster 36 T1151: □Y1→Y2 Y_1→ Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 65 0.52% 12 0.30% T1195: □Y1→◇Y2 Y_1→ Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 39 0.31% 5 0.13% T1192: □Y1→◇Y1 Y_1→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 4 0.03% 1 0.03% T1223: □Y1→¬(◇Y2) Y_1→ ( Y_2 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 17 0.14% 2 0.05% T1184: □Y1→□(¬Y1) Y_1→ ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 4 0.03% 1 0.03% T1169: □Y1→□Y1 Y_1→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% ⌈ == T1175: □Y1→□Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% ⌊ == T1182: □Y1→□(◇(¬Y1)) Y_1→ ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 37 T134: Y2∧◇Y1Y_2 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 65 0.52% 10 0.25% T358: ¬(◇Y1)∧◇Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 24 0.19% 1 0.03% ⌈ == T319: ¬Y1∧◇Y1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 18 0.14% 1 0.03% ⌊ == T326: ¬Y1∧◇Y2 Y_1 Y_2 ↝ Y2→◇(¬Y1)Y_2→ ( Y_1 ) 18 0.14% 1 0.03% T61: Y1∧◇Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 11 0.09% 1 0.03% T211: ◇Y1∧◇Y1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 4 0.03% 1 0.03% T148: Y1∧¬Y1∧◇Y1Y_1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 38 T951: Y1→Y2Y_1→ Y_2 ↝ Y1∧Y2Y_1 Y_2 65 0.52% 8 0.20% T1069: Y1→¬(◇Y2)Y_1→ ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 2 0.02% 2 0.05% Cluster 39 T23: Y1∧Y2Y_1 Y_2 ↝ Y1∨Y2Y_1 Y_2 59 0.47% 9 0.23% T48: Y1∧□(¬Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 32 0.26% 1 0.03% T1522: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬(Y1∨Y2) (Y_1 Y_2 ) 7 0.06% 1 0.03% ⌈ == T308: ¬Y1∧Y2 Y_1 Y_2 ↝ ¬Y1∨Y2 Y_1 Y_2 1 0.01% 1 0.03% ⌊ == T504: □(¬Y1∧¬Y2) ( Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% T551: □(◇(Y1∧Y2∧¬(◇Y3))) ( (Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 40 T35: Y1∧□Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 58 0.46% 5 0.13% T47: Y1∧□(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 47 0.38% 1 0.03% Cluster 41 T895: □Y1↔(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 55 0.44% 1 0.03% Cluster 42 T1728: ◇Y1∨□Y1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 55 0.44% 1 0.03% Cluster 43 T479: □(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 54 0.43% 2 0.05% Cluster 44 T1648: (Y1∧Y2)∨□Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 52 0.42% 2 0.05% Cluster 45 T1550: ¬(◇Y1) ( Y_1 ) ↝ ◇(¬Y1) ( Y_1 ) 51 0.41% 3 0.08% Cluster 46 T1227: □Y1→(Y2∨◇Y2) Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 51 0.41% 2 0.05% Cluster 47 T791: ◇(¬Y1) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 51 0.41% 1 0.03% Cluster 48 T1057: Y1→¬Y2Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 51 0.41% 1 0.03% Cluster 49 T389: (Y1∨□Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨□Y3)Y_3→ (Y_1 Y_3 ) 50 0.40% 5 0.13% T388: (Y1∨□Y1)∧Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% T390: (Y1∨□(◇Y2))∧Y2 (Y_1 ( Y_2 ) ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 50 ⌈ == T688: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ ◇Y2 Y_2 49 0.39% 6 0.15% || == T711: ◇(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ◇(¬Y2) ( Y_2 ) 49 0.39% 6 0.15% ⌊ == T714: ◇(Y2∧¬Y1) (Y_2 Y_1 ) ↝ ◇(¬Y1) ( Y_1 ) 49 0.39% 6 0.15% T722: ◇((Y1∨Y2∨Y3)∧¬Y4) ( (Y_1 Y_2 Y_3 ) Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 42 0.34% 2 0.05% Cluster 51 T995: Y1→□Y2Y_1→ Y_2 ↝ □Y1→Y2 Y_1→ Y_2 43 0.34% 2 0.05% Cluster 52 T470: □(Y1∧◇(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 43 0.34% 1 0.03% Cluster 53 T674: ◇Y1 Y_1 ↝ Y1Y_1 42 0.34% 20 0.51% T547: □(◇Y1) ( Y_1 ) ↝ □Y1 Y_1 10 0.08% 6 0.15% T1337: ◇Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 9 0.07% 1 0.03% T1358: ◇Y1→(◇Y2∨◇(◇Y2)) Y_1→ ( Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 5 0.04% 2 0.05% ⌈ == T727: ◇(□Y1) ( Y_1 ) ↝ □Y1 Y_1 3 0.02% 2 0.05% ⌊ == T1616: Y1∨◇(□Y2)Y_1 ( Y_2 ) ↝ Y1∨□Y2Y_1 Y_2 3 0.02% 2 0.05% T1024: Y1→◇Y2Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 3 0.02% 2 0.05% T1194: □Y1→◇Y1 Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% T754: ◇(◇Y1) ( Y_1 ) ↝ ◇Y1 Y_1 2 0.02% 2 0.05% T696: ◇(Y1∧◇Y2) (Y_1 Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 2 0.02% 1 0.03% T775: ◇(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% T1092: Y1→(◇Y2∨□Y1)Y_1→ ( Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 54 T1144: □Y1→Y2 Y_1→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 40 0.32% 16 0.40% ⌈ == T1296: □(Y1∨Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ □Y1∧□Y2 Y_1 Y_2 8 0.06% 1 0.03% ⌊ == T1302: □(Y1∨□Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 8 0.06% 1 0.03% T1142: □Y1→Y1 Y_1→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 5 0.04% 1 0.03% T1243: □(Y1∧□Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 55 T1353: ◇Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 39 0.31% 1 0.03% Cluster 56 T356: ¬(◇Y1)∧□(◇(Y2∨Y3)) ( Y_1 ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 38 0.30% 1 0.03% Cluster 57 T1749: ◇(◇Y1)∨□Y1 ( Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 37 0.30% 1 0.03% Cluster 58 T133: Y2∧□(¬Y1)Y_2 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 33 0.26% 2 0.05% T48: Y1∧□(¬Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 32 0.26% 1 0.03% Cluster 59 T1018: Y1→□(Y2∨◇Y2)Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 33 0.26% 2 0.05% Cluster 60 T527: □(□Y1) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 33 0.26% 1 0.03% Cluster 61 T623: □(¬Y1) ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 33 0.26% 1 0.03% Cluster 62 T1010: Y1→□(¬Y2)Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 33 0.26% 1 0.03% Cluster 63 T159: □Y1∧Y2 Y_1 Y_2 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 31 0.25% 4 0.10% T177: □Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 2 0.05% T174: □Y1∧□(¬Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 64 T952: Y1→Y2Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 30 0.24% 2 0.05% Cluster 65 T223: ◇Y1∧◇(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 30 0.24% 1 0.03% Cluster 66 T465: □(Y1∧◇Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 30 0.24% 1 0.03% Cluster 67 T1138: (¬Y1∧¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 30 0.24% 1 0.03% Cluster 68 T950: Y1→Y2Y_1→ Y_2 ↝ Y2Y_2 29 0.23% 10 0.25% T773: ◇(Y1→Y2) (Y_1→ Y_2 ) ↝ ◇Y2 Y_2 19 0.15% 4 0.10% T1063: Y1→¬(□Y1)Y_1→ ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% T1406: (Y1→□(Y2∧Y3))→Y4 (Y_1→ (Y_2 Y_3 ) )→ Y_4 ↝ □(Y2∧Y3)→Y4 (Y_2 Y_3 )→ Y_4 1 0.01% 1 0.03% T1566: ¬(Y1→□Y1) (Y_1→ Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 69 T16: Y1∧Y2Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 28 0.22% 1 0.03% Cluster 70 T110: Y1∧¬Y2Y_1 Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 28 0.22% 1 0.03% Cluster 71 T339: ¬(□Y1)∧□(◇Y2) ( Y_1 ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 28 0.22% 1 0.03% Cluster 72 ⌈ == T100: Y1∧◇(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(◇Y2∨◇Y3)Y_1→ ( Y_2 Y_3 ) 27 0.22% 2 0.05% ⌊ == T102: Y1∧◇(Y2∨◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 27 0.22% 2 0.05% Cluster 73 T381: (Y1∨Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 26 0.21% 1 0.03% Cluster 74 T1249: □(¬Y1∧¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 26 0.21% 1 0.03% Cluster 75 T1551: ¬(◇Y1) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 26 0.21% 1 0.03% Cluster 76 T546: □(◇Y1) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 25 0.20% 1 0.03% Cluster 77 T1586: Y1∨Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 24 0.19% 8 0.20% T1609: Y1∨◇Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 13 0.10% 5 0.13% ⌈ == T1585: Y1∨Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 8 0.06% 2 0.05% ⌊ == T1620: Y1∨◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 8 0.06% 2 0.05% T1603: Y1∨◇Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T1615: Y1∨◇(Y2∧¬Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% T1632: Y1∨¬(◇Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 8 0.06% 1 0.03% Cluster 78 T702: ◇(Y1∧◇(¬Y2)) (Y_1 ( Y_2 ) ) ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 24 0.19% 4 0.10% Cluster 79 T50: Y1∧□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 24 0.19% 1 0.03% Cluster 80 ⌈ == T1584: Y1∨Y2Y_1 Y_2 ↝ ¬Y1↔Y2 Y_1 Y_2 24 0.19% 1 0.03% ⌊ == T1612: Y1∨◇(Y1∧Y2)Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) 24 0.19% 1 0.03% Cluster 81 T1818: ¬Y1∨¬Y2 Y_1 Y_2 ↝ ¬(Y1∨Y2) (Y_1 Y_2 ) 24 0.19% 1 0.03% Cluster 82 ⌈ == T447: □Y1 Y_1 ↝ ◇(◇Y1) ( Y_1 ) 23 0.18% 2 0.05% ⌊ == T1093: Y1→(◇Y2∨□Y2)Y_1→ ( Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 23 0.18% 2 0.05% T1758: ◇(¬Y1)∨□(¬Y1) ( Y_1 ) ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 16 0.13% 1 0.03% Cluster 83 T667: □(◇Y1∨◇(◇Y1)) ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 23 0.18% 1 0.03% Cluster 84 T818: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 22 0.18% 8 0.20% T840: Y1↔◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 7 0.06% 1 0.03% ⌈ == T584: □(¬(Y1∨Y2)↔Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% ⌊ == T930: ¬Y1↔Y2 Y_1 Y_2 ↝ ¬Y1→Y2 Y_1→ Y_2 1 0.01% 1 0.03% Cluster 85 T1589: Y1∨□Y1Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 21 0.17% 1 0.03% Cluster 86 T1475: (Y1∨□Y1)→Y2 (Y_1 Y_1 )→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 20 0.16% 4 0.10% T1460: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y1∧Y2Y_1 Y_2 9 0.07% 1 0.03% T1474: (Y1∨□Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 8 0.06% 1 0.03% Cluster 87 ⌈ == T108: Y1∧¬Y2∧¬Y3Y_1 Y_2 Y_3 ↝ ¬(Y2∨Y3)→Y1 (Y_2 Y_3 )→ Y_1 20 0.16% 1 0.03% ⌊ == T476: □(Y1∧¬Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 20 0.16% 1 0.03% Cluster 88 T231: ◇(Y1∧Y2)∧◇(□Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 20 0.16% 1 0.03% Cluster 89 T510: □(¬(◇Y1)∧◇Y2) ( ( Y_1 ) Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 20 0.16% 1 0.03% Cluster 90 T759: ◇(◇((Y1∨Y2)∧□(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 20 0.16% 1 0.03% Cluster 91 ⌈ == T1145: □Y1→Y2 Y_1→ Y_2 ↝ □(Y1→Y2) (Y_1→ Y_2 ) 20 0.16% 1 0.03% ⌊ == T1293: □(¬(Y1∨Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 20 0.16% 1 0.03% Cluster 92 T432: (◇(□Y1)∨□Y1)∧Y2 ( ( Y_1 ) Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 19 0.15% 2 0.05% Cluster 93 T726: ◇(□Y1) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 19 0.15% 1 0.03% Cluster 94 T1016: Y1→□(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 19 0.15% 1 0.03% Cluster 95 T1159: □Y1→(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 19 0.15% 1 0.03% Cluster 96 T483: □(Y1∧¬(◇Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 18 0.14% 1 0.03% Cluster 97 T708: ◇(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 18 0.14% 1 0.03% Cluster 98 T1733: ◇Y1∨◇Y2∨◇Y3 Y_1 Y_2 Y_3 ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 18 0.14% 1 0.03% Cluster 99 T480: □(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 17 0.14% 2 0.05% Cluster 100 T1002: Y1→□(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 17 0.14% 1 0.03% Cluster 101 T1215: □Y1→¬Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 17 0.14% 1 0.03% Cluster 102 T1308: □(¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 17 0.14% 1 0.03% Cluster 103 T1735: ◇Y1∨◇Y2 Y_1 Y_2 ↝ ◇Y2∨◇(◇Y2) Y_2 ( Y_2 ) 16 0.13% 8 0.20% ⌈ == T679: ◇Y1 Y_1 ↝ ◇(◇Y1) ( Y_1 ) 8 0.06% 2 0.05% ⌊ == T1732: ◇Y1∨◇Y1 Y_1 Y_1 ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 8 0.06% 2 0.05% T1097: Y1→(◇(◇Y2→Y1)∨◇Y2)Y_1→ ( ( Y_2→ Y_1 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 104 T119: Y1∧¬(□Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 16 0.13% 1 0.03% Cluster 105 T507: □(¬(□Y1)∧◇Y2) ( ( Y_1 ) Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 16 0.13% 1 0.03% Cluster 106 T989: Y1→□Y2Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 15 0.12% 2 0.05% Cluster 107 T1025: Y1→◇Y2Y_1→ Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 14 0.11% 4 0.10% Cluster 108 T84: Y1∧◇(◇Y2)Y_1 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 14 0.11% 2 0.05% Cluster 109 T1650: (Y1∧Y2)∨◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 14 0.11% 2 0.05% Cluster 110 T681: ◇Y1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 14 0.11% 1 0.03% Cluster 111 T1281: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 14 0.11% 1 0.03% Cluster 112 T1536: ¬(□(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 14 0.11% 1 0.03% Cluster 113 T962: Y1→Y2Y_1→ Y_2 ↝ Y2→(◇(¬Y2)∨◇(◇(¬Y2)))Y_2→ ( ( Y_2 ) ( ( Y_2 ) ) ) 13 0.10% 10 0.25% T1463: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→(◇(¬Y3)∨◇(◇(¬Y3)))Y_3→ ( ( Y_3 ) ( ( Y_3 ) ) ) 9 0.07% 6 0.15% Cluster 114 T1593: Y1∨□Y2Y_1 Y_2 ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 13 0.10% 4 0.10% T1590: Y1∨□Y1Y_1 Y_1 ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 8 0.06% 1 0.03% Cluster 115 ⌈ == T31: Y1∧□Y2Y_1 Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 13 0.10% 3 0.08% ⌊ == T451: □Y1 Y_1 ↝ ¬(◇Y1) ( Y_1 ) 13 0.10% 3 0.08% Cluster 116 T1008: Y1→□(¬Y2)Y_1→ ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 13 0.10% 3 0.08% Cluster 117 T394: (Y1∨◇Y1)∧□Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 13 0.10% 2 0.05% Cluster 118 T959: Y1→Y2Y_1→ Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 13 0.10% 2 0.05% Cluster 119 T206: ◇Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 13 0.10% 1 0.03% Cluster 120 T228: ◇(Y1∧Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 13 0.10% 1 0.03% Cluster 121 T567: □(◇(¬Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 13 0.10% 1 0.03% Cluster 122 T758: ◇(◇(Y1∧¬(□Y2))) ( (Y_1 ( Y_2 ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 13 0.10% 1 0.03% Cluster 123 T1080: Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 13 0.10% 1 0.03% Cluster 124 T1225: □Y1→(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 12 0.10% 9 0.23% T1229: □Y1→((Y1∧Y1)∨Y1) Y_1→ ( (Y_1 Y_1 ) Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 125 T1459: (Y1∨Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 12 0.10% 4 0.10% T1474: (Y1∨□Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 8 0.06% 1 0.03% T1485: (Y1∨◇(□Y1))→Y1 (Y_1 ( Y_1 ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% T1486: (Y1∨¬Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 126 T1043: Y1→◇(Y2∨□Y2)Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 12 0.10% 2 0.05% Cluster 127 T1096: Y1→(◇(◇Y2)∨□Y2)Y_1→ ( ( Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 12 0.10% 2 0.05% Cluster 128 T1196: □Y1→◇Y2 Y_1→ Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 12 0.10% 2 0.05% T1201: □Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 11 0.09% 1 0.03% Cluster 129 T175: □Y1∧□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 12 0.10% 1 0.03% Cluster 130 T609: □(Y1→(¬Y1∨◇(¬Y1))) (Y_1→ ( Y_1 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 12 0.10% 1 0.03% Cluster 131 T869: (¬Y1∧¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 12 0.10% 1 0.03% Cluster 132 T1186: □Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 12 0.10% 1 0.03% Cluster 133 T1622: Y1∨◇(¬Y2)Y_1 ( Y_2 ) ↝ Y2→(◇(¬Y2)∨◇(◇(¬Y2)))Y_2→ ( ( Y_2 ) ( ( Y_2 ) ) ) 11 0.09% 6 0.15% T1621: Y1∨◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% T1707: (¬(◇Y1)∧□Y1)∨◇(¬Y1) ( ( Y_1 ) Y_1 ) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 134 T1204: □Y1→◇(Y2∨◇Y2) Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 11 0.09% 2 0.05% Cluster 135 T1639: (Y1∧Y2)∨(Y1∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 11 0.09% 2 0.05% Cluster 136 T263: ◇(¬Y1)∧□(◇(Y2∨Y3)) ( Y_1 ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 11 0.09% 1 0.03% Cluster 137 T765: ◇(◇(¬Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 11 0.09% 1 0.03% Cluster 138 T1171: □Y1→□Y2 Y_1→ Y_2 ↝ □(Y1→Y2) (Y_1→ Y_2 ) 11 0.09% 1 0.03% Cluster 139 T1253: □(¬Y1∧¬Y2)→◇Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 11 0.09% 1 0.03% Cluster 140 T1365: ◇(¬Y1∧¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧Y3) ( Y_1 Y_2 Y_3 ) 11 0.09% 1 0.03% Cluster 141 T1464: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 11 0.09% 1 0.03% Cluster 142 T1153: □Y1→Y2 Y_1→ Y_2 ↝ □Y1→Y1 Y_1→ Y_1 10 0.08% 6 0.15% T1170: □Y1→□Y1 Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 2 0.02% 1 0.03% T1194: □Y1→◇Y1 Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 143 T57: Y1∧□(Y2∨□Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 10 0.08% 2 0.05% Cluster 144 T69: Y1∧◇Y2Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 10 0.08% 2 0.05% T87: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 9 0.07% 1 0.03% Cluster 145 T93: Y1∧◇(¬Y2)Y_1 ( Y_2 ) ↝ Y2→(◇(¬Y2)∨◇(◇(¬Y2)))Y_2→ ( ( Y_2 ) ( ( Y_2 ) ) ) 10 0.08% 2 0.05% T87: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 9 0.07% 1 0.03% Cluster 146 T392: (Y1∨◇Y1)∧Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 10 0.08% 2 0.05% Cluster 147 T396: (Y1∨◇Y2)∧Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 10 0.08% 2 0.05% Cluster 148 ⌈ == T690: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ ◇Y1∨◇Y2 Y_1 Y_2 10 0.08% 2 0.05% || == T695: ◇(Y1∧◇Y1) (Y_1 Y_1 ) ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 10 0.08% 2 0.05% ⌊ == T1031: Y1→◇(Y2∧◇Y2)Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 10 0.08% 2 0.05% Cluster 149 T1643: (Y1∧Y2)∨(Y2∧□Y2) (Y_1 Y_2 ) (Y_2 Y_2 ) ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 10 0.08% 2 0.05% Cluster 150 T40: Y1∧□(¬Y2∧¬Y3)Y_1 ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 10 0.08% 1 0.03% Cluster 151 T115: Y1∧¬(□Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 10 0.08% 1 0.03% Cluster 152 T172: □Y1∧□(◇(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 10 0.08% 1 0.03% Cluster 153 T514: □((Y1∨Y2∨Y3)∧¬Y4) ( (Y_1 Y_2 Y_3 ) Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 10 0.08% 1 0.03% Cluster 154 T1331: ◇Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 10 0.08% 1 0.03% Cluster 155 T1366: ◇(¬Y1∧¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 10 0.08% 1 0.03% Cluster 156 T1432: ¬(□Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 10 0.08% 1 0.03% Cluster 157 T1602: Y1∨◇Y1Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 10 0.08% 1 0.03% Cluster 158 T1516: ¬Y1 Y_1 ↝ Y1Y_1 9 0.07% 9 0.23% T790: ◇(¬Y1) ( Y_1 ) ↝ ◇Y1 Y_1 2 0.02% 2 0.05% T1562: ¬(◇(¬Y1)) ( ( Y_1 ) ) ↝ ¬(◇Y1) ( Y_1 ) 1 0.01% 1 0.03% T1549: ¬(◇Y1) ( Y_1 ) ↝ ◇Y1 Y_1 2 0.02% 2 0.05% T1081: Y1→(Y2∨□(¬Y1))Y_1→ (Y_2 ( Y_1 ) ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% T1530: ¬(□Y1) ( Y_1 ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 159 T1465: (Y1∨Y2)→□Y1 (Y_1 Y_2 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 6 0.15% T1476: (Y1∨□Y1)→□Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% T1481: (Y1∨◇Y1)→□Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% T1487: (Y1∨¬Y1)→□Y2 (Y_1 Y_1 )→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 1 0.01% 1 0.03% Cluster 160 T1064: Y1→¬(□Y2)Y_1→ ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 9 0.07% 3 0.08% Cluster 161 T1105: Y2→(□Y1∨□(□Y1))Y_2→ ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 3 0.08% Cluster 162 T111: Y1∧¬Y2Y_1 Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 9 0.07% 1 0.03% Cluster 163 T128: Y1∧¬(◇Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 9 0.07% 1 0.03% Cluster 164 T161: □Y1∧□Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 9 0.07% 1 0.03% Cluster 165 T343: ¬(□Y1)∧◇Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 9 0.07% 1 0.03% Cluster 166 T373: (Y1∨Y2∨Y3)∧¬Y4 (Y_1 Y_2 Y_3 ) Y_4 ↝ ◇(¬Y4) ( Y_4 ) 9 0.07% 1 0.03% Cluster 167 T404: (Y1∨¬Y2)∧(Y2∨¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 9 0.07% 1 0.03% Cluster 168 T683: ◇Y1 Y_1 ↝ ¬(□Y1) ( Y_1 ) 9 0.07% 1 0.03% Cluster 169 T804: ◇(Y1∨□Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 1 0.03% Cluster 170 T806: ◇(Y1∨◇Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 1 0.03% Cluster 171 ⌈ == T991: Y1→□Y2Y_1→ Y_2 ↝ □(Y1→Y2) (Y_1→ Y_2 ) 9 0.07% 1 0.03% ⌊ == T1454: ¬(Y1∨Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 9 0.07% 1 0.03% Cluster 172 T1149: □Y1→Y2 Y_1→ Y_2 ↝ □(¬Y2∨Y1) ( Y_2 Y_1 ) 9 0.07% 1 0.03% Cluster 173 T1513: (¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 9 0.07% 1 0.03% Cluster 174 T1736: ◇Y1∨◇(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 9 0.07% 1 0.03% Cluster 175 T837: Y1↔◇Y2Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 8 0.06% 2 0.05% T840: Y1↔◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 7 0.06% 1 0.03% Cluster 176 T1771: (Y1→Y2)∨◇Y1 (Y_1→ Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 8 0.06% 2 0.05% Cluster 177 T1: Y1Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 8 0.06% 1 0.03% Cluster 178 T8: Y1∧Y1∧□Y2Y_1 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 8 0.06% 1 0.03% Cluster 179 T51: Y1∧□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 8 0.06% 1 0.03% Cluster 180 T98: Y1∧◇(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 8 0.06% 1 0.03% Cluster 181 T706: ◇(Y1∧¬Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 8 0.06% 1 0.03% Cluster 182 T779: ◇(Y1→¬Y2) (Y_1→ Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 8 0.06% 1 0.03% Cluster 183 T858: Y1↔¬(◇Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 8 0.06% 1 0.03% Cluster 184 T1203: □Y1→◇(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 8 0.06% 1 0.03% Cluster 185 T1444: ¬(◇Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 8 0.06% 1 0.03% Cluster 186 T1468: (Y1∨Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 8 0.06% 1 0.03% Cluster 187 T1155: □Y1→Y2 Y_1→ Y_2 ↝ □Y2→Y2 Y_2→ Y_2 7 0.06% 5 0.13% T1285: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ □Y2→Y2 Y_2→ Y_2 3 0.02% 2 0.05% Cluster 188 T912: ◇Y1↔Y2 Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 7 0.06% 4 0.10% T919: ◇Y1↔◇(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 189 T803: ◇(Y1∨Y2) (Y_1 Y_2 ) ↝ ◇Y2 Y_2 7 0.06% 3 0.08% T814: ◇((Y1∧¬Y2∧¬Y3)∨(Y2∧¬Y1∧¬Y3)∨(Y3∧¬Y1∧¬Y2)∨¬Y4) ( (Y_1 Y_2 Y_3 ) (Y_2 Y_1 Y_3 ) (Y_3 Y_1 Y_2 ) Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 190 T11: Y1∧Y2∧□Y2Y_1 Y_2 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 7 0.06% 2 0.05% Cluster 191 T203: ◇Y1∧□Y2 Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 7 0.06% 2 0.05% Cluster 192 T810: ◇(Y1∨¬Y2) (Y_1 Y_2 ) ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 7 0.06% 2 0.05% T809: ◇(Y1∨¬Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% Cluster 193 T1082: Y1→(Y2∨◇(□Y2))Y_1→ (Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 7 0.06% 2 0.05% Cluster 194 T1598: Y1∨□(¬Y2)Y_1 ( Y_2 ) ↝ Y2∨□(¬Y2)Y_2 ( Y_2 ) 7 0.06% 2 0.05% Cluster 195 T1814: ¬Y1∨◇Y2 Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 7 0.06% 2 0.05% Cluster 196 T4: Y1Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 7 0.06% 1 0.03% Cluster 197 T126: Y1∧¬(◇Y2)Y_1 ( Y_2 ) ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 7 0.06% 1 0.03% Cluster 198 T363: ¬(◇Y1)∧◇(◇(Y2∨Y3)) ( Y_1 ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 7 0.06% 1 0.03% Cluster 199 T491: □(◇Y1∧◇(¬Y2)) ( Y_1 ( Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 7 0.06% 1 0.03% Cluster 200 T515: □((Y1∨Y2)∧¬Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 7 0.06% 1 0.03% Cluster 201 T1228: □Y1→(Y2∨¬Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 7 0.06% 1 0.03% Cluster 202 T1344: ◇Y1→(Y2↔¬Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 7 0.06% 1 0.03% Cluster 203 T1409: ¬Y1→Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 7 0.06% 1 0.03% Cluster 204 T1413: ¬Y1→Y2 Y_1→ Y_2 ↝ ¬Y2∨¬Y1 Y_2 Y_1 7 0.06% 1 0.03% Cluster 205 T1431: ¬(Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 7 0.06% 1 0.03% Cluster 206 T1490: ((Y1∧¬Y2)∨(Y2∧¬Y1))→□Y3 ( (Y_1 Y_2 ) (Y_2 Y_1 ) )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 7 0.06% 1 0.03% Cluster 207 T1521: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 7 0.06% 1 0.03% Cluster 208 T1573: ¬(Y1∨Y2) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 7 0.06% 1 0.03% Cluster 209 T1775: (Y1→Y2)∨(Y1→□(¬Y1)) (Y_1→ Y_2 ) (Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 6 0.05% 5 0.13% T1791: (Y1→¬Y1)∨(Y1→□(¬Y1)) (Y_1→ Y_1 ) (Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 210 T815: Y1↔Y2Y_1 Y_2 ↝ Y2Y_2 6 0.05% 4 0.10% Cluster 211 T325: ¬Y1∧◇Y2 Y_1 Y_2 ↝ ◇(¬Y1) ( Y_1 ) 6 0.05% 3 0.08% Cluster 212 T816: Y1↔Y2Y_1 Y_2 ↝ Y1∧Y2Y_1 Y_2 6 0.05% 3 0.08% T829: Y1↔□(Y1∧Y2)Y_1 (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 213 T66: Y1∧◇Y2Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 6 0.05% 2 0.05% Cluster 214 T179: □Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 6 0.05% 2 0.05% Cluster 215 T645: □(Y1∨◇(□Y2)) (Y_1 ( Y_2 ) ) ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 6 0.05% 2 0.05% Cluster 216 T958: Y1→Y2Y_1→ Y_2 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 6 0.05% 2 0.05% Cluster 217 T1313: ◇Y1→Y2 Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 6 0.05% 2 0.05% Cluster 218 T1764: (Y1↔Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 6 0.05% 2 0.05% Cluster 219 T214: ◇Y1∧◇Y2 Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 6 0.05% 1 0.03% Cluster 220 T473: □(Y1∧¬Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% Cluster 221 T516: □((Y1∨Y2)∧¬(□Y3)) ( (Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 6 0.05% 1 0.03% Cluster 222 T548: □(◇(Y1∧Y2∧¬(◇Y3))) ( (Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 6 0.05% 1 0.03% Cluster 223 T573: □(◇(Y1∨◇Y1)) ( (Y_1 Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 6 0.05% 1 0.03% Cluster 224 T599: □(Y1→◇(¬Y1)) (Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 6 0.05% 1 0.03% Cluster 225 T628: □(¬(◇Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% Cluster 226 T675: ◇Y1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 6 0.05% 1 0.03% Cluster 227 T894: □Y1↔¬(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 6 0.05% 1 0.03% Cluster 228 T969: Y1→(Y1∧Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 6 0.05% 1 0.03% Cluster 229 T976: Y1→(□Y1∧□Y2)Y_1→ ( Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 6 0.05% 1 0.03% Cluster 230 T1028: Y1→◇(Y1∧Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 6 0.05% 1 0.03% Cluster 231 T1058: Y1→¬Y2Y_1→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 6 0.05% 1 0.03% Cluster 232 T1189: □Y1→□(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 6 0.05% 1 0.03% Cluster 233 T1346: ◇Y1→¬Y1 Y_1→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% Cluster 234 T1350: ◇Y1→¬(□Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 6 0.05% 1 0.03% Cluster 235 T1382: ◇(¬(Y1∨Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 6 0.05% 1 0.03% Cluster 236 T1449: ¬(◇(Y1∧Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 6 0.05% 1 0.03% Cluster 237 T1532: ¬(□Y1) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 6 0.05% 1 0.03% Cluster 238 T1760: ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 6 0.05% 1 0.03% Cluster 239 T821: Y1↔Y2Y_1 Y_2 ↝ Y2→Y1Y_2→ Y_1 5 0.04% 3 0.08% T828: Y1↔□Y1Y_1 Y_1 ↝ □Y1→Y1 Y_1→ Y_1 2 0.02% 1 0.03% T945: (Y1∨◇Y1)↔□Y2 (Y_1 Y_1 ) Y_2 ↝ □Y2→(Y1∨◇Y1) Y_2→ (Y_1 Y_1 ) 2 0.02% 1 0.03% T926: ◇(¬Y1)↔Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 240 T22: Y1∧Y2Y_1 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 5 0.04% 2 0.05% Cluster 241 T62: Y1∧◇Y1Y_1 Y_1 ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 5 0.04% 2 0.05% T331: ¬Y1∧◇(¬Y1) Y_1 ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 3 0.02% 1 0.03% Cluster 242 T316: ¬Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 5 0.04% 2 0.05% T314: ¬Y1∧□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% Cluster 243 T838: Y1↔◇Y2Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 5 0.04% 2 0.05% Cluster 244 T1315: ◇Y1→Y2 Y_1→ Y_2 ↝ ◇Y2 Y_2 5 0.04% 2 0.05% Cluster 245 T1334: ◇Y1→◇Y2 Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 5 0.04% 2 0.05% Cluster 246 T1610: Y1∨◇Y2Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 5 0.04% 2 0.05% T1621: Y1∨◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 247 T53: Y1∧□(¬(Y2∨Y3))Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 5 0.04% 1 0.03% Cluster 248 T90: Y1∧◇(¬Y2)Y_1 ( Y_2 ) ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 5 0.04% 1 0.03% Cluster 249 T91: Y1∧◇(¬Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 5 0.04% 1 0.03% Cluster 250 T129: Y1∧¬(◇Y2)Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 5 0.04% 1 0.03% Cluster 251 T158: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 5 0.04% 1 0.03% Cluster 252 T189: □(¬Y1)∧□(□Y2) ( Y_1 ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 5 0.04% 1 0.03% Cluster 253 T324: ¬Y1∧◇Y2 Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 5 0.04% 1 0.03% Cluster 254 T449: □Y1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 5 0.04% 1 0.03% Cluster 255 T613: □(¬Y1→Y2) ( Y_1→ Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 5 0.04% 1 0.03% Cluster 256 T650: □(Y1∨◇(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 5 0.04% 1 0.03% Cluster 257 T663: □(□Y1∨□(□Y1)) ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 5 0.04% 1 0.03% Cluster 258 T794: ◇(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 5 0.04% 1 0.03% Cluster 259 T850: Y1↔¬Y2Y_1 Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 5 0.04% 1 0.03% Cluster 260 T856: Y1↔¬(◇Y1∧□Y2)Y_1 ( Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 5 0.04% 1 0.03% Cluster 261 T898: □(¬Y1∧¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 5 0.04% 1 0.03% Cluster 262 T968: Y1→Y2Y_1→ Y_2 ↝ Y1∨Y2Y_1 Y_2 5 0.04% 1 0.03% Cluster 263 T1056: Y1→¬Y2Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 5 0.04% 1 0.03% Cluster 264 T1168: □Y1→□Y1 Y_1→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 5 0.04% 1 0.03% Cluster 265 T1197: □Y1→◇Y2 Y_1→ Y_2 ↝ □Y1→(Y2∨◇Y2) Y_1→ (Y_2 Y_2 ) 5 0.04% 1 0.03% Cluster 266 T1199: □Y1→◇(□Y1) Y_1→ ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 5 0.04% 1 0.03% Cluster 267 T1220: □Y1→¬(□Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 5 0.04% 1 0.03% Cluster 268 T1318: ◇Y1→Y2 Y_1→ Y_2 ↝ □Y1→¬Y2 Y_1→ Y_2 5 0.04% 1 0.03% Cluster 269 T1325: ◇Y1→□Y1 Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 5 0.04% 1 0.03% Cluster 270 T1415: ¬Y1→□Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 5 0.04% 1 0.03% Cluster 271 T1439: ¬(□(Y1∧Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 5 0.04% 1 0.03% Cluster 272 T1637: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 5 0.04% 1 0.03% Cluster 273 T1640: (Y1∧Y2)∨(Y1∧◇Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 5 0.04% 1 0.03% Cluster 274 T1713: □Y1∨□Y2 Y_1 Y_2 ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 5 0.04% 1 0.03% Cluster 275 T1781: (Y1→□Y2)∨(Y3→□Y2) (Y_1→ Y_2 ) (Y_3→ Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 5 0.04% 1 0.03% Cluster 276 T335: ¬Y1∧¬Y2 Y_1 Y_2 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 4 0.03% 3 0.08% T336: ¬Y1∧¬(◇Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% T334: ¬Y1∧¬Y1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 277 T597: □(Y1→□Y2) (Y_1→ Y_2 ) ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 4 0.03% 3 0.08% T596: □(Y1→□Y1) (Y_1→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 278 T1027: Y1→◇Y2Y_1→ Y_2 ↝ □Y2→Y1 Y_2→ Y_1 4 0.03% 3 0.08% T1022: Y1→◇Y1Y_1→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 2 0.02% 1 0.03% T1452: ¬(Y1↔Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 279 T1730: ◇Y1∨□Y2 Y_1 Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 4 0.03% 3 0.08% Cluster 280 T34: Y1∧□Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 4 0.03% 2 0.05% Cluster 281 T73: Y1∧◇(Y2∧◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 4 0.03% 2 0.05% T75: Y1∧◇(¬Y1∧◇(¬Y1))Y_1 ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 282 T77: Y1∧◇(□Y2)Y_1 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 4 0.03% 2 0.05% T79: Y1∧◇(□(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 283 T604: □(Y1→¬Y2) (Y_1→ Y_2 ) ↝ ◇(¬Y2) ( Y_2 ) 4 0.03% 2 0.05% Cluster 284 T655: □((Y1∧□Y2)∨Y2) ( (Y_1 Y_2 ) Y_2 ) ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 4 0.03% 2 0.05% T654: □((Y1∧□Y1)∨Y1) ( (Y_1 Y_1 ) Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 285 T1039: Y1→◇(¬(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 4 0.03% 2 0.05% Cluster 286 T1078: Y1→(Y1∨◇Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 4 0.03% 2 0.05% Cluster 287 T1592: Y1∨□Y2Y_1 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 4 0.03% 2 0.05% Cluster 288 T1635: (Y1∧Y2)∨Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 4 0.03% 2 0.05% Cluster 289 T1769: (Y1→Y2)∨(Y1∧Y3) (Y_1→ Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y2∨◇Y2)Y_1→ (Y_2 Y_2 ) 4 0.03% 2 0.05% Cluster 290 ⌈ == T24: Y1∧Y2Y_1 Y_2 ↝ ¬Y1∨¬Y2 Y_1 Y_2 4 0.03% 1 0.03% ⌊ == T460: □(Y1∧Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 291 T120: Y1∧¬(□Y2)Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 292 T187: □(◇(Y1∨Y2))∧□(◇(◇(¬Y3))) ( (Y_1 Y_2 ) ) ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 293 T205: ◇Y1∧□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 4 0.03% 1 0.03% Cluster 294 T230: ◇(Y1∧Y2)∧□(□Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 295 T239: ◇(¬Y1∧¬Y2)∧◇Y3 ( Y_1 Y_2 ) Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 296 T254: ◇(◇(¬Y1))∧□Y1 ( ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 4 0.03% 1 0.03% Cluster 297 T260: ◇(¬Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 4 0.03% 1 0.03% Cluster 298 T273: ◇(¬(Y1∨Y2))∧Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ ◇(¬Y1∧¬Y2∧Y3) ( Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 299 T309: ¬Y1∧□Y2 Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 300 T333: ¬Y1∧◇(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ ◇((Y2∨Y3)∧¬(◇Y1)) ( (Y_2 Y_3 ) ( Y_1 ) ) 4 0.03% 1 0.03% Cluster 301 T500: □(¬Y1∧◇Y2) ( Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 302 T509: □(¬(◇Y1)∧□(Y2∨Y3)) ( ( Y_1 ) (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 4 0.03% 1 0.03% Cluster 303 T555: □(◇((Y1∨Y2)∧Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 304 T580: □(Y1↔¬Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 305 T582: □(¬Y1↔Y2) ( Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 306 T607: □(Y1→(Y2∨Y3)) (Y_1→ (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 307 T610: □((¬Y1∧¬Y2)→□Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 4 0.03% 1 0.03% Cluster 308 T615: □(¬Y1→Y2) ( Y_1→ Y_2 ) ↝ ◇(¬Y1) ( Y_1 ) 4 0.03% 1 0.03% Cluster 309 T631: □(¬(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 4 0.03% 1 0.03% Cluster 310 T724: ◇((Y1∨Y2)∧□(¬Y3)) ( (Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 311 T725: ◇((Y1∨Y2)∧¬(□Y3)) ( (Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 312 T728: ◇(□Y1) ( Y_1 ) ↝ □(◇Y1) ( Y_1 ) 4 0.03% 1 0.03% Cluster 313 T738: ◇(□((Y1∨Y2)∧□(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 314 T741: ◇(□((Y1∨Y2)∧¬(□Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 315 T760: ◇(◇((Y1∨Y2)∧◇Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 4 0.03% 1 0.03% Cluster 316 T785: ◇((¬Y1∧¬Y2)→Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ ◇(¬Y1∧¬Y2∧Y3) ( Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 317 T801: ◇(Y1∨Y2∨Y3∨Y4∨Y5) (Y_1 Y_2 Y_3 Y_4 Y_5 ) ↝ □(Y2∨Y3∨Y4) (Y_2 Y_3 Y_4 ) 4 0.03% 1 0.03% Cluster 318 T900: □(¬Y1)↔Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 319 T1009: Y1→□(¬Y2)Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 320 T1011: Y1→□(¬Y2)Y_1→ ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 321 T1017: Y1→□(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 322 T1065: Y1→¬(□Y2)Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 4 0.03% 1 0.03% Cluster 323 T1111: (Y1∧Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 324 T1125: (□(¬Y1)∧□(¬Y2))→Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 4 0.03% 1 0.03% Cluster 325 T1164: □Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 4 0.03% 1 0.03% Cluster 326 T1179: □Y1→□(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 4 0.03% 1 0.03% Cluster 327 T1202: □Y1→◇(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 4 0.03% 1 0.03% Cluster 328 T1239: □(Y1∧Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 329 T1274: □(◇Y1)→¬(□Y2) ( Y_1 )→ ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 4 0.03% 1 0.03% Cluster 330 T1294: □(¬(Y1∨Y2))→◇Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 4 0.03% 1 0.03% Cluster 331 T1297: □(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 4 0.03% 1 0.03% Cluster 332 T1351: ◇Y1→¬(◇Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 4 0.03% 1 0.03% Cluster 333 T1362: ◇(Y1∧Y2)→◇(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 334 T1396: (Y1↔Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 335 T1400: (Y1↔¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→¬(Y1↔Y2)Y_3→ (Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 336 T1467: (Y1∨Y2)→□(◇Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 4 0.03% 1 0.03% Cluster 337 T1477: (Y1∨□Y1)→□Y2 (Y_1 Y_1 )→ Y_2 ↝ □Y2→(Y1∨◇Y1) Y_2→ (Y_1 Y_1 ) 4 0.03% 1 0.03% Cluster 338 T1627: Y1∨¬Y2Y_1 Y_2 ↝ ¬(Y2↔Y1) (Y_2 Y_1 ) 4 0.03% 1 0.03% Cluster 339 T1711: □Y1∨□Y2∨□Y3 Y_1 Y_2 Y_3 ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 4 0.03% 1 0.03% Cluster 340 T1721: □(◇Y1)∨□(◇(◇Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 4 0.03% 1 0.03% Cluster 341 T1298: □(Y1∨Y2)→□Y1 (Y_1 Y_2 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 3 0.08% Cluster 342 T1691: (Y2∧□Y1)∨□Y1 (Y_2 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 3 0.08% Cluster 343 T64: Y1∧◇Y2∧◇(◇Y2)Y_1 Y_2 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 2 0.05% T85: Y1∧◇(¬Y1)∧◇(◇(¬Y1))Y_1 ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 344 T590: □(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→◇Y2Y_1→ Y_2 3 0.02% 2 0.05% T603: □(Y1→¬Y1) (Y_1→ Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 345 T591: □(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 2 0.05% Cluster 346 T707: ◇(Y1∧¬Y2) (Y_1 Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 3 0.02% 2 0.05% Cluster 347 T1054: Y1→(Y2→◇Y2)Y_1→ (Y_2→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 2 0.05% T1423: ¬Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ ◇(¬Y1)∨◇(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) 2 0.02% 1 0.03% Cluster 348 T1055: Y1→¬Y2Y_1→ Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 3 0.02% 2 0.05% T565: □(◇((Y1∨Y2)→¬Y3)) ( ( (Y_1 Y_2 )→ Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 349 T1245: □(Y1∧¬Y2∧¬Y3)→Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ □(¬(Y2∨Y3)→Y4) ( (Y_2 Y_3 )→ Y_4 ) 3 0.02% 2 0.05% Cluster 350 T1480: (Y1∨◇Y1)→Y2 (Y_1 Y_1 )→ Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 3 0.02% 2 0.05% Cluster 351 T1482: (Y1∨◇Y2)→Y2 (Y_1 Y_2 )→ Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 3 0.02% 2 0.05% Cluster 352 T1483: (Y1∨◇Y2)→□Y2 (Y_1 Y_2 )→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 3 0.02% 2 0.05% T1481: (Y1∨◇Y1)→□Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 353 T1501: (◇Y1∨◇Y2)→□Y1 ( Y_1 Y_2 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 2 0.05% T1504: (◇Y1∨◇(◇Y1))→□Y1 ( Y_1 ( Y_1 ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 354 T1681: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1∨Y2Y_1 Y_2 3 0.02% 2 0.05% Cluster 355 T1789: (Y1→◇(◇Y2))∨(Y1→□Y2) (Y_1→ ( Y_2 ) ) (Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 2 0.05% Cluster 356 T26: Y1∧□Y1Y_1 Y_1 ↝ □Y1 Y_1 3 0.02% 1 0.03% Cluster 357 T97: Y1∧◇(Y2∨Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 3 0.02% 1 0.03% Cluster 358 T101: Y1∧◇(Y2∨◇Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 3 0.02% 1 0.03% Cluster 359 T117: Y1∧¬(□Y2)∧□(◇Y3)Y_1 ( Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y3)∧¬(◇Y2))) ( ( (Y_1 Y_3 ) ( Y_2 ) ) ) 3 0.02% 1 0.03% Cluster 360 T157: ¬Y1∧¬Y2∧Y3 Y_1 Y_2 Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 361 T165: □Y1∧□Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 362 T182: □(Y1∧Y2)∧□Y1 (Y_1 Y_2 ) Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 363 T194: □(¬(◇Y1))∧□(□(Y2∨Y3)) ( ( Y_1 ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 364 T227: ◇(Y1∧Y2)∧□Y1 (Y_1 Y_2 ) Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 365 T246: ◇(□(¬Y1))∧□Y1 ( ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 366 T264: ◇(¬Y1)∧□(◇Y2∨◇Y3) ( Y_1 ) ( Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 367 T347: ¬(□(□Y1))∧□(◇Y2) ( ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 368 T355: ¬(◇Y1)∧□(□Y2) ( Y_1 ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 369 T357: ¬(◇Y1)∧□(◇Y2∨◇Y3) ( Y_1 ) ( Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 370 T370: ¬(Y1∨Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 371 T436: (◇(◇Y1)∨◇(◇Y2))∧¬(□Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 3 0.02% 1 0.03% Cluster 372 T453: □(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 373 T456: □(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 3 0.02% 1 0.03% Cluster 374 T462: □(Y1∧□(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% Cluster 375 T478: □(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 3 0.02% 1 0.03% Cluster 376 T522: □((◇Y1∨◇Y2)∧◇(¬Y3)) ( ( Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 3 0.02% 1 0.03% Cluster 377 T549: □(◇(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 378 T560: □(◇(◇Y1)) ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 379 T619: □((¬Y1∨¬Y2)→◇Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 380 T622: □(¬Y1) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 381 T672: □(¬Y1∨◇(¬Y1)) ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 382 T686: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ Y2∧◇Y1Y_2 Y_1 3 0.02% 1 0.03% Cluster 383 T752: ◇(◇Y1) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 384 T766: ◇(◇(¬Y1)) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 385 T778: ◇(Y1→¬Y1) (Y_1→ Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% Cluster 386 T782: ◇(Y1→(Y2∨◇Y1)) (Y_1→ (Y_2 Y_1 ) ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 3 0.02% 1 0.03% Cluster 387 ⌈ == T819: Y1↔Y2Y_1 Y_2 ↝ Y1→¬Y2Y_1→ Y_2 3 0.02% 1 0.03% ⌊ == T889: □Y1↔(Y2↔Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 3 0.02% 1 0.03% Cluster 388 T826: Y1↔(¬Y2∧¬Y3)Y_1 ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 3 0.02% 1 0.03% Cluster 389 T827: Y1↔□Y1Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 390 T831: Y1↔□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 391 T874: □Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 3 0.02% 1 0.03% Cluster 392 T882: □Y1↔□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 393 T886: □Y1↔◇(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 394 T909: □(¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 395 T913: ◇Y1↔(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 3 0.02% 1 0.03% Cluster 396 T940: ¬(Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 397 T966: Y1→Y2Y_1→ Y_2 ↝ ¬Y2→Y1 Y_2→ Y_1 3 0.02% 1 0.03% Cluster 398 T977: Y1→(◇Y1∧◇Y2)Y_1→ ( Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 399 T994: Y1→□Y2Y_1→ Y_2 ↝ Y2→Y1Y_2→ Y_1 3 0.02% 1 0.03% Cluster 400 T1005: Y1→□(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 3 0.02% 1 0.03% Cluster 401 T1007: Y1→□(¬Y1)Y_1→ ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 3 0.02% 1 0.03% Cluster 402 T1048: Y1→(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 3 0.02% 1 0.03% Cluster 403 T1075: Y1→¬(Y2∨Y3)Y_1→ (Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 3 0.02% 1 0.03% Cluster 404 T1099: Y1→((Y1→◇Y2)∨◇Y2)Y_1→ ( (Y_1→ Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 1 0.03% Cluster 405 T1108: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 406 T1115: (Y1∧Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 407 T1124: (□Y1∧□Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 408 T1126: (□(¬Y1)∧□(¬Y2))→□Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 409 T1140: (¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 410 T1187: □Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 411 T1222: □Y1→¬(◇Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 412 T1255: □(¬Y1∧¬Y2)→¬Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 413 T1259: □(□Y1)→□(¬Y2) ( Y_1 )→ ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 3 0.02% 1 0.03% Cluster 414 T1268: □(◇Y1)→□Y1 ( Y_1 )→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 3 0.02% 1 0.03% Cluster 415 T1286: □(¬Y1)→□Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 3 0.02% 1 0.03% Cluster 416 T1347: ◇Y1→¬Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 417 T1383: ◇(¬(Y1∨Y2))→□Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 418 T1384: ◇(¬(Y1∨Y2))→◇Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 419 T1386: ◇(Y1∨Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 420 T1394: ◇(¬Y1∨¬Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 421 T1411: ¬Y1→Y2 Y_1→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 3 0.02% 1 0.03% Cluster 422 T1436: ¬(□Y1)→◇Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 3 0.02% 1 0.03% Cluster 423 T1441: ¬(□(Y1∨Y2))→□Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 424 T1456: ¬(Y1∨Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 3 0.02% 1 0.03% Cluster 425 T1508: (◇(◇Y1)∨◇(◇Y2))→¬(□Y3) ( ( Y_1 ) ( Y_2 ) )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 3 0.02% 1 0.03% Cluster 426 T1512: (¬Y1∨◇(¬Y1))→□Y1 ( Y_1 ( Y_1 ) )→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 427 T1542: ¬(□(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 3 0.02% 1 0.03% Cluster 428 T1543: ¬(□(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 3 0.02% 1 0.03% Cluster 429 T1545: ¬(□(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 3 0.02% 1 0.03% Cluster 430 T1594: Y1∨□(◇Y1)Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 3 0.02% 1 0.03% Cluster 431 T1611: Y1∨◇Y2Y_1 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 432 T1614: Y1∨◇(Y2∧◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 1 0.03% Cluster 433 T1712: □Y1∨□Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 434 T1748: ◇(□Y1)∨□Y1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 435 T1776: (Y1→Y2)∨(Y3→Y2) (Y_1→ Y_2 ) (Y_3→ Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 3 0.02% 1 0.03% Cluster 436 T1795: (□Y1→((Y1∨Y2)→Y2))∨(□Y1→Y2) ( Y_1→ ( (Y_1 Y_2 )→ Y_2 ) ) ( Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 3 0.02% 1 0.03% Cluster 437 T1812: ¬Y1∨□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 3 0.02% 1 0.03% Cluster 438 T1822: ¬(◇Y1)∨□Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% Cluster 439 T1824: ¬(◇Y1)∨◇Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 3 0.02% 1 0.03% Cluster 440 T1829: Y1∨Y2∨□Y3Y_1 Y_2 Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 3 0.02% 1 0.03% Cluster 441 T12: Y1∧Y2∧◇Y2Y_1 Y_2 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% T106: Y1∧¬Y1∧◇(¬Y1)Y_1 Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 442 T54: Y1∧□(Y1∨Y2)Y_1 (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 2 0.05% T55: Y1∧□(Y1∨□Y1)Y_1 (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 443 T63: Y1∧◇Y2∧□Y2Y_1 Y_2 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 444 T70: Y1∧◇Y2Y_1 Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 2 0.02% 2 0.05% T320: ¬Y1∧◇Y1 Y_1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 445 T136: Y1∧Y2∧□Y2Y_1 Y_2 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 2 0.05% Cluster 446 T291: (Y1→Y2)∧Y3 (Y_1→ Y_2 ) Y_3 ↝ Y3∧◇Y2Y_3 Y_2 2 0.02% 2 0.05% T303: (◇Y1→Y2)∧Y3 ( Y_1→ Y_2 ) Y_3 ↝ Y3∧◇Y2Y_3 Y_2 1 0.01% 1 0.03% Cluster 447 T305: (¬Y1→Y2)∧□(◇Y3) ( Y_1→ Y_2 ) ( Y_3 ) ↝ □(◇(Y3∧¬(◇Y2))) ( (Y_3 ( Y_2 ) ) ) 2 0.02% 2 0.05% Cluster 448 T422: (◇Y1∨□Y2)∧Y2 ( Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 2 0.05% Cluster 449 T431: (◇Y1∨◇(¬Y2))∧Y2 ( Y_1 ( Y_2 ) ) Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 2 0.02% 2 0.05% Cluster 450 T461: □(Y1∧Y2) (Y_1 Y_2 ) ↝ Y2→Y1Y_2→ Y_1 2 0.02% 2 0.05% Cluster 451 T653: □(Y1∨¬Y2) (Y_1 Y_2 ) ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 2 0.02% 2 0.05% Cluster 452 T691: ◇(Y1∧□Y2) (Y_1 Y_2 ) ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 2 0.02% 2 0.05% Cluster 453 T834: Y1↔□(Y2∨◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 454 T835: Y1↔□(Y2∨◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 2 0.05% Cluster 455 T1015: Y1→□(Y2∨Y1)Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 2 0.05% Cluster 456 T1098: Y1→((Y1→Y2)∨Y2)Y_1→ ( (Y_1→ Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 457 T1190: □Y1→□(Y2∨◇Y2) Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 458 T1233: □Y1→(◇Y2∨□Y2) Y_1→ ( Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 459 T1280: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 2 0.02% 2 0.05% Cluster 460 T1307: □(◇Y1∨◇(◇Y1))→□Y2 ( Y_1 ( Y_1 ) )→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 2 0.02% 2 0.05% Cluster 461 T1357: ◇Y1→(◇Y2∨◇(◇Y1)) Y_1→ ( Y_2 ( Y_1 ) ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 2 0.05% Cluster 462 T1402: ((¬Y1∧¬Y2)↔Y3)→Y4 ( ( Y_1 Y_2 ) Y_3 )→ Y_4 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 2 0.05% T1403: ((¬Y1∧¬Y2)↔Y3)→◇Y4 ( ( Y_1 Y_2 ) Y_3 )→ Y_4 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 463 T1412: ¬Y1→Y2 Y_1→ Y_2 ↝ □Y2→Y2 Y_2→ Y_2 2 0.02% 2 0.05% T1530: ¬(□Y1) ( Y_1 ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 464 T1686: (Y1∧¬(□Y2))∨Y2 (Y_1 ( Y_2 ) ) Y_2 ↝ Y2∨□(¬Y2)Y_2 ( Y_2 ) 2 0.02% 2 0.05% Cluster 465 T1695: (◇Y1∧□Y2)∨Y2 ( Y_1 Y_2 ) Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 2 0.02% 2 0.05% T1694: (◇Y1∧□Y1)∨Y1 ( Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 466 T1714: □Y1∨□Y2 Y_1 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 2 0.05% Cluster 467 T1770: (Y1→Y2)∨□(◇Y1) (Y_1→ Y_2 ) ( Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 2 0.05% Cluster 468 T1780: (Y1→□Y2)∨(Y1→□(◇Y2)) (Y_1→ Y_2 ) (Y_1→ ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 469 T1785: (Y1→◇Y2)∨(Y1→□Y2) (Y_1→ Y_2 ) (Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 2 0.05% Cluster 470 T1806: ((Y1∨Y2)→□Y3)∨□Y3 ( (Y_1 Y_2 )→ Y_3 ) Y_3 ↝ □Y3∧□(□Y3) Y_3 ( Y_3 ) 2 0.02% 2 0.05% Cluster 471 T28: Y1∧□Y1Y_1 Y_1 ↝ Y1∨◇Y1Y_1 Y_1 2 0.02% 1 0.03% Cluster 472 T29: Y1∧□Y2Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 473 T36: Y1∧□Y2Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 474 T56: Y1∧□(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 2 0.02% 1 0.03% Cluster 475 T60: Y1∧◇Y1Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 476 T99: Y1∧◇(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→(Y2∨Y3)Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 477 T112: Y1∧¬Y2Y_1 Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 478 T135: Y1∧Y2∧□Y1Y_1 Y_2 Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 479 T154: ◇Y1∧◇Y2∧Y1 Y_1 Y_2 Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 480 T156: ¬Y1∧◇Y1∧Y1 Y_1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 481 T170: □Y1∧□(□(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 482 T171: □Y1∧□(◇((Y1∨Y2)→¬Y1)) Y_1 ( ( (Y_1 Y_2 )→ Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 483 T181: □Y1∧□(¬(Y2∨Y3)) Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 484 T191: □(¬Y1)∧□(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 485 T199: □(¬Y1∨¬Y2)∧□Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 486 T200: ◇Y1∧Y2 Y_1 Y_2 ↝ ◇(Y1∧Y2) (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 487 T207: ◇Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 488 T209: ◇Y1∧□(¬(Y2∨Y3)) Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 489 T213: ◇Y1∧◇Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 490 T219: ◇Y1∧◇(◇Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 491 T220: ◇Y1∧◇(◇Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 492 T222: ◇Y1∧◇(◇(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 493 T232: ◇(Y1∧◇Y1)∧□Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 2 0.02% 1 0.03% Cluster 494 T250: ◇(◇Y1)∧□(¬(◇Y2)) ( Y_1 ) ( ( Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 495 T258: ◇(¬Y1)∧Y2 ( Y_1 ) Y_2 ↝ ◇(¬Y1) ( Y_1 ) 2 0.02% 1 0.03% Cluster 496 T261: ◇(¬Y1)∧□Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 497 T270: ◇(¬(□Y1))∧◇(◇(Y2∨Y3)) ( ( Y_1 ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 498 T274: ◇(Y1∨Y2∨Y3)∧◇(¬Y4) (Y_1 Y_2 Y_3 ) ( Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 2 0.02% 1 0.03% Cluster 499 T275: ◇(Y1∨Y2)∧◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 500 T277: ◇(Y1∨◇Y1)∧◇Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 2 0.02% 1 0.03% Cluster 501 T310: ¬Y1∧□Y2 Y_1 Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 502 T311: ¬Y1∧□Y2 Y_1 Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 503 T332: ¬Y1∧◇(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 504 T368: ¬(◇(◇(◇Y1)))∧◇(◇(Y2∨Y3)) ( ( ( Y_1 ) ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 505 T383: (Y1∨Y2)∧◇Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 506 T397: (Y1∨◇Y2)∧◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 507 T409: (□Y1∨□Y2)∧□(¬Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 508 T413: (□(Y1∧¬Y2)∨□(Y2∧¬Y1))∧¬(□Y3) ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 509 T429: (◇Y1∨◇Y2)∧¬(◇(◇Y3)) ( Y_1 Y_2 ) ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 510 T434: (◇(◇Y1)∨◇(◇Y2))∧□Y3 ( ( Y_1 ) ( Y_2 ) ) Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 511 T435: (◇(◇Y1)∨◇(◇Y2))∧□(¬Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 512 T452: □(Y1∧Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 513 T455: □(Y1∧Y2∧¬Y3) (Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 514 T466: □(Y1∧◇Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 515 T468: □(Y1∧◇(◇Y1)) (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 516 T469: □(Y1∧◇(◇(¬Y1))) (Y_1 ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 517 T482: □(Y1∧¬(□Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 518 T487: □(□(Y1∨Y2)∧□(□(¬Y3))) ( (Y_1 Y_2 ) ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 519 T489: □(◇Y1∧◇Y2) ( Y_1 Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 520 T493: □(◇Y1∧◇(¬(□Y2))) ( Y_1 ( ( Y_2 ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 521 T501: □(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 522 T508: □(¬(□Y1)∧◇(Y2∧Y3)) ( ( Y_1 ) (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 523 T517: □((Y1∨□Y1)∧Y1) ( (Y_1 Y_1 ) Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 524 T523: □((◇Y1∨◇Y2)∧¬Y3) ( ( Y_1 Y_2 ) Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 525 T525: □((¬Y1∨¬Y2)∧Y3) ( ( Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 526 T539: □(□((Y1∨Y2)∧¬Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 527 T550: □(◇(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 528 T568: □(◇(¬Y1)) ( ( Y_1 ) ) ↝ ¬(□Y1) ( Y_1 ) 2 0.02% 1 0.03% Cluster 529 T587: □(Y1→Y2) (Y_1→ Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 530 T608: □(Y1→(Y2∨◇Y1)) (Y_1→ (Y_2 Y_1 ) ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 531 T616: □(¬Y1→(¬Y2∧¬Y3)) ( Y_1→ ( Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 532 T618: □((¬Y1∨¬Y2)→□Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 533 T634: □(Y1∨Y2) (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 534 T671: □(¬Y1∨□(¬Y1)) ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 535 T678: ◇Y1 Y_1 ↝ □(¬Y1) ( Y_1 ) 2 0.02% 1 0.03% Cluster 536 T685: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 2 0.02% 1 0.03% Cluster 537 T699: ◇(Y1∧◇(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 538 T719: ◇(¬Y1∧◇Y1) ( Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 539 T720: ◇(¬(□Y1)∧◇Y2) ( ( Y_1 ) Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 540 T732: ◇(□(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 541 T733: ◇(□(Y1∧¬Y1)) ( (Y_1 Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 542 T734: ◇(□(Y1∧¬Y2∧¬Y3)) ( (Y_1 Y_2 Y_3 ) ) ↝ ◇(¬Y2∧¬Y3∧□Y1) ( Y_2 Y_3 Y_1 ) 2 0.02% 1 0.03% Cluster 543 T739: ◇(□((Y1∨Y2)∧◇(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 544 T755: ◇(◇Y1) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 545 T757: ◇(◇(Y1∧◇(¬Y1))) ( (Y_1 ( Y_1 ) ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 546 T761: ◇(◇((Y1∨Y2)∧¬Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 547 T784: ◇((¬Y1∧¬Y2)→Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 548 T796: ◇(¬((Y1∨Y2∨Y3)∧Y4)) ( ( (Y_1 Y_2 Y_3 ) Y_4 ) ) ↝ ◇(¬Y4) ( Y_4 ) 2 0.02% 1 0.03% Cluster 549 T797: ◇(¬((Y1∨Y2)∧□Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 550 T798: ◇(¬(□Y1)) ( ( Y_1 ) ) ↝ □(¬Y1) ( Y_1 ) 2 0.02% 1 0.03% Cluster 551 T808: ◇(Y1∨◇(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 552 T811: ◇(Y1∨¬(◇Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 553 T832: Y1↔□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 554 T836: Y1↔□(¬Y1∨□(¬Y1))Y_1 ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 555 T843: Y1↔◇(Y2∨Y3)Y_1 (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 2 0.02% 1 0.03% Cluster 556 T851: Y1↔¬Y2Y_1 Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 557 T863: Y1↔(¬Y1∨□(¬Y1))Y_1 ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 558 T864: Y1↔(¬Y1∨◇(¬Y1))Y_1 ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 559 T871: □Y1↔Y1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 560 T887: □Y1↔◇(¬Y1) Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 561 T888: □Y1↔◇(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 562 T893: □Y1↔¬(◇Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 563 T905: □(¬(Y1∨Y2))↔Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 564 T910: □(¬Y1∨¬Y2)↔□Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 565 T923: ◇(¬Y1∧¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 566 T942: (Y1∨Y2)↔Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 567 T948: (¬Y1∨¬Y2)↔Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 568 ⌈ == T955: Y1→Y2Y_1→ Y_2 ↝ □(¬Y1→Y2) ( Y_1→ Y_2 ) 2 0.02% 1 0.03% ⌊ == T1461: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 569 T964: Y1→Y2Y_1→ Y_2 ↝ □Y1→¬Y2 Y_1→ Y_2 2 0.02% 1 0.03% Cluster 570 ⌈ == T967: Y1→Y2Y_1→ Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 0.02% 1 0.03% ⌊ == T1207: □Y1→(Y2→Y3) Y_1→ (Y_2→ Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 571 T970: Y1→(Y1∧□Y1)Y_1→ (Y_1 Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 2 0.02% 1 0.03% Cluster 572 T983: Y1→(¬Y2∧¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ ¬(Y2∨Y3)→Y1 (Y_2 Y_3 )→ Y_1 2 0.02% 1 0.03% Cluster 573 T992: Y1→□Y2Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 574 T1006: Y1→□(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 2 0.02% 1 0.03% Cluster 575 T1021: Y1→□(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 576 T1044: Y1→◇(Y2∨◇Y1)Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 577 T1045: Y1→◇(Y2∨¬Y2)Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 578 T1052: Y1→(◇Y2↔¬(◇Y3))Y_1→ ( Y_2 ( Y_3 ) ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 579 T1059: Y1→¬Y2Y_1→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 580 T1061: Y1→¬(◇Y2∧◇Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 2 0.02% 1 0.03% Cluster 581 T1066: Y1→¬(□Y2)Y_1→ ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 582 T1068: Y1→¬(□(Y2∨Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 583 T1087: Y1→((Y2∧◇Y1)∨Y2)Y_1→ ( (Y_2 Y_1 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 584 T1102: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 585 T1109: (Y1∧Y2)→□Y2 (Y_1 Y_2 )→ Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 586 T1110: (Y1∧Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 587 T1116: (Y1∧Y2)→◇(◇Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 588 T1134: (◇(¬Y1)∧◇(¬Y2))→◇Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 589 T1181: □Y1→□(◇Y1) Y_1→ ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 590 T1183: □Y1→□(Y2↔Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 591 T1214: □Y1→¬Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 592 T1234: □Y1→(◇Y2∨◇Y3) Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 593 T1236: □Y1→(((Y1∨Y2)→◇Y2)∨◇Y2) Y_1→ ( ( (Y_1 Y_2 )→ Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 594 T1238: □Y1→(¬Y2∨¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 595 T1250: □(¬Y1∧¬Y2)→□(□Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 596 T1254: □(¬Y1∧¬Y2)→◇Y3 ( Y_1 Y_2 )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 597 T1257: □(□Y1)→□Y1 ( Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 598 T1266: □(◇Y1)→Y2 ( Y_1 )→ Y_2 ↝ □Y1→¬Y2 Y_1→ Y_2 2 0.02% 1 0.03% Cluster 599 T1267: □(◇Y1)→(¬(◇Y2)∧◇(Y3∨Y4)) ( Y_1 )→ ( ( Y_2 ) (Y_3 Y_4 ) ) ↝ □(◇((Y3∨Y4)∧¬(◇Y2))) ( ( (Y_3 Y_4 ) ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 600 T1271: □(◇Y1)→◇(¬Y2) ( Y_1 )→ ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 601 T1272: □(◇Y1)→(Y2↔¬Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 602 T1300: □(Y1∨Y2)→¬(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 603 T1309: □(¬Y1∨¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 604 T1311: □(¬Y1∨¬Y2)→◇Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 605 T1312: ◇Y1→Y1 Y_1→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 606 T1314: ◇Y1→Y2 Y_1→ Y_2 ↝ ◇Y1 Y_1 2 0.02% 1 0.03% Cluster 607 T1320: ◇Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 608 T1324: ◇Y1→□Y1 Y_1→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 609 T1328: ◇Y1→□(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 2 0.02% 1 0.03% Cluster 610 T1339: ◇Y1→◇(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 611 T1348: ◇Y1→¬Y2 Y_1→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 612 T1361: ◇(Y1∧Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 613 T1372: ◇(□Y1)→(Y2∨Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 614 T1387: ◇(Y1∨Y2)→□(□(¬Y3)) (Y_1 Y_2 )→ ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 615 T1392: ◇(Y1∨◇Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 616 T1410: ¬Y1→Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 617 T1418: ¬Y1→□Y2 Y_1→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 618 T1433: ¬(□Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 619 T1434: ¬(□Y1)→□Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 620 T1440: ¬(□(Y1∨Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 2 0.02% 1 0.03% Cluster 621 T1446: ¬(◇Y1)→◇Y2 ( Y_1 )→ Y_2 ↝ □(¬Y1→Y2) ( Y_1→ Y_2 ) 2 0.02% 1 0.03% Cluster 622 T1455: ¬(Y1∨Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 623 T1469: (Y1∨Y2)→◇(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 624 T1489: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 2 0.02% 1 0.03% Cluster 625 T1495: (□Y1∨□(◇Y1))→□Y2 ( Y_1 ( Y_1 ) )→ Y_2 ↝ □Y2∧□(□Y2) Y_2 ( Y_2 ) 2 0.02% 1 0.03% Cluster 626 T1502: (◇Y1∨◇Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 627 T1503: (◇Y1∨◇(◇Y1))→Y1 ( Y_1 ( Y_1 ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 628 T1506: (◇(□Y1)∨◇(□Y2))→◇(□(□(¬Y3))) ( ( Y_1 ) ( Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 2 0.02% 1 0.03% Cluster 629 T1523: ¬(Y1∧□Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 630 T1527: ¬(Y1∧◇Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 631 T1528: ¬(Y1∧◇Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 632 T1544: ¬(□(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 633 T1546: ¬(□(Y1→¬Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 634 T1547: ¬(□(Y1→¬Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 635 T1558: ¬(◇(◇Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 2 0.02% 1 0.03% Cluster 636 T1559: ¬(◇(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 637 T1560: ¬(◇(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 2 0.02% 1 0.03% Cluster 638 T1578: Y1∨Y2∨□Y3Y_1 Y_2 Y_3 ↝ □(Y1∨Y3∨Y2) (Y_1 Y_3 Y_2 ) 2 0.02% 1 0.03% Cluster 639 T1599: Y1∨□(Y1∨Y2)Y_1 (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 640 T1607: Y1∨◇Y2Y_1 Y_2 ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 2 0.02% 1 0.03% Cluster 641 T1618: Y1∨◇(◇Y1)Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 642 T1641: (Y1∧Y2)∨(Y1∧◇(◇Y2)) (Y_1 Y_2 ) (Y_1 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 643 T1657: (Y1∧□Y2)∨(Y3∧□Y2)∨(¬Y1∧¬Y3) (Y_1 Y_2 ) (Y_3 Y_2 ) ( Y_1 Y_3 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 2 0.02% 1 0.03% Cluster 644 T1658: (Y1∧□Y2)∨(Y3∧□Y2) (Y_1 Y_2 ) (Y_3 Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 2 0.02% 1 0.03% Cluster 645 T1678: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 646 T1684: (Y1∧¬Y2)∨Y2∨¬Y1 (Y_1 Y_2 ) Y_2 Y_1 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 647 T1693: (□(◇Y1)∧□(◇Y2))∨(□(◇Y3)∧□(◇Y2)) ( ( Y_1 ) ( Y_2 ) ) ( ( Y_3 ) ( Y_2 ) ) ↝ □(◇((Y1∨Y3)∧¬(◇Y2))) ( ( (Y_1 Y_3 ) ( Y_2 ) ) ) 2 0.02% 1 0.03% Cluster 648 T1696: (◇Y1∧□Y2)∨(◇(◇Y1)∧□Y2) ( Y_1 Y_2 ) ( ( Y_1 ) Y_2 ) ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 2 0.02% 1 0.03% Cluster 649 T1724: □(¬Y1)∨□(□(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 650 T1725: □(Y1∨Y2)∨□(Y3∧Y4) (Y_1 Y_2 ) (Y_3 Y_4 ) ↝ □(¬(Y1∨Y2)→Y4) ( (Y_1 Y_2 )→ Y_4 ) 2 0.02% 1 0.03% Cluster 651 T1738: ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 652 T1752: ◇(◇(□Y1))∨□Y1 ( ( Y_1 ) ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 653 T1759: ◇(¬Y1)∨◇(□(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 654 T1762: ◇(Y1∨Y2)∨□Y1 (Y_1 Y_2 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 655 T1765: (Y1↔Y2)∨◇Y1 (Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 656 T1768: (Y1→Y2)∨Y1 (Y_1→ Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 2 0.02% 1 0.03% Cluster 657 T1773: (Y1→Y2)∨(Y1→Y2) (Y_1→ Y_2 ) (Y_1→ Y_2 ) ↝ Y1→(Y2∨◇Y2)Y_1→ (Y_2 Y_2 ) 2 0.02% 1 0.03% Cluster 658 T1790: (Y1→◇((Y1∨Y2)→◇Y2))∨(Y1→◇Y2) (Y_1→ ( (Y_1 Y_2 )→ Y_2 ) ) (Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 2 0.02% 1 0.03% Cluster 659 T1792: (Y1→¬Y1)∨(Y1→◇(¬Y1)) (Y_1→ Y_1 ) (Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 2 0.02% 1 0.03% Cluster 660 T1793: (□Y1→Y1)∨(□(□Y1)→Y1) ( Y_1→ Y_1 ) ( ( Y_1 )→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 2 0.02% 1 0.03% Cluster 661 T1794: (□Y1→Y2)∨(□Y1→Y3) ( Y_1→ Y_2 ) ( Y_1→ Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 2 0.02% 1 0.03% Cluster 662 T1813: ¬Y1∨◇Y2 Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 2 0.02% 1 0.03% Cluster 663 T1826: ¬(Y1∨Y2)∨□Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 664 T1827: ¬(Y1∨Y2)∨◇Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 2 0.02% 1 0.03% Cluster 665 T6: Y1Y_1 ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 666 T7: Y1Y_1 ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 667 T9: Y1∧Y1∧¬(□Y1)Y_1 Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 668 T10: Y1∧Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 669 T13: Y1∧Y2∧◇Y2Y_1 Y_2 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 670 T14: Y1∧Y2Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 671 T19: Y1∧Y2Y_1 Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 672 T33: Y1∧□Y2Y_1 Y_2 ↝ □(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 673 T38: Y1∧□(Y2∧Y1)Y_1 (Y_2 Y_1 ) ↝ Y2∧□(Y2∧Y1)Y_2 (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 674 T39: Y1∧□(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 675 T44: Y1∧□(◇(Y1∨Y2))Y_1 ( (Y_1 Y_2 ) ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 676 T46: Y1∧□(¬Y1)∧□(□(¬Y1))Y_1 ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 677 T49: Y1∧□(¬Y2)Y_1 ( Y_2 ) ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 1 0.01% 1 0.03% Cluster 678 T52: Y1∧□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 679 T59: Y1∧◇Y1∧◇Y2Y_1 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 680 T80: Y1∧◇(□(Y1∨Y2))Y_1 ( (Y_1 Y_2 ) ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 681 T81: Y1∧◇(◇Y1)Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 682 T83: Y1∧◇(◇Y2)Y_1 ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 683 T88: Y1∧◇(¬Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 684 T89: Y1∧◇(¬Y2)∧□(¬Y2)Y_1 ( Y_2 ) ( Y_2 ) ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 1 0.01% 1 0.03% Cluster 685 T95: Y1∧◇(¬(Y2∨Y3))Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 686 T103: Y1∧◇((Y2→◇Y2)∨Y2)Y_1 ( (Y_2→ Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 687 T105: Y1∧◇(¬Y2∨¬Y3)Y_1 ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 688 T116: Y1∧¬(□Y2)∧□Y3Y_1 ( Y_2 ) Y_3 ↝ □(◇((Y1∨Y3)∧¬(◇Y2))) ( ( (Y_1 Y_3 ) ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 689 T118: Y1∧¬(□Y2)Y_1 ( Y_2 ) ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 1 0.01% 1 0.03% Cluster 690 T121: Y1∧¬(◇Y1)∧◇Y1Y_1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 691 T122: Y1∧¬(◇Y1)∧◇(□(¬Y1))Y_1 ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 692 T125: Y1∧¬(◇Y1)Y_1 ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 693 T127: Y1∧¬(◇Y2)Y_1 ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 694 T130: Y1∧¬(◇(Y2∧Y3))Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 695 T137: Y1∧Y2∧□Y3Y_1 Y_2 Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 696 T138: Y1∧Y2∧□(¬Y3)Y_1 Y_2 ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 697 T139: Y1∧Y2∧◇Y2Y_1 Y_2 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 698 T140: Y1∧Y2∧◇(Y2∧¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ (Y1∧Y2)→◇(Y1∨Y2) (Y_1 Y_2 )→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 699 T141: Y1∧Y2∧◇(¬Y1)Y_1 Y_2 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 700 T143: Y1∧Y2∧¬(□Y3)Y_1 Y_2 ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 701 T144: Y1∧□Y2∧Y1Y_1 Y_2 Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 702 T145: Y1∧□(□Y2)∧¬(□Y3)Y_1 ( Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 703 T146: Y1∧◇Y1∧Y2Y_1 Y_1 Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 704 T147: Y1∧◇Y2∧¬(◇Y3)Y_1 Y_2 ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 705 T149: Y1∧¬Y2∧◇(Y2∨¬Y1)Y_1 Y_2 (Y_2 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 706 T150: Y1∧¬(◇Y1)∧Y1Y_1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 707 T151: □Y1∧□Y2∧□Y1 Y_1 Y_2 Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 708 T152: □(¬Y1)∧□(¬Y2)∧◇Y3 ( Y_1 ) ( Y_2 ) Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 709 T153: ◇Y1∧□Y1∧¬Y1 Y_1 Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 710 T155: ◇Y1∧◇(□Y2)∧Y1 Y_1 ( Y_2 ) Y_1 ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 711 T160: □Y1∧□Y2∧□Y3 Y_1 Y_2 Y_3 ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 712 T162: □Y1∧□Y2 Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 713 T163: □Y1∧□Y2 Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 714 T164: □Y1∧□Y2 Y_1 Y_2 ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 715 T166: □Y1∧□(□Y1) Y_1 ( Y_1 ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 716 T167: □Y1∧□(□Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 717 T168: □Y1∧□(□(□(¬Y1))) Y_1 ( ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 718 T169: □Y1∧□(□(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 719 T173: □Y1∧□(◇(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 720 T176: □Y1∧□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 721 T178: □Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬Y1→Y2) ( Y_1→ Y_2 ) 1 0.01% 1 0.03% Cluster 722 T180: □Y1∧□(¬(◇Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 723 T183: □(□(Y1∨Y2))∧□(□(◇Y3)) ( (Y_1 Y_2 ) ) ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 724 ⌈ == T184: □(◇Y1)∧□(◇Y2) ( Y_1 ) ( Y_2 ) ↝ □(◇(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% ⌊ == T188: □(◇(Y1∨Y2))∧□(◇(¬(◇Y3))) ( (Y_1 Y_2 ) ) ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 725 T185: □(◇(Y1∨Y2))∧□(□(□Y3)) ( (Y_1 Y_2 ) ) ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 726 T186: □(◇(Y1∨Y2))∧□(□(□(¬Y3))) ( (Y_1 Y_2 ) ) ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 727 T190: □(¬Y1)∧□(□(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 728 T192: □(¬Y1)∧□(¬Y2) ( Y_1 ) ( Y_2 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 729 T193: □(¬(□Y1))∧□(□(Y2∨Y3)) ( ( Y_1 ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 730 T195: □(¬(◇Y1))∧□(◇(Y2∨Y3)) ( ( Y_1 ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 731 T196: □(¬(◇(□(¬Y1))))∧□(◇Y2) ( ( ( ( Y_1 ) ) ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 732 T197: □(Y1∨Y2)∧□(¬Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 733 T198: □(◇Y1∨◇Y2)∧□(¬Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 734 T202: ◇Y1∧□Y1 Y_1 Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 735 T208: ◇Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 736 T210: ◇Y1∧□(Y2∨Y1) Y_1 (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 737 T212: ◇Y1∧◇Y2∧◇Y3 Y_1 Y_2 Y_3 ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 738 ⌈ == T215: ◇Y1∧◇Y2 Y_1 Y_2 ↝ ◇(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% ⌊ == T218: ◇Y1∧◇(□Y2) Y_1 ( Y_2 ) ↝ ◇(Y1∧□Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 739 T216: ◇Y1∧◇Y2 Y_1 Y_2 ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 740 T217: ◇Y1∧◇(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 741 T221: ◇Y1∧◇(◇(¬Y1))∧□Y1 Y_1 ( ( Y_1 ) ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 742 T224: ◇Y1∧◇(¬Y2) Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 743 T225: ◇Y1∧◇(¬(◇Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 744 T226: ◇Y1∧◇(¬(Y2∨Y3)) Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 745 T229: ◇(Y1∧Y2)∧□(□Y3)∧□(□(¬Y3)) (Y_1 Y_2 ) ( Y_3 ) ( ( Y_3 ) ) ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 746 T233: ◇(Y1∧¬Y2∧¬Y3)∧◇(Y2∧¬Y1∧¬Y3)∧◇(Y3∧¬Y1∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_2 Y_1 Y_3 ) (Y_3 Y_1 Y_2 ) ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 747 T234: ◇(Y1∧¬Y2)∧◇(◇Y3)∧◇(□Y3) (Y_1 Y_2 ) ( Y_3 ) ( Y_3 ) ↝ ◇(¬Y2∧¬Y1∧□Y3) ( Y_2 Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 748 T235: ◇(Y1∧¬Y2)∧◇(◇Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ ◇(¬Y2∧¬Y1∧□Y3) ( Y_2 Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 749 T236: ◇(¬Y1∧¬Y2)∧□(□(¬Y3)) ( Y_1 Y_2 ) ( ( Y_3 ) ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 750 T237: ◇(¬Y1∧¬Y2)∧□(□(Y1∨Y2∨Y3)) ( Y_1 Y_2 ) ( (Y_1 Y_2 Y_3 ) ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 751 T238: ◇(¬Y1∧¬Y2)∧◇Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 752 T241: ◇(□Y1)∧□Y1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 753 T242: ◇(□Y1)∧□Y2 ( Y_1 ) Y_2 ↝ Y2∧◇Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 754 T243: ◇(□Y1)∧◇(□(¬Y2)) ( Y_1 ) ( ( Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 755 T247: ◇(□(¬Y1))∧□(¬Y1) ( ( Y_1 ) ) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 756 T251: ◇(◇Y1)∧◇(□(¬Y2)) ( Y_1 ) ( ( Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 757 T252: ◇(◇(□Y1))∧◇(□Y1) ( ( Y_1 ) ) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 758 T253: ◇(◇(□(¬Y1)))∧□(□(Y2∨Y3)) ( ( ( Y_1 ) ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 759 T255: ◇(◇(¬Y1))∧□(□Y1) ( ( Y_1 ) ) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 760 T256: ◇(◇(Y1∨Y2))∧◇(□Y3) ( (Y_1 Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 761 T257: ◇(◇(Y1∨Y2))∧◇(◇Y3) ( (Y_1 Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 762 T265: ◇(¬Y1)∧◇(◇Y1) ( Y_1 ) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 763 T266: ◇(¬(Y1∧Y2))∧□(□Y3) ( (Y_1 Y_2 ) ) ( Y_3 ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 764 T267: ◇(¬(Y1∧Y2))∧◇(□Y3) ( (Y_1 Y_2 ) ) ( Y_3 ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 765 T268: ◇(¬(□Y1))∧□(◇(Y2∨Y3)) ( ( Y_1 ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 766 T269: ◇(¬(□Y1))∧◇(□Y2) ( ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 767 T272: ◇(¬(◇Y1))∧◇(◇Y2) ( ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 768 T276: ◇(Y1∨□Y2)∧◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 769 T278: ◇(Y1∨◇Y2)∧◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 770 T279: (Y1↔Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 771 T280: (Y1↔Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y2∨Y1)→Y3) ( (Y_2 Y_1 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 772 T281: (Y1↔Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 773 T282: (Y1↔Y2)∧(Y3↔Y2) (Y_1 Y_2 ) (Y_3 Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 774 T283: (Y1↔Y2)∧¬(◇(Y3∨Y4)) (Y_1 Y_2 ) ( (Y_3 Y_4 ) ) ↝ □(¬(Y3∨Y4)→Y2) ( (Y_3 Y_4 )→ Y_2 ) 1 0.01% 1 0.03% Cluster 775 T284: (Y1↔(Y2∧¬Y3))∧□(Y1↔(Y2∧¬Y3)) (Y_1 (Y_2 Y_3 ) ) (Y_1 (Y_2 Y_3 ) ) ↝ □(¬Y1∨¬Y3) ( Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 776 T285: (Y1↔◇Y3)∧(Y2↔◇Y3) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 777 T286: (□Y1↔□Y2)∧Y1 ( Y_1 Y_2 ) Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 778 T287: (◇Y1↔◇Y2)∧(◇Y3↔◇Y2) ( Y_1 Y_2 ) ( Y_3 Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 779 T288: (¬Y1↔Y2)∧Y3 ( Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 780 T289: (¬Y1↔Y2)∧Y3 ( Y_1 Y_2 ) Y_3 ↝ ¬(Y2∨Y1)→Y3 (Y_2 Y_1 )→ Y_3 1 0.01% 1 0.03% Cluster 781 T290: (¬Y1↔◇Y1)∧□Y1 ( Y_1 Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 782 T292: (Y1→Y2)∧(Y1→Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 783 T293: (Y1→Y2)∧(Y1∨◇Y1) (Y_1→ Y_2 ) (Y_1 Y_1 ) ↝ □Y2→(Y1∨◇Y1) Y_2→ (Y_1 Y_1 ) 1 0.01% 1 0.03% Cluster 784 T294: (Y1→Y3)∧(Y2→Y3) (Y_1→ Y_3 ) (Y_2→ Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 785 T295: (Y1→□Y3)∧(Y2→□Y3) (Y_1→ Y_3 ) (Y_2→ Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 786 T296: (Y1→◇Y1)∧Y2 (Y_1→ Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 787 T297: (Y1→◇Y2)∧(Y1→◇Y3) (Y_1→ Y_2 ) (Y_1→ Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 788 T298: (Y1→◇Y2)∧(Y3→◇Y2) (Y_1→ Y_2 ) (Y_3→ Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 789 T299: (Y1→¬Y2)∧□(Y1→¬Y2) (Y_1→ Y_2 ) (Y_1→ Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 790 T300: (Y1→(Y2∨◇(◇Y2)))∧Y1 (Y_1→ (Y_2 ( Y_2 ) ) ) Y_1 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 791 T301: (□Y1→Y1)∧(□(□Y1)→Y1) ( Y_1→ Y_1 ) ( ( Y_1 )→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 792 T302: (□Y1→¬Y2)∧¬Y1 ( Y_1→ Y_2 ) Y_1 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 793 T304: (◇Y1→¬Y2)∧¬Y1 ( Y_1→ Y_2 ) Y_1 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 794 ⌈ == T306: (¬Y1→Y2)∧(¬Y2→Y1) ( Y_1→ Y_2 ) ( Y_2→ Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% ⌊ == T1163: □Y1→((¬Y2→Y3)∧(¬Y3→Y2)) Y_1→ ( ( Y_2→ Y_3 ) ( Y_3→ Y_2 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 795 ⌈ == T307: ¬Y1∧Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% ⌊ == T330: ¬Y1∧◇(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 796 T313: ¬Y1∧□(◇Y2) Y_1 ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 797 T315: ¬Y1∧□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 798 T317: ¬Y1∧□(Y1∨¬Y1) Y_1 (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 799 T318: ¬Y1∧◇Y1∧◇(¬Y1) Y_1 Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 800 T321: ¬Y1∧◇Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 801 T322: ¬Y1∧◇Y2 Y_1 Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 802 T323: ¬Y1∧◇Y2 Y_1 Y_2 ↝ Y2∧◇Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 803 T327: ¬Y1∧◇(◇Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 804 T328: ¬Y1∧◇(◇(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 805 T329: ¬Y1∧◇(¬Y1)∧□Y1 Y_1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 806 T337: ¬(□Y1)∧□(□(Y2∧Y3)) ( Y_1 ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 807 T338: ¬(□Y1)∧□(□(◇(Y2∧Y3))) ( Y_1 ) ( ( (Y_2 Y_3 ) ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 808 T340: ¬(□Y1)∧□(Y2∨◇Y3) ( Y_1 ) (Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 809 T341: ¬(□Y1)∧□(□Y2∨□Y3) ( Y_1 ) ( Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 810 T342: ¬(□Y1)∧◇Y2 ( Y_1 ) Y_2 ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 811 T344: ¬(□Y1)∧◇(¬Y2∧¬Y3) ( Y_1 ) ( Y_2 Y_3 ) ↝ ◇(¬Y2∧¬Y3∧□Y1) ( Y_2 Y_3 Y_1 ) 1 0.01% 1 0.03% Cluster 812 T345: ¬(□Y1)∧◇(□(Y2∧Y3)) ( Y_1 ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 813 T346: ¬(□Y1)∧¬(□Y2) ( Y_1 ) ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 814 T348: ¬(□(□Y1))∧◇Y2 ( ( Y_1 ) ) Y_2 ↝ ◇(Y2∧¬(◇Y1)) (Y_2 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 815 T349: ¬(□(□(□(□(□(□Y1))))))∧□(◇(Y2∨Y3)) ( ( ( ( ( ( Y_1 ) ) ) ) ) ) ( (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 816 T350: ¬(□(□(□(◇Y1))))∧□(□(□(Y2∨Y3))) ( ( ( ( Y_1 ) ) ) ) ( ( (Y_2 Y_3 ) ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 817 T352: ¬(□(◇Y1))∧□(◇Y2) ( ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 818 T354: ¬(◇Y1)∧□Y2 ( Y_1 ) Y_2 ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 819 T359: ¬(◇Y1)∧◇Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 820 T360: ¬(◇Y1)∧◇Y2 ( Y_1 ) Y_2 ↝ ¬Y2∨¬Y1 Y_2 Y_1 1 0.01% 1 0.03% Cluster 821 T361: ¬(◇Y1)∧◇(□(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 822 T362: ¬(◇Y1)∧◇(◇Y1) ( Y_1 ) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 823 T364: ¬(◇Y1)∧¬(◇(◇Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 824 T365: ¬(◇(Y1∧Y2))∧□Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 825 T366: ¬(◇(□Y1))∧□(◇Y2) ( ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 826 T367: ¬(◇(◇Y1))∧Y2 ( ( Y_1 ) ) Y_2 ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% Cluster 827 T369: ¬(Y1↔¬Y2)∧□(Y1↔¬Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 828 T371: ¬(Y1∨Y2)∧◇Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 829 T372: (Y1∨Y2∨Y3∨Y4∨Y5)∧□(Y1∨Y2∨Y3∨Y4∨Y5) (Y_1 Y_2 Y_3 Y_4 Y_5 ) (Y_1 Y_2 Y_3 Y_4 Y_5 ) ↝ □(Y2∨Y3∨Y4) (Y_2 Y_3 Y_4 ) 1 0.01% 1 0.03% Cluster 830 T374: (Y1∨Y2∨Y3)∧¬(◇Y4) (Y_1 Y_2 Y_3 ) ( Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 831 T375: (Y1∨Y2)∧Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 832 T378: (Y1∨Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 833 T379: (Y1∨Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 834 T382: (Y1∨Y2)∧◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 835 T384: (Y1∨Y2)∧◇(¬Y1∧¬Y2)∧◇(□Y3) (Y_1 Y_2 ) ( Y_1 Y_2 ) ( Y_3 ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 836 T385: (Y1∨Y2)∧¬Y3 (Y_1 Y_2 ) Y_3 ↝ ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.01% 1 0.03% Cluster 837 T386: (Y1∨Y2)∧¬(Y1∧Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 838 T387: (Y1∨□Y1)∧Y1 (Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 839 T391: (Y1∨□(◇Y2))∧¬(□Y3) (Y_1 ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 840 T395: (Y1∨◇Y1)∧¬Y2 (Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 841 T398: (Y1∨◇Y2)∧¬(◇Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 842 T399: (Y1∨◇(□Y2))∧(¬Y1∨◇(□Y2)) (Y_1 ( Y_2 ) ) ( Y_1 ( Y_2 ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 843 T401: (Y1∨¬Y1)∧Y1 (Y_1 Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 844 T402: (Y1∨¬Y2)∧Y3 (Y_1 Y_2 ) Y_3 ↝ ¬(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 1 0.01% 1 0.03% Cluster 845 T403: (Y1∨¬Y2)∧□Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 846 T405: (Y1∨¬(◇Y2))∧□Y2 (Y_1 ( Y_2 ) ) Y_2 ↝ Y2→◇(¬Y2)Y_2→ ( Y_2 ) 1 0.01% 1 0.03% Cluster 847 T406: ((Y1∧Y2)∨(Y1∧¬Y2))∧Y3 ( (Y_1 Y_2 ) (Y_1 Y_2 ) ) Y_3 ↝ Y1→Y3Y_1→ Y_3 1 0.01% 1 0.03% Cluster 848 T407: (((Y1∨Y2)∧◇Y2)∨◇Y2)∧◇Y1 ( ( (Y_1 Y_2 ) Y_2 ) Y_2 ) Y_1 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 849 T408: (□Y1∨□Y2)∧□Y3 ( Y_1 Y_2 ) Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 850 T410: (□Y1∨□Y2)∧¬Y3 ( Y_1 Y_2 ) Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 851 T411: (□Y1∨□Y2)∧¬(□Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 852 T414: (□(□Y1)∨□(□Y2))∧¬(□Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 853 T415: (□(◇Y1)∨□(◇Y2))∧□(□(¬(◇Y3))) ( ( Y_1 ) ( Y_2 ) ) ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 854 T416: (□(◇Y1)∨□(◇Y2))∧□(◇Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 855 T417: (□(◇Y1)∨□(◇Y2))∧□(◇(¬Y3)) ( ( Y_1 ) ( Y_2 ) ) ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 856 T418: (□(◇Y1)∨□(◇Y2))∧□(¬Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 857 T419: (□(◇Y1)∨□(◇Y2))∧◇(□(¬Y3)) ( ( Y_1 ) ( Y_2 ) ) ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 858 T420: (□(◇Y1)∨□(◇Y2))∧¬(◇Y3) ( ( Y_1 ) ( Y_2 ) ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 859 T423: (◇Y1∨□Y2)∧◇Y2 ( Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 860 T425: (◇Y1∨◇Y1)∧Y2 ( Y_1 Y_1 ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 861 T426: (◇Y1∨◇Y2)∧Y3 ( Y_1 Y_2 ) Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 862 T427: (◇Y1∨◇Y2)∧□(¬Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 863 T428: (◇Y1∨◇Y2)∧¬Y3 ( Y_1 Y_2 ) Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 864 T430: (◇Y1∨◇(◇(◇Y1)))∧Y2 ( Y_1 ( ( Y_1 ) ) ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 865 T433: (◇(□(¬Y1))∨□(¬Y1))∧□Y1 ( ( ( Y_1 ) ) ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 866 T437: (◇(◇Y1)∨◇(◇Y2))∧¬(◇(◇(□Y3))) ( ( Y_1 ) ( Y_2 ) ) ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 867 T438: (◇(◇(¬Y1))∨□Y1)∧□Y1 ( ( ( Y_1 ) ) Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 868 T441: (¬Y1∨□(¬Y1))∧□Y1 ( Y_1 ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 869 T442: (¬Y1∨¬Y2)∧Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 870 T443: (¬(◇Y1)∨¬(□Y1))∧□(◇Y2) ( ( Y_1 ) ( Y_1 ) ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 871 T448: □Y1 Y_1 ↝ ◇(¬Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 872 T450: □Y1 Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 873 T454: □(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 874 T457: □(Y1∧Y2) (Y_1 Y_2 ) ↝ Y2∧◇Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 875 T458: □(Y1∧Y2) (Y_1 Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 876 T463: □(Y1∧□(¬Y2)) (Y_1 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 877 T464: □(Y1∧□(¬Y2)) (Y_1 ( Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 878 T467: □(Y1∧◇(Y1∧◇(Y1∧◇Y1))) (Y_1 (Y_1 (Y_1 Y_1 ) ) ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 879 T471: □(Y1∧◇(¬Y2)) (Y_1 ( Y_2 ) ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 880 T472: □(Y1∧¬Y1∧◇(¬Y1)) (Y_1 Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 881 T474: □(Y1∧¬Y1) (Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 882 T475: □(Y1∧¬Y2∧◇Y3) (Y_1 Y_2 Y_3 ) ↝ □(◇(Y3∧¬(◇Y1))) ( (Y_3 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 883 T477: □(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 884 T481: □(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 885 T484: □(Y1∧¬(◇Y2)) (Y_1 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 886 T485: □(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 887 T486: □(□Y1∧□(¬(◇Y2))) ( Y_1 ( ( Y_2 ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 888 T488: □(◇Y1∧◇Y2) ( Y_1 Y_2 ) ↝ □(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 889 T490: □(◇Y1∧◇(◇Y1)) ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 890 T492: □(◇Y1∧◇(¬Y2)) ( Y_1 ( Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 891 T494: □(◇(Y1∨Y2)∧□Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 892 T495: □(◇(Y1∨Y2)∧◇(◇(¬Y3))) ( (Y_1 Y_2 ) ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 893 T496: □((Y1↔Y2)∧Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 894 T497: □((Y1→Y2)∧¬(□Y3)) ( (Y_1→ Y_2 ) ( Y_3 ) ) ↝ □(◇((Y2∨Y1)∧¬(◇Y3))) ( ( (Y_2 Y_1 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 895 T498: □(¬Y1∧□Y1) ( Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 896 T499: □(¬Y1∧□Y2) ( Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 897 T502: □(¬Y1∧¬Y2∧¬Y3) ( Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 898 T503: □(¬Y1∧¬Y2) ( Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 899 T505: □(¬Y1∧¬(◇Y1)) ( Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 900 T506: □(¬(□Y1)∧□Y2) ( ( Y_1 ) Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 901 T511: □(¬(◇Y1)∧◇Y2) ( ( Y_1 ) Y_2 ) ↝ ◇(Y2∧¬(◇Y1)) (Y_2 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 902 T512: □(¬(◇(□Y1))∧◇(Y2∨Y3)) ( ( ( Y_1 ) ) (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 903 T513: □(¬(◇(¬Y1))∧□(Y2∨Y3)) ( ( ( Y_1 ) ) (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 904 T518: □((Y1∨◇Y2)∧¬(□Y3)) ( (Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 905 T519: □((Y1∨◇Y2)∧¬(◇(□Y3))) ( (Y_1 Y_2 ) ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 906 T520: □((Y1∨¬Y2)∧◇Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 907 T521: □((□Y1∨□Y2)∧□(□(¬Y3))) ( ( Y_1 Y_2 ) ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 908 T524: □((◇Y1∨◇Y2)∧¬(□Y3)) ( ( Y_1 Y_2 ) ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 909 T526: □((¬Y1∨¬Y2)∧□Y3) ( ( Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 910 T531: □(□Y1) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 911 T532: □(□Y1) ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 912 T533: □(□Y1) ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 913 T534: □(□(Y1∧□(¬Y1))) ( (Y_1 ( Y_1 ) ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 914 T535: □(□((Y1↔¬Y2)∧◇(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 915 T536: □(□((Y1↔¬Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 916 T537: □(□((Y1∨Y2)∧□Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 917 T538: □(□((Y1∨Y2)∧◇Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 918 T540: □(□(□Y1)) ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 919 T541: □(□(□Y1)) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 920 T542: □(□((Y1∨Y2)→□(¬Y3))) ( ( (Y_1 Y_2 )→ ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 921 T543: □(□((Y1∨Y2)→¬(□Y3))) ( ( (Y_1 Y_2 )→ ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 922 T544: □(□((Y1∨Y2)→¬(□(¬Y3)))) ( ( (Y_1 Y_2 )→ ( ( Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 923 T552: □(◇((Y1↔¬Y2)∧□(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y2∨Y1)∧¬(◇Y3))) ( ( (Y_2 Y_1 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 924 T553: □(◇(¬Y1∧□Y2)) ( ( Y_1 Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 925 T554: □(◇(¬Y1∧¬Y2∧□(¬Y3))) ( ( Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 926 T556: □(◇((Y1∨Y2)∧◇(¬(Y1∨Y2∨Y3∨Y4)))) ( ( (Y_1 Y_2 ) ( (Y_1 Y_2 Y_3 Y_4 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y4))) ( ( (Y_1 Y_2 ) ( Y_4 ) ) ) 1 0.01% 1 0.03% Cluster 927 T557: □(◇(((Y1∧¬Y2)∨(Y2∧¬Y1))∧¬(□Y3))) ( ( ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 928 T558: □(◇(□(Y1∧◇(¬Y2)))) ( ( (Y_1 ( Y_2 ) ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 929 T559: □(◇(□(¬Y1))) ( ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 930 T561: □(◇(Y1→□(¬Y2))) ( (Y_1→ ( Y_2 ) ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 931 T562: □(◇(Y1→¬Y1)) ( (Y_1→ Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 932 T563: □(◇(□Y1→□(¬Y2))) ( ( Y_1→ ( Y_2 ) ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 933 T564: □(◇(◇(¬Y1)→(Y2∨Y3))) ( ( ( Y_1 )→ (Y_2 Y_3 ) ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 934 T566: □(◇((Y1∨◇Y1)→□Y1)) ( ( (Y_1 Y_1 )→ Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 935 T569: □(◇(Y1∨Y2∨◇(¬Y3))) ( (Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 936 T570: □(◇(Y1∨Y2∨¬Y3)) ( (Y_1 Y_2 Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 937 T571: □(◇(Y1∨Y2∨¬(◇Y3))) ( (Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 938 T572: □(◇(Y1∨□Y1)) ( (Y_1 Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 939 T574: □(◇(¬Y1∨◇(¬Y1))) ( ( Y_1 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 940 T575: □(Y1↔Y2) (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 941 T576: □(Y1↔Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 942 T577: □(Y1↔□(◇Y1)) (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 943 T578: □(Y1↔□(¬Y2)) (Y_1 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 944 T579: □(Y1↔¬Y1) (Y_1 Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 945 T581: □(Y1↔¬Y2) (Y_1 Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 946 T583: □(¬Y1↔¬Y2) ( Y_1 Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 947 T585: □((Y1∨Y2∨Y3)↔¬Y4) ( (Y_1 Y_2 Y_3 ) Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 948 T586: □(Y1→Y2) (Y_1→ Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 949 T588: □(Y1→Y2) (Y_1→ Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 950 T592: □(Y1→Y2) (Y_1→ Y_2 ) ↝ □Y2→Y1 Y_2→ Y_1 1 0.01% 1 0.03% Cluster 951 T593: □(Y1→(Y2∧□(¬Y1))) (Y_1→ (Y_2 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 952 T594: □(Y1→(□(¬Y1)∧□(□(¬Y1)))) (Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 953 T595: □(Y1→(◇(¬Y1)∧◇(◇(¬Y1)))) (Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 954 T598: □(Y1→◇(¬Y1∧◇(¬Y1))) (Y_1→ ( Y_1 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 955 T600: □(Y1→◇(Y1∨◇Y1)) (Y_1→ (Y_1 Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 956 T601: □(Y1→(Y2↔Y3)) (Y_1→ (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 957 T602: □(Y1→(¬Y2↔Y3)) (Y_1→ ( Y_2 Y_3 ) ) ↝ □(¬(Y3∨Y2)→Y1) ( (Y_3 Y_2 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 958 T605: □(Y1→¬(◇Y1)) (Y_1→ ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 959 T606: □(Y1→¬(◇Y1)) (Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 960 T611: □(◇Y1→Y1) ( Y_1→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 961 T612: □(◇Y1→(Y2∨Y3)) ( Y_1→ (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 962 T614: □(¬Y1→Y2) ( Y_1→ Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 963 T617: □(¬Y1→¬Y2) ( Y_1→ Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 964 T620: □(¬Y1) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 965 T624: □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 966 T625: □(¬((Y1∨Y2)∧Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 967 T626: □(¬((Y1∨Y2)∧¬Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 968 T629: □(¬(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 969 T630: □(¬(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 970 T632: □(¬(Y1∨Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 971 T635: □(Y1∨Y2) (Y_1 Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 972 T638: □(Y1∨Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 973 T644: □(Y1∨◇Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 974 T647: □(Y1∨◇(◇Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 975 ⌈ == T648: □(Y1∨◇(◇Y1)) (Y_1 ( Y_1 ) ) ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% ⌊ == T1019: Y1→□(Y2∨◇(◇Y2))Y_1→ (Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 976 T652: □(Y1∨¬Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 977 T656: □((Y1∧◇Y1)∨Y1) ( (Y_1 Y_1 ) Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 978 ⌈ == T657: □((Y1∧¬Y2)∨(Y2∧¬Y1)) ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% ⌊ == T1679: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 979 T658: □((Y1∧¬(◇Y3))∨(Y2∧¬(◇Y3))) ( (Y_1 ( Y_3 ) ) (Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 980 T659: □((¬Y1∧◇Y1)∨Y1) ( ( Y_1 Y_1 ) Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 981 T660: □((¬Y1∧¬Y2)∨Y3) ( ( Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 982 T661: □((¬(◇Y1)∧◇Y2)∨(¬(◇Y1)∧◇Y3)) ( ( ( Y_1 ) Y_2 ) ( ( Y_1 ) Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 983 T665: □(◇Y1∨□(□Y1)) ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 984 T666: □(◇Y1∨◇Y2∨◇Y3) ( Y_1 Y_2 Y_3 ) ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 985 T668: □(◇(¬Y1)∨◇(◇(¬Y1))) ( ( Y_1 ) ( ( Y_1 ) ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 986 T669: □((Y1→◇Y1)∨(Y1→□Y1)) ( (Y_1→ Y_1 ) (Y_1→ Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 987 T670: □((Y1→¬Y1)∨(Y1→◇(¬Y1))) ( (Y_1→ Y_1 ) (Y_1→ ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 988 T673: □(Y1∨Y2∨□(¬Y3)) (Y_1 Y_2 ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 989 T682: ◇Y1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 990 T687: ◇(Y1∧Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 991 T693: ◇(Y1∧◇Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 992 T697: ◇(Y1∧◇Y2) (Y_1 Y_2 ) ↝ Y2∧□(Y2∧Y1)Y_2 (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 993 T698: ◇(Y1∧◇Y2) (Y_1 Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 994 T700: ◇(Y1∧◇(¬Y1)) (Y_1 ( Y_1 ) ) ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 995 T701: ◇(Y1∧◇(¬Y2)) (Y_1 ( Y_2 ) ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 996 T705: ◇(Y1∧¬Y1) (Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 997 T709: ◇(Y1∧¬Y2) (Y_1 Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 998 T710: ◇(Y1∧¬Y2) (Y_1 Y_2 ) ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 999 T712: ◇(Y1∧¬(◇Y2)) (Y_1 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1000 T713: ◇(Y1∧¬(Y2∨Y3)) (Y_1 (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1001 T715: ◇(Y1∧Y2∧◇Y3) (Y_1 Y_2 Y_3 ) ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1002 T716: ◇(Y1∧¬Y2∧Y2∧¬Y1) (Y_1 Y_2 Y_2 Y_1 ) ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1003 T717: ◇(Y1∧¬Y2∧◇Y3) (Y_1 Y_2 Y_3 ) ↝ ◇(¬Y2∧¬Y1∧□Y3) ( Y_2 Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 1004 T718: ◇((Y1→◇Y2)∧Y2) ( (Y_1→ Y_2 ) Y_2 ) ↝ ◇Y2∨◇(◇Y2) Y_2 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1005 T721: ◇(¬(◇(◇Y1))∧◇(Y2∨Y3)) ( ( ( Y_1 ) ) (Y_2 Y_3 ) ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1006 T723: ◇((Y1∨Y2)∧Y3) ( (Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1007 T730: ◇(□Y1) ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1008 T731: ◇(□Y1) ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1009 T735: ◇(□(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1010 T736: ◇(□(¬Y1∧◇(◇(◇Y2)))) ( ( Y_1 ( ( Y_2 ) ) ) ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1011 T737: ◇(□((Y1∨Y2)∧□Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1012 T740: ◇(□((Y1∨Y2)∧¬Y3)) ( ( (Y_1 Y_2 ) Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1013 T742: ◇(□((Y1∨◇Y2)∧◇(¬Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1014 T743: ◇(□((◇Y1∨◇Y2)∧◇(¬Y3))) ( ( ( Y_1 Y_2 ) ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1015 T744: ◇(□(□Y1)) ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1016 T745: ◇(□(◇((Y1∨Y2)∧□(¬Y3)))) ( ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1017 T746: ◇(□(◇((Y1∨Y2)∧◇(¬Y3)))) ( ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1018 T747: ◇(□(◇(◇((Y1∨Y2)∧¬Y3)))) ( ( ( ( (Y_1 Y_2 ) Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1019 T748: ◇(□(Y1→¬Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1020 T749: ◇(□((Y1∨Y2)→□(¬Y3))) ( ( (Y_1 Y_2 )→ ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1021 T750: ◇(□(Y1∨Y2∨¬Y3)) ( (Y_1 Y_2 Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1022 T751: ◇(□(Y1∨Y2∨¬(◇Y3))) ( (Y_1 Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1023 T756: ◇(◇(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1024 T762: ◇(◇(◇((Y1∨Y2)∧◇(¬Y3)))) ( ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1025 T763: ◇(◇(◇(◇(◇(◇(◇(Y1∨Y2∨Y3))))))) ( ( ( ( ( ( (Y_1 Y_2 Y_3 ) ) ) ) ) ) ) ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1026 T764: ◇(◇(Y1→□(¬Y2))) ( (Y_1→ ( Y_2 ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1027 T767: ◇(◇(Y1∨Y2∨◇Y3)) ( (Y_1 Y_2 Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1028 T768: ◇(Y1↔Y2) (Y_1 Y_2 ) ↝ □(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1029 T769: ◇(Y1↔Y2) (Y_1 Y_2 ) ↝ □(Y1→Y2) (Y_1→ Y_2 ) 1 0.01% 1 0.03% Cluster 1030 T770: ◇(□Y1↔□(¬Y2)) ( Y_1 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1031 T771: ◇((¬Y1↔Y2)↔Y3) ( ( Y_1 Y_2 ) Y_3 ) ↝ □(¬(Y2∨Y1)→Y3) ( (Y_2 Y_1 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1032 T774: ◇(Y1→Y2) (Y_1→ Y_2 ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 1033 T776: ◇(Y1→□Y1) (Y_1→ Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1034 T777: ◇(Y1→□(¬Y2)) (Y_1→ ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1035 T780: ◇(Y1→¬(□Y2)) (Y_1→ ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1036 T781: ◇(Y1→¬(◇Y1)) (Y_1→ ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1037 T783: ◇(Y1→(¬Y1∨◇(¬Y1))) (Y_1→ ( Y_1 ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1038 T786: ◇((¬Y1∧¬Y2)→□Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1039 T787: ◇((¬Y1∧¬Y2)→◇(□Y3)) ( ( Y_1 Y_2 )→ ( Y_3 ) ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1040 T788: ◇((¬Y1↔Y2)→Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y2∨Y1)→Y3) ( (Y_2 Y_1 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1041 T789: ◇((¬Y1∨¬Y2)→Y3) ( ( Y_1 Y_2 )→ Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1042 T792: ◇(¬Y1) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1043 ⌈ == T795: ◇(¬(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ ◇(Y1↔¬Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% ⌊ == T1040: Y1→◇(¬(Y2∧¬Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1044 T799: ◇(¬((Y1∨Y2)→□Y3)) ( ( (Y_1 Y_2 )→ Y_3 ) ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1045 T800: ◇(Y1∨Y1) (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1046 T802: ◇(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) ↝ ◇(Y1∨Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1047 T805: ◇(Y1∨□(¬Y1)) (Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1048 T807: ◇(Y1∨◇Y2) (Y_1 Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1049 T812: ◇((Y1∧Y2)∨Y1) ( (Y_1 Y_2 ) Y_1 ) ↝ □(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1050 T813: ◇((Y1∧¬(◇Y3))∨(Y2∧¬(◇Y3))) ( (Y_1 ( Y_3 ) ) (Y_2 ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1051 T817: Y1↔Y2Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1052 T820: Y1↔Y2Y_1 Y_2 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1053 T823: Y1↔(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1054 T824: Y1↔(◇Y1∧□Y2)Y_1 ( Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1055 T825: Y1↔(◇(¬Y1)∧◇(□Y2))Y_1 ( ( Y_1 ) ( Y_2 ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1056 T830: Y1↔□(¬Y1)Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1057 T833: Y1↔□(Y1∨□Y1)Y_1 (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1058 T839: Y1↔◇(□Y1)Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1059 T841: Y1↔◇(¬Y2)Y_1 ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1060 T842: Y1↔◇(¬Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1061 T844: Y1↔◇(Y2∨◇Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1062 T845: Y1↔◇(Y2∨¬Y2)Y_1 (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1063 T846: Y1↔(◇(¬Y1)→□Y2)Y_1 ( ( Y_1 )→ Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1064 T847: Y1↔¬Y1Y_1 Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1065 T848: Y1↔¬Y1Y_1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1066 T849: Y1↔¬Y2Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1067 T852: Y1↔¬Y2Y_1 Y_2 ↝ ¬(Y2∨Y1) (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1068 T853: Y1↔¬Y2Y_1 Y_2 ↝ Y2∨Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 1069 T854: Y1↔¬(Y1∧Y2)Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1070 T855: Y1↔¬(Y1∧◇Y1)Y_1 (Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1071 T857: Y1↔¬(◇Y1∧◇(□Y2))Y_1 ( Y_1 ( Y_2 ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1072 T859: Y1↔¬(Y2∨□Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1073 T860: Y1↔(Y2∨◇Y1)Y_1 (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1074 T861: Y1↔(Y2∨◇(◇Y2))Y_1 (Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1075 T862: Y1↔(◇Y2∨□Y2)Y_1 ( Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1076 T865: (Y1∧Y2)↔□(◇Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1077 T866: (Y1∧Y2)↔◇(□Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1078 T867: (□Y1∧□Y2)↔□Y3 ( Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1079 T868: (◇(◇Y1)∧◇(□(¬Y2)))↔(◇(◇Y3)∧◇(□(¬Y2))) ( ( Y_1 ) ( ( Y_2 ) ) ) ( ( Y_3 ) ( ( Y_2 ) ) ) ↝ □(◇((Y1∨Y3)∧¬(◇Y2))) ( ( (Y_1 Y_3 ) ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1080 T870: (¬Y1∧¬Y2)↔□Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1081 T872: □Y1↔Y2 Y_1 Y_2 ↝ □(¬Y1→Y2) ( Y_1→ Y_2 ) 1 0.01% 1 0.03% Cluster 1082 T873: □Y1↔Y2 Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% Cluster 1083 T875: □Y1↔(□Y2∧□Y3) Y_1 ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1084 T876: □Y1↔□Y1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1085 T877: □Y1↔□Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1086 T878: □Y1↔□(□(¬Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1087 T879: □Y1↔□(◇Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1088 T880: □Y1↔□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1089 T881: □Y1↔□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1090 T883: □Y1↔□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1091 T884: □Y1↔□(¬Y2) Y_1 ( Y_2 ) ↝ ◇(Y2↔¬Y1) (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1092 T885: □Y1↔□(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1093 T890: □Y1↔¬Y1 Y_1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1094 T891: □Y1↔¬Y2 Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1095 T892: □Y1↔¬(Y2∧Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1096 T896: □Y1↔(Y2∨¬Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1097 T897: □Y1↔(□(¬Y1)∨□(¬Y1)) Y_1 ( ( Y_1 ) ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1098 T899: □(◇(Y1∧Y2))↔◇Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1099 T901: □(¬Y1)↔Y2 ( Y_1 ) Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1100 T902: □(¬Y1)↔◇Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1101 T903: □(¬Y1)↔¬Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1102 T904: □(¬Y1)↔(Y2∨Y3) ( Y_1 ) (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1103 T906: □(¬(Y1∨Y2))↔□Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1104 T907: □(Y1∨Y2)↔□Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1105 T908: □(◇Y1∨□Y1)↔Y1 ( Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1106 T911: □(¬Y1∨¬Y2)↔◇Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1107 T914: ◇Y1↔(¬Y2∧¬Y3) Y_1 ( Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1108 T915: ◇Y1↔□Y1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1109 T916: ◇Y1↔□Y1 Y_1 Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1110 T917: ◇Y1↔□(Y1∨◇Y1) Y_1 (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1111 T918: ◇Y1↔◇Y2 Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1112 T920: ◇Y1↔¬(□Y1) Y_1 ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1113 T921: ◇Y1↔¬(Y2∨Y3) Y_1 (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1114 T922: ◇(Y1∧Y2)↔□Y3 (Y_1 Y_2 ) Y_3 ↝ ◇(Y1∧Y2∧Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1115 T924: ◇(¬Y1∧¬Y2)↔□Y3 ( Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1116 T925: ◇(□(Y1∧Y2))↔◇Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1117 T927: ◇(¬(Y1∧Y2))↔□Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1118 T928: ◇(¬(Y1∨Y2))↔Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1119 T929: (¬Y1↔Y2)↔□Y3 ( Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1120 T931: ¬Y1↔Y2 Y_1 Y_2 ↝ ¬Y2∨¬Y1 Y_2 Y_1 1 0.01% 1 0.03% Cluster 1121 T933: ¬Y1↔□(¬Y2) Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1122 T934: ¬Y1↔¬Y2 Y_1 Y_2 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1123 T935: ¬(□Y1)↔Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1124 T936: ¬(□Y1)↔¬(Y2∨Y3) ( Y_1 ) (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1125 T937: ¬(◇Y1)↔Y1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1126 T938: ¬(◇Y1)↔Y2 ( Y_1 ) Y_2 ↝ Y2∧¬(◇Y1)Y_2 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1127 T939: ¬(◇(Y1∧Y2))↔Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1128 T941: ¬(Y1∨Y2)↔◇Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1129 T943: (Y1∨Y2)↔□Y3 (Y_1 Y_2 ) Y_3 ↝ Y3→(Y1∨Y2)Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1130 T944: (Y1∨Y2)↔◇Y3 (Y_1 Y_2 ) Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1131 T946: ((Y1∧¬Y2)∨(Y2∧¬Y1))↔Y3 ( (Y_1 Y_2 ) (Y_2 Y_1 ) ) Y_3 ↝ Y3→¬(Y1↔Y2)Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1132 T947: (□Y1∨□Y2)↔□(¬Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1133 T949: Y1→Y1Y_1→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1134 T956: Y1→Y2Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1135 T965: Y1→Y2Y_1→ Y_2 ↝ □Y2→Y1 Y_2→ Y_1 1 0.01% 1 0.03% Cluster 1136 T971: Y1→(Y1∧◇Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1137 T972: Y1→(Y1∧¬(◇Y1))Y_1→ (Y_1 ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1138 T973: Y1→(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ¬(Y2∨Y3)→Y1 (Y_2 Y_3 )→ Y_1 1 0.01% 1 0.03% Cluster 1139 T974: Y1→(Y2∧¬Y1)Y_1→ (Y_2 Y_1 ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1140 T975: Y1→(□Y1∧Y2)Y_1→ ( Y_1 Y_2 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1141 T978: Y1→(◇(¬Y1)∧Y2)Y_1→ ( ( Y_1 ) Y_2 ) ↝ ¬Y1↔◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1142 T979: Y1→((□Y1→Y1)∧□Y1)Y_1→ ( ( Y_1→ Y_1 ) Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1143 T980: Y1→((□Y1→Y1)∧◇Y1)Y_1→ ( ( Y_1→ Y_1 ) Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1144 T982: Y1→(¬Y2∧□(¬Y2))Y_1→ ( Y_2 ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1145 T984: Y1→(¬(□Y2)∧□Y1)Y_1→ ( ( Y_2 ) Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1146 T985: Y1→(¬(◇Y2)∧◇Y3)Y_1→ ( ( Y_2 ) Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1147 T986: Y1→((Y2∨¬Y3)∧◇(Y3∨¬Y2))Y_1→ ( (Y_2 Y_3 ) (Y_3 Y_2 ) ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1148 T988: Y1→□Y1Y_1→ Y_1 ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 1149 T990: Y1→□Y2Y_1→ Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1150 T993: Y1→□Y2Y_1→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1151 T996: Y1→□(Y1∧¬Y2∧¬Y3)Y_1→ (Y_1 Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1152 T997: Y1→□(Y1∧¬Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1153 T998: Y1→□(Y1∧¬Y2)Y_1→ (Y_1 Y_2 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1154 T999: Y1→□(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1155 T1000: Y1→□(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1156 T1001: Y1→□((□Y1→Y1)∧Y1)Y_1→ ( ( Y_1→ Y_1 ) Y_1 ) ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1157 T1003: Y1→□(◇Y2)Y_1→ ( Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1158 T1004: Y1→□(◇(¬Y1))Y_1→ ( ( Y_1 ) ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 1159 T1012: Y1→□(¬Y2)Y_1→ ( Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1160 T1013: Y1→□(¬(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1161 T1020: Y1→□(Y2∨¬Y2)Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1162 T1023: Y1→◇Y2Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1163 T1026: Y1→◇Y2Y_1→ Y_2 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1164 T1029: Y1→◇(Y1∧Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1165 T1030: Y1→◇(Y2∧Y3)Y_1→ (Y_2 Y_3 ) ↝ ◇(Y2∧Y3∧□Y1) (Y_2 Y_3 Y_1 ) 1 0.01% 1 0.03% Cluster 1166 T1032: Y1→◇((Y1→Y2)∧Y2)Y_1→ ( (Y_1→ Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1167 T1033: Y1→◇((Y2∨¬Y3)∧(Y3∨¬Y2))Y_1→ ( (Y_2 Y_3 ) (Y_3 Y_2 ) ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1168 T1034: Y1→◇(Y2→◇Y2)Y_1→ (Y_2→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1169 T1036: Y1→◇(¬Y1)Y_1→ ( Y_1 ) ↝ ¬(□Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 1170 T1037: Y1→◇(¬Y2)Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1171 T1038: Y1→◇(¬(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ ◇(¬Y2∧¬Y3∧□Y1) ( Y_2 Y_3 Y_1 ) 1 0.01% 1 0.03% Cluster 1172 T1041: Y1→◇(Y1∨Y2)Y_1→ (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1173 T1042: Y1→◇(Y2∨Y1)Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1174 T1046: Y1→◇((◇Y2→Y1)∨Y2)Y_1→ ( ( Y_2→ Y_1 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1175 T1047: Y1→(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1176 T1049: Y1→(□Y2↔□Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1177 T1050: Y1→(◇Y1↔◇Y2)Y_1→ ( Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1178 T1051: Y1→(◇Y2↔◇(¬Y3))Y_1→ ( Y_2 ( Y_3 ) ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1179 T1053: Y1→(Y2→Y3)Y_1→ (Y_2→ Y_3 ) ↝ □Y1→¬(Y3↔Y2) Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1180 T1060: Y1→¬(□Y2∧□Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1181 T1062: Y1→¬((Y2∨Y3)∧(¬Y2∨¬Y3))Y_1→ ( (Y_2 Y_3 ) ( Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1182 T1067: Y1→¬(□Y2)Y_1→ ( Y_2 ) ↝ Y1∨□(¬Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1183 T1070: Y1→¬(◇Y2)Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1184 T1071: Y1→¬(◇Y2)Y_1→ ( Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1185 T1072: Y1→¬(◇(Y2∧Y3))Y_1→ ( (Y_2 Y_3 ) ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1186 T1073: Y1→¬(◇(◇Y1))Y_1→ ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1187 T1074: Y1→¬(Y2↔Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1188 T1077: Y1→(Y1∨□Y2)Y_1→ (Y_1 Y_2 ) ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1189 T1084: Y1→(Y2∨◇(◇(◇Y2)))Y_1→ (Y_2 ( ( Y_2 ) ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1190 T1085: Y1→(Y2∨¬Y3)Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y2↔¬Y3)Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1191 T1086: Y1→((Y1∧Y2)∨(Y1∧◇Y2))Y_1→ ( (Y_1 Y_2 ) (Y_1 Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1192 T1089: Y1→(□Y2∨□Y2)Y_1→ ( Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1193 T1090: Y1→(□Y2∨□Y3)Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1194 T1094: Y1→(◇Y2∨◇Y3)Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1195 T1095: Y1→(◇((Y1∨Y2)∧◇Y2)∨□Y2)Y_1→ ( ( (Y_1 Y_2 ) Y_2 ) Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1196 T1100: Y1→((Y2→Y3)∨(Y3→Y2))Y_1→ ( (Y_2→ Y_3 ) (Y_3→ Y_2 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1197 T1101: Y1→(¬Y2∨◇Y2)Y_1→ ( Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1198 T1103: Y1→(¬Y2∨¬Y3)Y_1→ ( Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1199 T1106: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y1→Y3Y_1→ Y_3 1 0.01% 1 0.03% Cluster 1200 T1107: (Y1∧Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1201 T1112: (Y1∧Y2)→□(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1202 T1113: (Y1∧Y2)→□(Y1∨◇Y1) (Y_1 Y_2 )→ (Y_1 Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1203 T1114: (Y1∧Y2)→□(Y1∨◇(◇Y1)) (Y_1 Y_2 )→ (Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1204 T1117: (Y1∧□Y1)→Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1205 T1118: (Y1∧□Y1)→□Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1206 T1119: (Y1∧□Y1)→(¬Y1∨◇(¬Y1)) (Y_1 Y_1 )→ ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1207 T1120: (Y1∧◇Y1)→¬Y1 (Y_1 Y_1 )→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1208 T1121: (Y1∧¬Y2∧¬Y3)→Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ □(¬(Y2∨Y3)→Y4) ( (Y_2 Y_3 )→ Y_4 ) 1 0.01% 1 0.03% Cluster 1209 T1122: (□Y1∧□Y2)→Y1 ( Y_1 Y_2 )→ Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1210 T1123: (□Y1∧□Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1211 T1127: (□(¬Y1)∧□(¬Y2))→◇Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1212 T1128: (□(¬Y1)∧□(¬Y2))→◇Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1213 T1129: (◇Y1∧◇Y2)→Y1 ( Y_1 Y_2 )→ Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1214 T1130: (◇Y1∧◇Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1215 T1131: (◇Y1∧◇Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1216 T1132: (◇(¬Y1)∧◇(¬Y2))→Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1217 T1133: (◇(¬Y1)∧◇(¬Y2))→□Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1218 T1135: ((□Y1→Y1)∧□Y1)→Y1 ( ( Y_1→ Y_1 ) Y_1 )→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1219 T1137: (¬Y1∧¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1220 T1139: (¬Y1∧¬Y2)→◇Y3 ( Y_1 Y_2 )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1221 T1141: (¬(◇Y1)∧¬(◇Y2))→◇Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1222 T1143: □Y1→Y2 Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1223 T1146: □Y1→Y2 Y_1→ Y_2 ↝ □(Y2→Y1) (Y_2→ Y_1 ) 1 0.01% 1 0.03% Cluster 1224 T1147: □Y1→Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1225 T1148: □Y1→Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1226 T1154: □Y1→Y2 Y_1→ Y_2 ↝ □Y2→Y1 Y_2→ Y_1 1 0.01% 1 0.03% Cluster 1227 T1156: □Y1→(Y1∧Y2) Y_1→ (Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1228 T1158: □Y1→(Y1∧¬Y2∧¬Y3) Y_1→ (Y_1 Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1229 T1160: □Y1→(Y2∧□Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y3↔Y2) Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1230 T1161: □Y1→(Y2∧Y3∧(Y2∨Y3)) Y_1→ (Y_2 Y_3 (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1231 T1162: □Y1→(◇Y2∧◇Y3) Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1232 T1165: □Y1→(¬Y2∧¬Y3) Y_1→ ( Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1233 T1166: □Y1→((Y2∨Y3)∧¬Y2∧¬Y3) Y_1→ ( (Y_2 Y_3 ) Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1234 T1167: □Y1→((Y2∨Y3)∧¬(Y1∨Y4)) Y_1→ ( (Y_2 Y_3 ) (Y_1 Y_4 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1235 T1172: □Y1→□Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1236 T1173: □Y1→□Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1237 T1174: □Y1→□Y2 Y_1→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1238 T1177: □Y1→□(Y1∧¬Y2∧¬Y3) Y_1→ (Y_1 Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1239 T1178: □Y1→□(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1240 T1180: □Y1→□(□(¬Y2)) Y_1→ ( ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1241 T1185: □Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1242 T1188: □Y1→□(¬(Y2∨Y3)) Y_1→ ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1243 T1191: □Y1→◇Y1 Y_1→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1244 T1198: □Y1→◇Y2 Y_1→ Y_2 ↝ □Y2→(Y1∨◇Y1) Y_2→ (Y_1 Y_1 ) 1 0.01% 1 0.03% Cluster 1245 T1200: □Y1→◇(Y2↔Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1246 T1206: □Y1→(◇Y2↔◇(¬Y3)) Y_1→ ( Y_2 ( Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1247 T1208: □Y1→(Y2→¬Y3) Y_1→ (Y_2→ Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1248 T1209: □Y1→(◇Y1→Y2) Y_1→ ( Y_1→ Y_2 ) ↝ □(◇Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 1249 T1211: □Y1→¬Y2 Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1250 T1212: □Y1→¬Y2 Y_1→ Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1251 T1213: □Y1→¬Y2 Y_1→ Y_2 ↝ □(¬Y1→Y2) ( Y_1→ Y_2 ) 1 0.01% 1 0.03% Cluster 1252 T1216: □Y1→¬Y2 Y_1→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1253 T1217: □Y1→¬Y2 Y_1→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1254 T1218: □Y1→¬(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1255 T1219: □Y1→¬(□Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1256 T1221: □Y1→¬(□Y2) Y_1→ ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1257 T1230: □Y1→((Y2∧Y3)∨(¬Y2∧¬Y3)) Y_1→ ( (Y_2 Y_3 ) ( Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1258 T1231: □Y1→(□(◇Y2)∨□(◇Y3)) Y_1→ ( ( Y_2 ) ( Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1259 T1240: □(Y1∧Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ ◇(Y1∧Y2∧□Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1260 T1241: □(Y1∧Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1261 T1242: □(Y1∧Y2)→(Y1∨Y2) (Y_1 Y_2 )→ (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1262 T1244: □(Y1∧◇Y1)→◇(¬Y1) (Y_1 Y_1 )→ ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1263 T1246: □(Y1∧¬Y2∧¬Y3)→□Y1 (Y_1 Y_2 Y_3 )→ Y_1 ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1264 T1247: □(Y1∧¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1265 T1251: □(¬Y1∧¬Y2)→□(◇Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1266 T1252: □(¬Y1∧¬Y2)→□(¬Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1267 T1256: □(□Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1268 T1258: □(□Y1)→□Y2 ( Y_1 )→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1269 T1260: □(□Y1)→¬(□Y2) ( Y_1 )→ ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1270 T1261: □(□Y1)→(Y2∨Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1271 T1262: □(□(¬Y1))→Y2 ( ( Y_1 ) )→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1272 T1263: □(□(¬Y1))→□(¬Y2∨¬Y3) ( ( Y_1 ) )→ ( Y_2 Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1273 T1264: □(□(Y1∨Y2))→□(□(□(¬Y3))) ( (Y_1 Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1274 T1265: □(◇Y1)→Y2 ( Y_1 )→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1275 T1269: □(◇Y1)→□(Y2↔¬Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1276 T1270: □(◇Y1)→◇(◇Y2) ( Y_1 )→ ( Y_2 ) ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1277 T1273: □(◇Y1)→¬Y1 ( Y_1 )→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1278 T1275: □(◇(Y1∧Y2))→¬(◇Y3) ( (Y_1 Y_2 ) )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1279 T1276: □(◇(Y1∨Y2))→□(◇(◇(¬Y3))) ( (Y_1 Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1280 T1277: □(◇(Y1∨Y2))→¬(□(◇(◇Y3))) ( (Y_1 Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1281 T1278: □(◇(Y1∨Y2))→¬(□(◇(◇(¬Y3)))) ( (Y_1 Y_2 ) )→ ( ( ( ( Y_3 ) ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1282 ⌈ == T1279: □(¬Y1)→Y1 ( Y_1 )→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% ⌊ == T1284: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ Y2→◇(¬Y1)Y_2→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1283 T1282: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1284 T1283: □(¬Y1)→Y2 ( Y_1 )→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1285 T1287: □(¬Y1)→◇Y1 ( Y_1 )→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1286 T1288: □(¬Y1)→(Y2↔Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1287 T1289: □(¬Y1)→(◇(¬Y1)∨◇(□(¬Y1))) ( Y_1 )→ ( ( Y_1 ) ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1288 T1290: □(¬(Y1∧Y2))→◇Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1289 T1291: □(¬(Y1∧Y2))→◇Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1290 T1292: □(¬(Y1∧Y2))→¬Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1291 T1295: □(Y1∨Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1292 T1299: □(Y1∨Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1293 T1301: □(Y1∨Y2)→(◇Y1∨◇(◇Y1)) (Y_1 Y_2 )→ ( Y_1 ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1294 T1303: □(Y1∨□Y2)→□(□(¬Y3)) (Y_1 Y_2 )→ ( ( Y_3 ) ) ↝ □(◇((Y2∨Y1)∧¬(◇Y3))) ( ( (Y_2 Y_1 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1295 T1304: □(Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1296 T1305: □(◇Y1∨◇Y2)→◇(¬Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1297 T1306: □(◇Y1∨◇Y2)→¬(□Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1298 T1310: □(¬Y1∨¬Y2)→□(¬Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1299 T1316: ◇Y1→Y2 Y_1→ Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1300 T1319: ◇Y1→(Y1∧¬Y2) Y_1→ (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1301 T1321: ◇Y1→((Y2∨Y3)∧¬(Y1∨Y3)) Y_1→ ( (Y_2 Y_3 ) (Y_1 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1302 T1322: ◇Y1→((Y2∨¬Y3)∧(Y3∨¬Y2)) Y_1→ ( (Y_2 Y_3 ) (Y_3 Y_2 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1303 T1323: ◇Y1→((□Y2∨□Y3)∧¬Y4) Y_1→ ( ( Y_2 Y_3 ) Y_4 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y4))) ( ( (Y_2 Y_3 ) ( Y_4 ) ) ) 1 0.01% 1 0.03% Cluster 1304 T1326: ◇Y1→□Y2 Y_1→ Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1305 T1327: ◇Y1→□Y2 Y_1→ Y_2 ↝ □Y1→¬Y2 Y_1→ Y_2 1 0.01% 1 0.03% Cluster 1306 T1329: ◇Y1→□(□(¬Y2)) Y_1→ ( ( Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1307 T1330: ◇Y1→□(◇(¬Y1)) Y_1→ ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1308 T1332: ◇Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 1309 T1333: ◇Y1→□(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1310 T1335: ◇Y1→◇Y2 Y_1→ Y_2 ↝ Y1→Y2Y_1→ Y_2 1 0.01% 1 0.03% Cluster 1311 T1336: ◇Y1→◇(□(¬Y1)) Y_1→ ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1312 T1338: ◇Y1→◇(¬Y1) Y_1→ ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1313 T1340: ◇Y1→◇(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1314 T1341: ◇Y1→◇(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1315 T1342: ◇Y1→◇(Y2∨◇Y1) Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1316 T1343: ◇Y1→◇(Y2∨◇Y2) Y_1→ (Y_2 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1317 T1345: ◇Y1→(□Y2↔□Y3) Y_1→ ( Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1318 T1349: ◇Y1→¬(□Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1319 T1352: ◇Y1→(Y1∨¬(◇Y1)) Y_1→ (Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1320 T1354: ◇Y1→(Y2∨◇Y1) Y_1→ (Y_2 Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1321 T1355: ◇Y1→((Y1∧¬Y2)∨(Y2∧¬Y3)) Y_1→ ( (Y_1 Y_2 ) (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1322 T1356: ◇Y1→(◇Y1∨□(□Y1)) Y_1→ ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1323 T1359: ◇Y1→(◇(◇(□(¬Y1)))∨◇(□(¬Y1))) Y_1→ ( ( ( ( Y_1 ) ) ) ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1324 T1360: ◇Y1→(¬Y1∨□(¬Y1)) Y_1→ ( Y_1 ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1325 T1363: ◇(Y1∧Y2)→◇(□(¬Y3)) (Y_1 Y_2 )→ ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1326 T1367: ◇(¬Y1∧¬Y2)→◇(Y3∧¬Y1∧¬Y2) ( Y_1 Y_2 )→ (Y_3 Y_1 Y_2 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1327 T1368: ◇(¬Y1∧¬Y2)→◇(¬Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1328 T1369: ◇(□Y1)→□Y1 ( Y_1 )→ Y_1 ↝ □Y1→Y1 Y_1→ Y_1 1 0.01% 1 0.03% Cluster 1329 T1370: ◇(□Y1)→□(□(¬Y2)) ( Y_1 )→ ( ( Y_2 ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1330 T1371: ◇(□Y1)→¬(◇Y2) ( Y_1 )→ ( Y_2 ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1331 T1373: ◇(◇Y1)→□(□(□(¬Y2))) ( Y_1 )→ ( ( ( Y_2 ) ) ) ↝ □(◇(Y1∧¬(◇Y2))) ( (Y_1 ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1332 T1374: ◇(◇(Y1∧Y2))→◇(□(¬Y3)) ( (Y_1 Y_2 ) )→ ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1333 T1375: ◇(◇(¬Y1))→□Y1 ( ( Y_1 ) )→ Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1334 T1376: ◇(◇(Y1∨Y2))→◇(□(¬Y3)) ( (Y_1 Y_2 ) )→ ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1335 T1377: ◇(◇(Y1∨Y2))→¬(◇Y3) ( (Y_1 Y_2 ) )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1336 T1379: ◇(¬(Y1∧Y2))→□Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1337 T1380: ◇(¬(Y1∧Y2))→◇Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1338 T1381: ◇(¬(Y1↔Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y2∨Y1)→Y3) ( (Y_2 Y_1 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1339 T1385: ◇(Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1340 T1388: ◇(Y1∨Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1341 T1389: ◇(Y1∨Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1342 T1390: ◇(Y1∨Y2)→◇(¬Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1343 T1391: ◇(Y1∨Y2)→¬(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1344 T1393: ◇(Y1∨◇Y1)→□Y1 (Y_1 Y_1 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1345 T1395: ◇(¬Y1∨¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1346 T1397: (Y1↔Y2)→□(◇Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1347 T1398: (Y1↔Y2)→◇Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1348 T1399: (Y1↔□Y1)→□Y2 (Y_1 Y_1 )→ Y_2 ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1349 T1401: (Y1↔¬(◇Y1))→□Y2 (Y_1 ( Y_1 ) )→ Y_2 ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1350 T1404: (¬Y1↔Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1351 T1405: (¬Y1↔□Y1)→◇Y2 ( Y_1 Y_1 )→ Y_2 ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1352 T1407: ((Y1∨Y2)→(◇Y1∨◇(◇Y1)))→Y1 ( (Y_1 Y_2 )→ ( Y_1 ( Y_1 ) ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1353 T1408: ((Y1∨Y2)→(◇(Y1∨Y2)∨◇(◇(Y1∨Y2))))→Y1 ( (Y_1 Y_2 )→ ( (Y_1 Y_2 ) ( (Y_1 Y_2 ) ) ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1354 T1414: ¬Y1→(◇Y2∧◇(◇Y2)) Y_1→ ( Y_2 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1355 T1416: ¬Y1→□Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1356 T1417: ¬Y1→□Y2 Y_1→ Y_2 ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1357 T1419: ¬Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1358 T1420: ¬Y1→□(¬Y2) Y_1→ ( Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1359 T1421: ¬Y1→◇Y1 Y_1→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1360 T1422: ¬Y1→◇Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1361 T1424: ¬Y1→◇(Y2∨Y3) Y_1→ (Y_2 Y_3 ) ↝ Y1→◇(Y3↔¬Y2)Y_1→ (Y_3 Y_2 ) 1 0.01% 1 0.03% Cluster 1362 T1425: ¬Y1→¬Y2 Y_1→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1363 T1426: ¬Y1→¬Y2 Y_1→ Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1364 T1427: ¬Y1→¬(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1365 T1428: ¬Y1→¬(Y2∧Y3) Y_1→ (Y_2 Y_3 ) ↝ ¬(Y2∨Y3)→Y1 (Y_2 Y_3 )→ Y_1 1 0.01% 1 0.03% Cluster 1366 T1429: ¬Y1→(□(¬Y1)∨□(□(¬Y1))) Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1367 T1430: ¬Y1→(□(¬Y1)∨□(◇(¬Y1))) Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1368 T1435: ¬(□Y1)→□Y2 ( Y_1 )→ Y_2 ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1369 T1437: ¬(□Y1)→¬Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1370 T1438: ¬(□Y1)→¬(Y2∨Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1371 T1442: ¬(◇Y1)→Y1 ( Y_1 )→ Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1372 T1443: ¬(◇Y1)→Y2 ( Y_1 )→ Y_2 ↝ Y2∧◇Y1Y_2 Y_1 1 0.01% 1 0.03% Cluster 1373 T1445: ¬(◇Y1)→Y2 ( Y_1 )→ Y_2 ↝ □Y1→¬Y2 Y_1→ Y_2 1 0.01% 1 0.03% Cluster 1374 T1447: ¬(◇Y1)→◇Y2 ( Y_1 )→ Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1375 T1448: ¬(◇Y1)→¬(Y2∨Y3) ( Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1376 T1450: ¬(◇(Y1∨Y2))→Y3 ( (Y_1 Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1377 T1457: (Y1∨Y2∨Y3)→¬Y4 (Y_1 Y_2 Y_3 )→ Y_4 ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 1378 T1458: (Y1∨Y2)→Y1 (Y_1 Y_2 )→ Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1379 T1462: (Y1∨Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1380 T1470: (Y1∨Y2)→¬Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1381 T1471: (Y1∨Y2)→¬(□Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1382 T1472: (Y1∨Y2)→¬(◇Y3) (Y_1 Y_2 )→ ( Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1383 T1473: (Y1∨□Y1∨Y2)→Y1 (Y_1 Y_1 Y_2 )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1384 T1478: (Y1∨□Y1)→◇Y2 (Y_1 Y_1 )→ Y_2 ↝ □Y2→(Y1∨◇Y1) Y_2→ (Y_1 Y_1 ) 1 0.01% 1 0.03% Cluster 1385 T1479: (Y1∨□Y1)→(Y2∨Y3) (Y_1 Y_1 )→ (Y_2 Y_3 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1386 T1484: (Y1∨◇Y2)→□Y3 (Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1387 T1488: (Y1∨¬Y2)→Y3 (Y_1 Y_2 )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1388 T1491: (□Y1∨□Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ Y3→◇(Y2↔¬Y1)Y_3→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1389 T1492: (□Y1∨□Y2)→Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1390 T1493: (□Y1∨□Y2)→□(□Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1391 T1494: (□Y1∨□Y2)→¬(□Y3) ( Y_1 Y_2 )→ ( Y_3 ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1392 T1496: (□Y1∨□(¬Y1))→□Y1 ( Y_1 ( Y_1 ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1393 T1497: (□(Y1∧Y2)∨□(◇(Y1∧Y2)))→Y1 ( (Y_1 Y_2 ) ( (Y_1 Y_2 ) ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1394 T1498: (□(◇Y1)∨□(◇Y2))→◇(□(□(¬Y3))) ( ( Y_1 ) ( Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1395 T1499: (□(¬Y1)∨□(¬Y2))→Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1396 T1500: (◇Y1∨□Y1)→Y2 ( Y_1 Y_1 )→ Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1397 T1505: (◇(□Y1)∨◇(□Y2))→□(□(¬Y3)) ( ( Y_1 ) ( Y_2 ) )→ ( ( Y_3 ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1398 T1507: (◇(◇Y1)∨◇(◇Y2))→◇(◇(¬(□Y3))) ( ( Y_1 ) ( Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1399 T1509: (◇(◇Y1)∨◇(◇Y2))→¬(◇(◇(□Y3))) ( ( Y_1 ) ( Y_2 ) )→ ( ( ( Y_3 ) ) ) ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1400 T1510: (◇(Y1∨Y2)∨□(Y1∨Y2))→Y1 ( (Y_1 Y_2 ) (Y_1 Y_2 ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1401 T1511: (◇(Y1∨Y2)∨◇(◇(Y1∨Y2)))→□Y1 ( (Y_1 Y_2 ) ( (Y_1 Y_2 ) ) )→ Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1402 T1514: (¬Y1∨¬Y2)→□Y3 ( Y_1 Y_2 )→ Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1403 T1515: (¬(□Y1)∨¬(□Y2))→Y3 ( ( Y_1 ) ( Y_2 ) )→ Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1404 T1517: ¬Y1 Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1405 T1520: ¬(Y1∧Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1406 T1524: ¬(Y1∧□Y2) (Y_1 Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1407 T1525: ¬(Y1∧□Y2) (Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1408 T1526: ¬(Y1∧□(¬(Y1∧◇Y2))) (Y_1 ( (Y_1 Y_2 ) ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1409 T1529: ¬(◇Y1∧□Y2) ( Y_1 Y_2 ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1410 T1534: ¬(□Y1) ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1411 T1537: ¬(□(Y1∧Y2)) ( (Y_1 Y_2 ) ) ↝ ◇(¬Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 1412 T1538: ¬(□(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1413 T1539: ¬(□((Y1∨Y2∨Y3)∧¬Y4)) ( ( (Y_1 Y_2 Y_3 ) Y_4 ) ) ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 1414 T1540: ¬(□(◇Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1415 T1541: ¬(□(Y1↔Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1416 T1548: ¬(□(Y1∨Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1417 T1553: ¬(◇Y1) ( Y_1 ) ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1418 T1554: ¬(◇(Y1∧◇Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1419 T1555: ¬(◇(Y1∧¬Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1420 T1556: ¬(◇(□Y1)) ( ( Y_1 ) ) ↝ □(¬Y1) ( Y_1 ) 1 0.01% 1 0.03% Cluster 1421 T1557: ¬(◇(□Y1)) ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1422 T1561: ¬(◇(Y1→Y2)) ( (Y_1→ Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1423 T1563: ¬(◇(Y1∨Y2)) ( (Y_1 Y_2 ) ) ↝ □(¬Y1∨¬Y2) ( Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1424 T1564: ¬(◇Y1↔◇Y2) ( Y_1 Y_2 ) ↝ ◇(Y1↔¬Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1425 T1565: ¬(◇Y1↔◇Y2) ( Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1426 T1567: ¬(Y1→¬Y2) (Y_1→ Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1427 T1568: ¬(□Y1→Y2) ( Y_1→ Y_2 ) ↝ □(¬Y2∨¬Y1) ( Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1428 T1569: ¬(□Y1→(Y2∨Y3)) ( Y_1→ (Y_2 Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1429 T1570: ¬(◇Y1→Y2) ( Y_1→ Y_2 ) ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1430 T1571: ¬(Y1∨Y2∨◇Y3) (Y_1 Y_2 Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1431 T1572: ¬(Y1∨Y2∨¬(□Y3)) (Y_1 Y_2 ( Y_3 ) ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1432 T1574: ¬(◇Y1∨◇Y2) ( Y_1 Y_2 ) ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1433 T1575: ¬(◇Y1∨◇Y2) ( Y_1 Y_2 ) ↝ □(Y1∧Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1434 T1576: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ ¬(□Y2) ( Y_2 ) 1 0.01% 1 0.03% Cluster 1435 T1577: Y1∨Y2∨□Y2Y_1 Y_2 Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1436 T1579: Y1∨Y2∨□Y3Y_1 Y_2 Y_3 ↝ □(Y3∨Y1∨Y2) (Y_3 Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1437 T1581: Y1∨Y2Y_1 Y_2 ↝ Y1∧◇Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1438 T1582: Y1∨Y2Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1439 T1591: Y1∨□Y2Y_1 Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1440 T1595: Y1∨□(◇(¬Y1))Y_1 ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1441 T1596: Y1∨□(¬Y2)Y_1 ( Y_2 ) ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1442 T1597: Y1∨□(¬Y2)Y_1 ( Y_2 ) ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1443 T1600: Y1∨□(Y1∨Y2)Y_1 (Y_1 Y_2 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1444 T1601: Y1∨◇Y1∨◇Y2∨◇(◇Y2)Y_1 Y_1 Y_2 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1445 T1605: Y1∨◇Y2∨◇(◇Y2)Y_1 Y_2 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1446 T1606: Y1∨◇Y2Y_1 Y_2 ↝ Y1∧¬(◇Y2)Y_1 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1447 T1608: Y1∨◇Y2Y_1 Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1448 T1613: Y1∨◇(Y2∧Y1)Y_1 (Y_2 Y_1 ) ↝ ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1449 T1617: Y1∨◇(□(¬Y1))∨□(¬Y1)Y_1 ( ( Y_1 ) ) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1450 T1619: Y1∨◇(◇Y1)Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1451 T1623: Y1∨◇(¬(Y2∧Y3))Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1452 T1624: Y1∨¬Y1∨□(¬Y1)Y_1 Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1453 T1625: Y1∨¬Y1∨◇(¬Y1)Y_1 Y_1 ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1454 T1626: Y1∨¬Y2Y_1 Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1455 T1628: Y1∨¬(Y2∧Y3)Y_1 (Y_2 Y_3 ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1456 T1629: Y1∨¬(□Y1)∨¬(□(□Y1))Y_1 ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1457 T1631: Y1∨¬(◇Y1)∨◇Y1Y_1 ( Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1458 T1633: Y1∨¬(◇(Y2∧Y3))Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1459 T1634: (Y1∧Y2)∨Y1 (Y_1 Y_2 ) Y_1 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1460 T1636: (Y1∧Y2)∨Y3 (Y_1 Y_2 ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1461 T1638: (Y1∧Y2)∨(Y1∧Y2∧Y3)∨Y2 (Y_1 Y_2 ) (Y_1 Y_2 Y_3 ) Y_2 ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1462 T1642: (Y1∧Y2)∨(Y2∧□Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1463 T1644: (Y1∧Y2)∨(Y2∧◇Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1464 T1645: (Y1∧Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1465 T1646: (Y1∧Y2)∨(◇Y2∧◇(□Y2)) (Y_1 Y_2 ) ( Y_2 ( Y_2 ) ) ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1466 T1647: (Y1∧Y2)∨(¬Y1∧Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ ¬Y1↔Y2 Y_1 Y_2 1 0.01% 1 0.03% Cluster 1467 T1649: (Y1∧Y2)∨◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1468 T1651: (Y1∧Y2)∨¬(◇(¬Y2)) (Y_1 Y_2 ) ( ( Y_2 ) ) ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1469 T1652: (Y1∧Y2)∨¬(Y1∨Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1470 T1653: (Y1∧□Y1)∨(◇Y1∧□Y1) (Y_1 Y_1 ) ( Y_1 Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1471 T1654: (Y1∧□Y2)∨Y1 (Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1472 T1655: (Y1∧□Y2)∨(Y1∧□Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1473 T1656: (Y1∧□Y2)∨(Y1∧□(□Y2)) (Y_1 Y_2 ) (Y_1 ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1474 T1659: (Y1∧□Y2)∨◇Y1 (Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1475 T1660: (Y1∧□Y2)∨◇(◇Y2) (Y_1 Y_2 ) ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1476 T1661: (Y1∧□(¬Y1))∨◇(Y1∧□Y2) (Y_1 ( Y_1 ) ) (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1477 T1662: (Y1∧◇Y1)∨□Y1 (Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1478 T1663: (Y1∧◇Y2)∨Y1 (Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1479 T1664: (Y1∧◇Y2)∨(Y1∧□Y3) (Y_1 Y_2 ) (Y_1 Y_3 ) ↝ Y1→(Y3∨□Y1)Y_1→ (Y_3 Y_1 ) 1 0.01% 1 0.03% Cluster 1480 T1665: (Y1∧◇Y2)∨(Y1∧◇Y2) (Y_1 Y_2 ) (Y_1 Y_2 ) ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1481 T1666: (Y1∧◇Y2)∨(Y2∧◇Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1482 T1667: (Y1∧◇Y2)∨(◇Y1∧◇Y2) (Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1483 T1668: (Y1∧◇Y2)∨□Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1484 T1669: (Y1∧◇Y2)∨◇Y2 (Y_1 Y_2 ) Y_2 ↝ ◇Y2∨◇(◇Y2) Y_2 ( Y_2 ) 1 0.01% 1 0.03% Cluster 1485 T1670: (Y1∧◇Y2)∨¬Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→Y1Y_2→ Y_1 1 0.01% 1 0.03% Cluster 1486 T1671: (Y1∧◇(Y1∧◇Y2))∨(Y1∧◇Y2) (Y_1 (Y_1 Y_2 ) ) (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1487 T1672: (Y1∧◇(□Y2))∨(Y1∧□Y2) (Y_1 ( Y_2 ) ) (Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1488 T1673: (Y1∧◇(□Y2))∨◇(◇Y2) (Y_1 ( Y_2 ) ) ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1489 T1674: (Y1∧◇(¬Y1))∨Y1 (Y_1 ( Y_1 ) ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1490 T1675: (Y1∧◇(¬(Y1∧Y2)))∨(¬Y1∧◇(Y1∧Y2)) (Y_1 ( (Y_1 Y_2 ) ) ) ( Y_1 (Y_1 Y_2 ) ) ↝ ¬Y1↔◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1491 T1676: (Y1∧¬Y2∧¬Y3)∨(Y2∧¬Y1∧¬Y3)∨(Y3∧¬Y1∧¬Y2) (Y_1 Y_2 Y_3 ) (Y_2 Y_1 Y_3 ) (Y_3 Y_1 Y_2 ) ↝ □(Y1∨Y2∨Y3) (Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1492 T1677: (Y1∧¬Y2)∨Y2 (Y_1 Y_2 ) Y_2 ↝ □(¬(Y2∧Y1)) ( (Y_2 Y_1 ) ) 1 0.01% 1 0.03% Cluster 1493 T1680: (Y1∧¬Y2)∨(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ¬(Y1∨Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1494 T1682: (Y1∧¬Y2)∨◇Y1 (Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1495 T1683: (Y1∧¬Y2)∨◇(Y2∧¬Y1) (Y_1 Y_2 ) (Y_2 Y_1 ) ↝ ◇(Y1↔¬Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1496 T1685: (Y1∧¬Y4)∨(Y2∧¬Y4)∨(Y3∧¬Y4) (Y_1 Y_4 ) (Y_2 Y_4 ) (Y_3 Y_4 ) ↝ ◇(¬Y4) ( Y_4 ) 1 0.01% 1 0.03% Cluster 1497 T1687: (Y1∧¬(◇Y1)∧¬(◇(□Y2)))∨(¬Y1∧◇Y1∧◇(□Y2)) (Y_1 ( Y_1 ) ( ( Y_2 ) ) ) ( Y_1 Y_1 ( Y_2 ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1498 T1688: (Y1∧¬(◇Y1))∨¬Y1 (Y_1 ( Y_1 ) ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1499 T1689: (Y1∧¬(◇(Y1∧□Y2)))∨¬Y1∨◇(Y1∧□Y2) (Y_1 ( (Y_1 Y_2 ) ) ) Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1500 T1690: (Y1∧¬(Y1∨Y2))∨□Y3 (Y_1 (Y_1 Y_2 ) ) Y_3 ↝ Y3→(Y1∨□Y3)Y_3→ (Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 1501 T1692: (◇Y1∧◇(□Y2)∧¬Y1)∨(Y1∧¬(◇(Y1∧□Y2))) ( Y_1 ( Y_2 ) Y_1 ) (Y_1 ( (Y_1 Y_2 ) ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1502 T1697: (◇Y1∧□Y2)∨□Y1 ( Y_1 Y_2 ) Y_1 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1503 T1698: (◇Y1∧□Y2)∨◇(Y2∧◇Y1) ( Y_1 Y_2 ) (Y_2 Y_1 ) ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1504 T1699: (◇Y1∧□Y2)∨◇(◇Y1) ( Y_1 Y_2 ) ( Y_1 ) ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1505 T1700: (◇Y1∧◇Y2)∨(◇Y1∧◇Y2) ( Y_1 Y_2 ) ( Y_1 Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1506 T1701: (◇Y1∧◇Y2)∨◇(◇Y2) ( Y_1 Y_2 ) ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1507 T1702: (◇Y1∧◇(◇Y1))∨Y2 ( Y_1 ( Y_1 ) ) Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1508 T1703: (◇Y1∧◇(◇Y2))∨Y1 ( Y_1 ( Y_2 ) ) Y_1 ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1509 T1704: (◇(¬Y1)∧□Y1)∨¬Y1 ( ( Y_1 ) Y_1 ) Y_1 ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1510 T1705: ((◇Y1→◇(□Y2))∧¬Y1)∨(Y1∧¬(◇Y1→◇(□Y2))) ( ( Y_1→ ( Y_2 ) ) Y_1 ) (Y_1 ( Y_1→ ( Y_2 ) ) ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1511 T1706: (¬(□Y1)∧□Y2)∨(¬(□Y1)∧□Y3) ( ( Y_1 ) Y_2 ) ( ( Y_1 ) Y_3 ) ↝ □(◇((Y2∨Y3)∧¬(◇Y1))) ( ( (Y_2 Y_3 ) ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1512 T1710: □Y1∨□Y2∨□Y3∨□Y4∨□Y5 Y_1 Y_2 Y_3 Y_4 Y_5 ↝ □(Y2∨Y3∨Y4) (Y_2 Y_3 Y_4 ) 1 0.01% 1 0.03% Cluster 1513 T1716: □Y1∨□(□Y1) Y_1 ( Y_1 ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 1514 T1718: □Y1∨□(¬(Y2∨Y3)) Y_1 ( (Y_2 Y_3 ) ) ↝ □(¬(Y2∨Y3)→Y1) ( (Y_2 Y_3 )→ Y_1 ) 1 0.01% 1 0.03% Cluster 1515 T1719: □((Y1∨Y2)∧□Y1)∨□Y1 ( (Y_1 Y_2 ) Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1516 T1720: □((Y1∨Y2)∧¬Y3)∨□(Y3∧¬(Y1∨Y2)) ( (Y_1 Y_2 ) Y_3 ) (Y_3 (Y_1 Y_2 ) ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1517 T1722: □(Y1→(Y1∨Y2))∨□Y1 (Y_1→ (Y_1 Y_2 ) ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1518 T1723: □(◇(Y1∨Y2)→Y1)∨□Y1 ( (Y_1 Y_2 )→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1519 T1726: □(Y1∨Y2)∨□(¬Y3) (Y_1 Y_2 ) ( Y_3 ) ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1520 T1727: □(Y1∨□Y1)∨□Y1 (Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1521 T1729: ◇Y1∨□Y2 Y_1 Y_2 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1522 T1731: ◇Y1∨□(□(□Y1)) Y_1 ( ( Y_1 ) ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1523 T1734: ◇Y1∨◇Y2 Y_1 Y_2 ↝ Y1∧□(Y1∧Y2)Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1524 T1737: ◇Y1∨◇(◇Y1) Y_1 ( Y_1 ) ↝ □Y1 Y_1 1 0.01% 1 0.03% Cluster 1525 T1739: ◇Y1∨◇(◇Y2) Y_1 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1526 T1740: ◇Y1∨◇(◇(□Y1)) Y_1 ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1527 T1741: ◇(Y1∧Y2)∨□Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1528 T1742: ◇(Y1∧Y2)∨◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1529 T1743: ◇(Y1∧◇Y2)∨◇Y2 (Y_1 Y_2 ) Y_2 ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1530 T1744: ◇(Y1∧◇Y2)∨◇(◇Y2) (Y_1 Y_2 ) ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1531 T1745: ◇(◇Y1∧□Y1)∨□Y1 ( Y_1 Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1532 T1746: ◇(¬Y1∧¬Y2)∨□(¬Y3) ( Y_1 Y_2 ) ( Y_3 ) ↝ ◇(¬Y1∧¬Y2∧□Y3) ( Y_1 Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1533 T1750: ◇(◇Y1)∨□(□Y1) ( Y_1 ) ( Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1534 T1751: ◇(◇Y1)∨◇(◇(◇Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1535 T1753: ◇(Y1→(Y1∨Y2))∨□Y1 (Y_1→ (Y_1 Y_2 ) ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1536 T1754: ◇((Y1∨Y2)→Y1)∨□Y1 ( (Y_1 Y_2 )→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1537 T1755: ◇(¬Y1)∨□Y1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1538 T1756: ◇(¬Y1)∨□(◇Y1) ( Y_1 ) ( Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1539 T1757: ◇(¬Y1)∨□(◇(¬Y1)) ( Y_1 ) ( ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1540 T1761: ◇(¬(Y1∨Y2))∨□Y3 ( (Y_1 Y_2 ) ) Y_3 ↝ □(¬(Y1∨Y2)→Y3) ( (Y_1 Y_2 )→ Y_3 ) 1 0.01% 1 0.03% Cluster 1541 T1763: ◇(Y1∨Y2)∨◇Y1 (Y_1 Y_2 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1542 T1766: (Y1↔Y3)∨(Y2↔Y3) (Y_1 Y_3 ) (Y_2 Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1543 T1767: (□Y2↔□Y1)∨(□Y3↔□Y1) ( Y_2 Y_1 ) ( Y_3 Y_1 ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1544 T1772: (Y1→Y2)∨◇Y2 (Y_1→ Y_2 ) Y_2 ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1545 T1774: (Y1→Y2)∨(Y1→□Y2) (Y_1→ Y_2 ) (Y_1→ Y_2 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1546 T1777: (Y1→□Y1)∨□Y1 (Y_1→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1547 T1778: (Y1→□Y1)∨(◇Y1→Y1) (Y_1→ Y_1 ) ( Y_1→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1548 T1779: (Y1→□Y2)∨◇(◇(◇Y2)) (Y_1→ Y_2 ) ( ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1549 T1782: (Y1→□(□Y3))∨(Y2→□(□Y3)) (Y_1→ ( Y_3 ) ) (Y_2→ ( Y_3 ) ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1550 T1783: (Y1→□(¬Y1))∨(Y1→□(□(¬Y1))) (Y_1→ ( Y_1 ) ) (Y_1→ ( ( Y_1 ) ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1551 T1784: (Y1→◇Y1)∨(Y1→□Y1) (Y_1→ Y_1 ) (Y_1→ Y_1 ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1552 T1786: (Y1→◇Y2)∨(Y1→◇(¬Y2)) (Y_1→ Y_2 ) (Y_1→ ( Y_2 ) ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1553 T1787: (Y1→◇Y2)∨(Y3→◇Y2) (Y_1→ Y_2 ) (Y_3→ Y_2 ) ↝ □Y2→¬(Y1↔Y3) Y_2→ (Y_1 Y_3 ) 1 0.01% 1 0.03% Cluster 1554 T1788: (Y1→◇(□Y2))∨(Y1→□(◇Y3)) (Y_1→ ( Y_2 ) ) (Y_1→ ( Y_3 ) ) ↝ □Y1→¬(Y2↔Y3) Y_1→ (Y_2 Y_3 ) 1 0.01% 1 0.03% Cluster 1555 T1796: (□Y1→¬Y1)∨(□Y1→□(¬Y1)) ( Y_1→ Y_1 ) ( Y_1→ ( Y_1 ) ) ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1556 T1797: (□(Y1∨Y2)→□Y1)∨□Y1 ( (Y_1 Y_2 )→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1557 T1798: (◇Y1→Y1)∨□Y1 ( Y_1→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1558 T1799: (◇Y1→Y1)∨(□Y1→Y1) ( Y_1→ Y_1 ) ( Y_1→ Y_1 ) ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1559 T1800: (◇Y1→Y2)∨□(◇Y1) ( Y_1→ Y_2 ) ( Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1560 T1801: (◇Y1→Y2)∨(□Y1→Y2) ( Y_1→ Y_2 ) ( Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1561 T1802: (◇Y1→□Y1)∨□Y1 ( Y_1→ Y_1 ) Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1562 T1803: (◇Y1→□Y2)∨□(◇Y1) ( Y_1→ Y_2 ) ( Y_1 ) ↝ Y1→(Y2∨□Y1)Y_1→ (Y_2 Y_1 ) 1 0.01% 1 0.03% Cluster 1563 T1804: (◇Y1→((Y1∨Y2)→Y2))∨(□Y1→Y2) ( Y_1→ ( (Y_1 Y_2 )→ Y_2 ) ) ( Y_1→ Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1564 T1805: (◇(◇Y1)→◇(◇(□(¬Y2))))∨(◇(◇Y3)→◇(◇(□(¬Y2)))) ( ( Y_1 )→ ( ( ( Y_2 ) ) ) ) ( ( Y_3 )→ ( ( ( Y_2 ) ) ) ) ↝ □(◇((Y1∨Y3)∧¬(◇Y2))) ( ( (Y_1 Y_3 ) ( Y_2 ) ) ) 1 0.01% 1 0.03% Cluster 1565 T1807: ((Y1∨¬Y2)→□Y3)∨((Y2∨¬Y1)→□Y3) ( (Y_1 Y_2 )→ Y_3 ) ( (Y_2 Y_1 )→ Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1566 T1808: ¬Y1∨□Y1 Y_1 Y_1 ↝ Y1∨□(¬Y1)Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1567 T1809: ¬Y1∨□(Y1∧◇Y2) Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧□Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1568 T1811: ¬Y1∨□(¬Y1) Y_1 ( Y_1 ) ↝ Y1→◇(¬Y1)Y_1→ ( Y_1 ) 1 0.01% 1 0.03% Cluster 1569 T1815: ¬Y1∨◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) ↝ ¬Y1↔◇(Y1∧Y2) Y_1 (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1570 T1816: ¬Y1∨◇(◇Y2) Y_1 ( Y_2 ) ↝ Y1→(◇Y2∨◇(◇Y2))Y_1→ ( Y_2 ( Y_2 ) ) 1 0.01% 1 0.03% Cluster 1571 T1817: ¬Y1∨¬Y2 Y_1 Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1572 T1819: ¬Y1∨¬Y2 Y_1 Y_2 ↝ Y1∨Y2Y_1 Y_2 1 0.01% 1 0.03% Cluster 1573 T1820: ¬(Y1∧Y2)∨□Y2 (Y_1 Y_2 ) Y_2 ↝ Y2→(Y1∨□Y2)Y_2→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1574 T1821: ¬(□Y1)∨◇Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1575 T1823: ¬(◇Y1)∨□(◇Y2) ( Y_1 ) ( Y_2 ) ↝ □(◇(Y2∧¬(◇Y1))) ( (Y_2 ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1576 T1825: ¬(◇Y1)∨◇Y2 ( Y_1 ) Y_2 ↝ □(¬(Y1∧Y2)) ( (Y_1 Y_2 ) ) 1 0.01% 1 0.03% Cluster 1577 T1828: Y1∨Y2∨Y3Y_1 Y_2 Y_3 ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1578 T1830: Y1∨Y2∨□(¬Y3)Y_1 Y_2 ( Y_3 ) ↝ □Y3→¬(Y1↔Y2) Y_3→ (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1579 T1831: Y1∨◇Y1∨Y2Y_1 Y_1 Y_2 ↝ Y2→(◇Y1∨◇(◇Y1))Y_2→ ( Y_1 ( Y_1 ) ) 1 0.01% 1 0.03% Cluster 1580 T1832: Y1∨◇Y1∨□Y1Y_1 Y_1 Y_1 ↝ □Y1∧□(□Y1) Y_1 ( Y_1 ) 1 0.01% 1 0.03% Cluster 1581 T1833: Y1∨¬Y2∨Y2∨¬Y1Y_1 Y_2 Y_2 Y_1 ↝ ¬(Y1↔Y2) (Y_1 Y_2 ) 1 0.01% 1 0.03% Cluster 1582 T1834: □(¬Y1)∨□(□(¬Y1))∨Y1 ( Y_1 ) ( ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1583 T1835: ◇(◇Y1)∨◇(◇Y2)∨□Y3 ( Y_1 ) ( Y_2 ) Y_3 ↝ □(◇((Y1∨Y2)∧¬(◇Y3))) ( ( (Y_1 Y_2 ) ( Y_3 ) ) ) 1 0.01% 1 0.03% Cluster 1584 T1836: ◇(¬Y1)∨◇(◇(¬Y1))∨□Y1 ( Y_1 ) ( ( Y_1 ) ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% Cluster 1585 T1837: ¬Y1∨□(¬Y1)∨Y1 Y_1 ( Y_1 ) Y_1 ↝ Y1→(◇(¬Y1)∨◇(◇(¬Y1)))Y_1→ ( ( Y_1 ) ( ( Y_1 ) ) ) 1 0.01% 1 0.03% B.5. CTL: Hierarchical Clustering of Transformations Table 40. Transformation hierarchy clusters Transformations # % #dst %dst Whole data set 7210 100.00% 2695 100.00% ANY transformation explained 2588 35.89% 409 15.18% Cluster 1 T2: Y1Y_1 ↝ Y1AGY_1 215 2.98% 9 0.33% T304: ¬Y1 Y_1 ↝ (¬Y1)AG ( Y_1 ) 36 0.50% 2 0.07% T222: (¬Y1)EF ( Y_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 28 0.39% 1 0.04% T199: Y1EFY_1 ↝ (Y1)AG (EFY_1 ) 27 0.37% 2 0.07% T262: Y1EXY_1 ↝ (Y1)AG (EXY_1 ) 23 0.32% 1 0.04% Cluster 2 T145: Y1AXY_1 ↝ Y1AGY_1 179 2.48% 6 0.22% T174: (Y1)AX (EFY_1 ) ↝ (Y1)AG (EFY_1 ) 18 0.25% 1 0.04% T192: (¬Y1)AX ( Y_1 ) ↝ (¬Y1)AG ( Y_1 ) 6 0.08% 1 0.04% Cluster 3 T11: Y1AFY_1 ↝ Y1AGY_1 119 1.65% 10 0.37% T46: (¬Y1)AF ( Y_1 ) ↝ (¬Y1)AG ( Y_1 ) 25 0.35% 2 0.07% T205: ((¬Y1))EF (AF ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 24 0.33% 1 0.04% T36: (Y1)AF (EFY_1 ) ↝ (Y1)AG (EFY_1 ) 16 0.22% 2 0.07% T17: (Y1)AF (AFY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 4 T148: Y1AXY_1 ↝ (Y1)AG (EXY_1 ) 107 1.48% 1 0.04% Cluster 5 T12: Y1AFY_1 ↝ (Y1)AG (EFY_1 ) 99 1.37% 2 0.07% Cluster 6 T265: Y1EXY_1 ↝ Y1EFY_1 96 1.33% 8 0.30% T112: (Y1)AG (EXY_1 ) ↝ (Y1)AG (EFY_1 ) 8 0.11% 2 0.07% T270: ((¬Y1))EX (AG ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 5 0.07% 1 0.04% Cluster 7 T151: Y1AXY_1 ↝ Y1EXY_1 94 1.30% 3 0.11% T86: (Y1)AG (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 84 1.17% 1 0.04% T314: ¬(Y1) (AXY_1 ) ↝ ¬(Y1) (EXY_1 ) 6 0.08% 1 0.04% T299: Y1→Y2EFY_1 _2 ↝ Y1→Y2EFY_1 _2 4 0.06% 1 0.04% Cluster 8 T7: Y1Y_1 ↝ Y1EFY_1 90 1.25% 6 0.22% T53: Y1AGY_1 ↝ (Y1)AG (EFY_1 ) 69 0.96% 2 0.07% T124: (¬Y1)AG ( Y_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 8 0.11% 1 0.04% T129: Y1∧Y2Y_1 Y_2 ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 9 T1: Y1Y_1 ↝ Y1AFY_1 71 0.98% 3 0.11% T52: Y1AGY_1 ↝ (Y1)AG (AFY_1 ) 58 0.80% 1 0.04% T51: Y1AGY_1 ↝ (Y1)AF (AGY_1 ) 5 0.07% 1 0.04% Cluster 10 T285: ((Y1))EX (EX (EFY_1 ) ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 70 0.97% 1 0.04% Cluster 11 T231: Y1EGY_1 ↝ Y1EFY_1 55 0.76% 7 0.26% T107: (Y1)AG (EGY_1 ) ↝ (Y1)AG (EFY_1 ) 5 0.07% 2 0.07% Cluster 12 ⌈ == T8: Y1Y_1 ↝ Y1EXY_1 54 0.75% 1 0.04% ⌊ == T54: Y1AGY_1 ↝ (Y1)AG (EXY_1 ) 54 0.75% 1 0.04% Cluster 13 T282: (Y1)EX (EXY_1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 48 0.67% 1 0.04% Cluster 14 T59: (Y1)AG (AFY_1 ) ↝ (Y1)AF (AGY_1 ) 45 0.62% 1 0.04% Cluster 15 T15: Y1AFY_1 ↝ Y1EFY_1 44 0.61% 7 0.26% T62: (Y1)AG (AFY_1 ) ↝ (Y1)AG (EFY_1 ) 36 0.50% 2 0.07% T24: (Y1)AF (AGY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% Cluster 16 T196: Y1EFY_1 ↝ Y1AFY_1 40 0.55% 3 0.11% T93: (Y1)AG (EFY_1 ) ↝ (Y1)AG (AFY_1 ) 17 0.24% 1 0.04% Cluster 17 T138: ¬(Y1)∧Y2 (EXY_1 ) Y_2 ↝ Y2→(¬Y1)Y_2 ( Y_1 ) 36 0.50% 1 0.04% Cluster 18 T90: (Y1)AG (EFY_1 ) ↝ (Y1)AF (AGY_1 ) 34 0.47% 1 0.04% Cluster 19 T14: Y1AFY_1 ↝ Y1AXY_1 33 0.46% 2 0.07% Cluster 20 T6: Y1Y_1 ↝ Y1AXY_1 32 0.44% 3 0.11% T115: (Y1→Y2)AG (Y_1→ Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 29 0.40% 1 0.04% Cluster 21 T263: Y1EXY_1 ↝ Y1AXY_1 30 0.42% 2 0.07% Cluster 22 T142: (Y1Y2)A (Y_1UY_2 ) ↝ (Y1Y2)E (Y_1UY_2 ) 27 0.37% 2 0.07% Cluster 23 T13: Y1AFY_1 ↝ (Y1)AG (EXY_1 ) 27 0.37% 1 0.04% Cluster 24 T143: Y1AXY_1 ↝ Y1Y_1 26 0.36% 8 0.30% T83: (Y1)AG (AXY_1 ) ↝ Y1AGY_1 6 0.08% 2 0.07% T156: (Y1)AX (AGY_1 ) ↝ Y1AGY_1 2 0.03% 1 0.04% T176: (Y1)AX (EFY_1 ) ↝ Y1EFY_1 1 0.01% 1 0.04% Cluster 25 T258: Y1EXY_1 ↝ Y1Y_1 25 0.35% 7 0.26% T110: (Y1)AG (EXY_1 ) ↝ Y1AGY_1 3 0.04% 1 0.04% ⌈ == T284: (Y1)EX (EXY_1 ) ↝ Y1EXY_1 1 0.01% 1 0.04% || == T321: ¬(Y1) (EXY_1 ) ↝ ¬Y1 Y_1 1 0.01% 1 0.04% ⌊ == T322: ¬((Y1)) (EX (EXY_1 ) ) ↝ ¬(Y1) (EXY_1 ) 1 0.01% 1 0.04% Cluster 26 T50: Y1AGY_1 ↝ Y1AFY_1 24 0.33% 3 0.11% T72: (Y1)AG (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 17 0.24% 1 0.04% Cluster 27 T49: Y1AGY_1 ↝ Y1Y_1 23 0.32% 5 0.19% T87: (Y1)AG (AXY_1 ) ↝ Y1AXY_1 2 0.03% 1 0.04% T96: (Y1)AG (EFY_1 ) ↝ Y1EFY_1 1 0.01% 1 0.04% Cluster 28 T147: Y1AXY_1 ↝ (Y1)AG (EFY_1 ) 23 0.32% 2 0.07% Cluster 29 T56: Y1AGY_1 ↝ Y1AXY_1 20 0.28% 3 0.11% Cluster 30 T169: (Y1)AX (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 20 0.28% 1 0.04% Cluster 31 T246: (¬Y1)EG ( Y_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 20 0.28% 1 0.04% Cluster 32 T152: (Y1)AX (AFY_1 ) ↝ (Y1)AG (EFY_1 ) 19 0.26% 2 0.07% Cluster 33 T150: Y1AXY_1 ↝ Y1EFY_1 18 0.25% 7 0.26% T85: (Y1)AG (AXY_1 ) ↝ (Y1)AG (EFY_1 ) 8 0.11% 2 0.07% T160: (Y1)AX (AGY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% Cluster 34 T210: (Y1∧Y2)EF (Y_1 Y_2 ) ↝ (Y2Y1)E (Y_2UY_1 ) 18 0.25% 1 0.04% Cluster 35 T197: Y1EFY_1 ↝ Y1AGY_1 16 0.22% 7 0.26% T217: (Y1)EF (EXY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 36 T226: Y1EGY_1 ↝ Y1AGY_1 16 0.22% 5 0.19% T241: (Y1)EG (EFY_1 ) ↝ (Y1)AG (EFY_1 ) 3 0.04% 1 0.04% Cluster 37 T201: Y1EFY_1 ↝ Y1AXY_1 16 0.22% 2 0.07% Cluster 38 T33: (Y1)AF (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 16 0.22% 1 0.04% Cluster 39 T218: ((Y1))EF (EX (EXY_1 ) ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 16 0.22% 1 0.04% Cluster 40 T259: Y1EXY_1 ↝ Y1AGY_1 15 0.21% 5 0.19% Cluster 41 T127: (¬(Y1))AG ( (EFY_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 15 0.21% 1 0.04% Cluster 42 T57: Y1AGY_1 ↝ Y1EFY_1 13 0.18% 4 0.15% Cluster 43 ⌈ == T223: (¬(Y1))EF ( (AGY_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 13 0.18% 1 0.04% ⌊ == T308: ¬(Y1) (AGY_1 ) ↝ (¬Y1)AG ( Y_1 ) 13 0.18% 1 0.04% Cluster 44 T306: ¬(Y1) (AFY_1 ) ↝ (¬Y1)AG ( Y_1 ) 11 0.15% 2 0.07% Cluster 45 T109: ((¬Y1))AG (EG ( Y_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 11 0.15% 1 0.04% Cluster 46 T195: Y1EFY_1 ↝ Y1Y_1 10 0.14% 4 0.15% T92: (Y1)AG (EFY_1 ) ↝ Y1AGY_1 1 0.01% 1 0.04% Cluster 47 T42: (Y1→Y2)AF (Y_1→ Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 10 0.14% 1 0.04% Cluster 48 T135: ¬Y1∧(¬Y1∧Y1) Y_1 ( Y_1 _1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 10 0.14% 1 0.04% Cluster 49 T303: ¬Y1 Y_1 ↝ Y1Y_1 9 0.12% 6 0.22% T323: ¬((¬Y1)) (EX ( Y_1 ) ) ↝ ¬(Y1) (EXY_1 ) 2 0.03% 1 0.04% T123: (¬Y1)AG ( Y_1 ) ↝ Y1AGY_1 1 0.01% 1 0.04% T311: ¬(Y1) (AXY_1 ) ↝ Y1AXY_1 1 0.01% 1 0.04% Cluster 50 T21: (Y1)AF (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 9 0.12% 1 0.04% Cluster 51 T29: (Y1∧Y2)AF (AXY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 9 0.12% 1 0.04% Cluster 52 T122: (Y1→Y2)AG (EXY_1 _2 ) ↝ Y1→Y2EFY_1 _2 9 0.12% 1 0.04% Cluster 53 T228: Y1EGY_1 ↝ (Y1)AG (EFY_1 ) 9 0.12% 1 0.04% Cluster 54 T144: Y1AXY_1 ↝ Y1AFY_1 8 0.11% 2 0.07% T84: (Y1)AG (AXY_1 ) ↝ (Y1)AG (AFY_1 ) 6 0.08% 1 0.04% Cluster 55 T89: (Y1)AG (EFY_1 ) ↝ Y1AFY_1 8 0.11% 1 0.04% Cluster 56 T234: (Y1)EG (AFY_1 ) ↝ (Y1)EF (AGY_1 ) 8 0.11% 1 0.04% Cluster 57 T276: (Y1)EX (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 8 0.11% 1 0.04% Cluster 58 T130: Y1∧Y2Y_1 _2 ↝ (Y2)AG (EXY_2 ) 7 0.10% 4 0.15% Cluster 59 T225: Y1EGY_1 ↝ Y1AFY_1 7 0.10% 2 0.07% T106: (Y1)AG (EGY_1 ) ↝ (Y1)AG (AFY_1 ) 5 0.07% 1 0.04% Cluster 60 T18: (Y1)AF (AFY_1 ) ↝ (Y1)AG (EFY_1 ) 7 0.10% 1 0.04% Cluster 61 T43: (Y1→Y2)AF (Y_1 _2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 7 0.10% 1 0.04% Cluster 62 T261: Y1EXY_1 ↝ (Y1)AG (EFY_1 ) 7 0.10% 1 0.04% Cluster 63 T9: Y1AFY_1 ↝ Y1Y_1 6 0.08% 6 0.22% T61: (Y1)AG (AFY_1 ) ↝ Y1AGY_1 2 0.03% 2 0.07% T20: (Y1)AF (AGY_1 ) ↝ Y1AGY_1 1 0.01% 1 0.04% Cluster 64 T22: (Y1)AF (AGY_1 ) ↝ (Y1)AG (EFY_1 ) 6 0.08% 2 0.07% Cluster 65 T111: (Y1)AG (EXY_1 ) ↝ (Y1)AG (AFY_1 ) 6 0.08% 1 0.04% Cluster 66 T158: (Y1)AX (AGY_1 ) ↝ (Y1)AG (EFY_1 ) 6 0.08% 1 0.04% Cluster 67 T229: Y1EGY_1 ↝ (Y1)AG (EXY_1 ) 6 0.08% 1 0.04% Cluster 68 T230: Y1EGY_1 ↝ Y1AXY_1 6 0.08% 1 0.04% Cluster 69 T266: (Y1)EX (AFY_1 ) ↝ (Y1)EF (AGY_1 ) 6 0.08% 1 0.04% Cluster 70 T312: ¬(Y1) (AXY_1 ) ↝ (¬Y1)AX ( Y_1 ) 6 0.08% 1 0.04% Cluster 71 T75: (Y1∧Y2)AG (Y_1 Y_2 ) ↝ Y1AGY_1 5 0.07% 3 0.11% Cluster 72 T4: Y1Y_1 ↝ (Y1)AG (EXY_1 ) 5 0.07% 1 0.04% Cluster 73 T88: ((¬Y1))AG (AX ( Y_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 5 0.07% 1 0.04% Cluster 74 T146: Y1AXY_1 ↝ (Y1)AG (AFY_1 ) 5 0.07% 1 0.04% Cluster 75 T219: (Y1→Y2)EF (Y_1→ Y_2 ) ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 5 0.07% 1 0.04% Cluster 76 T283: (Y1)EX (EXY_1 ) ↝ Y1EFY_1 5 0.07% 1 0.04% Cluster 77 T300: Y1→Y2EGY_1 _2 ↝ Y1→Y2Y_1 _2 5 0.07% 1 0.04% Cluster 78 T302: ¬(Y1)→¬(Y2) (EXY_1 )→ (EXY_2 ) ↝ Y2→Y1EFY_2 _1 5 0.07% 1 0.04% Cluster 79 T252: Y1↔Y2Y_1 Y_2 ↝ Y1→Y2Y_1→ Y_2 4 0.06% 3 0.11% T255: Y1↔Y2EFY_1 _2 ↝ Y1→Y2EFY_1 _2 1 0.01% 1 0.04% Cluster 80 T168: (Y1)AX (AXY_1 ) ↝ (Y1)AG (EFY_1 ) 4 0.06% 2 0.07% Cluster 81 T16: Y1AFY_1 ↝ (Y1)EF (AGY_1 ) 4 0.06% 1 0.04% Cluster 82 T27: (Y1∧Y1)AF (AFY_1 Y_1 ) ↝ (Y1)AG (AFY_1 ) 4 0.06% 1 0.04% Cluster 83 T125: (¬(Y1))AG ( (AFY_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 4 0.06% 1 0.04% Cluster 84 T139: ¬((Y1))∧Y1 (EX (EXY_1 ) ) _1 ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 4 0.06% 1 0.04% Cluster 85 T141: ¬((Y1))∧¬(Y1)∧¬Y1∧Y1 (EX (EXY_1 ) ) (EXY_1 ) Y_1 _1 ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 4 0.06% 1 0.04% Cluster 86 T163: (Y1∧Y2)AX (Y_1 Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 4 0.06% 1 0.04% Cluster 87 T206: (Y1)EF (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 4 0.06% 1 0.04% Cluster 88 T213: (Y1)EF (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 4 0.06% 1 0.04% Cluster 89 T227: Y1EGY_1 ↝ (Y1)AG (AFY_1 ) 4 0.06% 1 0.04% Cluster 90 T289: (¬Y1)EX ( Y_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 4 0.06% 1 0.04% Cluster 91 T293: Y1→Y2Y_1→ Y_2 ↝ (Y1→Y2)AG (Y_1 _2 ) 4 0.06% 1 0.04% Cluster 92 T114: (Y1)AG (EXY_1 ) ↝ Y1EFY_1 3 0.04% 3 0.11% Cluster 93 T38: (Y1)AF (EGY_1 ) ↝ (Y1)AG (AFY_1 ) 3 0.04% 1 0.04% Cluster 94 T76: (Y1∧Y2)AG (Y_1 Y_2 ) ↝ (Y1∨Y2)AG (Y_1 Y_2 ) 3 0.04% 1 0.04% Cluster 95 T91: (Y1)AG (EFY_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 96 ⌈ == T97: (Y1)AG (EFY_1 ) ↝ (Y1)EF (AGY_1 ) 3 0.04% 1 0.04% ⌊ == T102: ((¬Y1))AG (EF ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 97 T101: ((Y1))AG (EF (EGY_1 ) ) ↝ (Y1)AF (AGY_1 ) 3 0.04% 1 0.04% Cluster 98 T103: ((¬(Y1)))AG (EF ( (EFY_1 ) ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 99 T121: (Y1→Y2)AG (EXY_1 _2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 3 0.04% 1 0.04% Cluster 100 T131: Y1∧Y2EFY_1 _2 ↝ Y1→Y2EFY_1 _2 3 0.04% 1 0.04% Cluster 101 T159: (Y1)AX (AGY_1 ) ↝ (Y1)AG (EXY_1 ) 3 0.04% 1 0.04% Cluster 102 T162: ((Y1))AX (AG (AXY_1 ) ) ↝ (Y1)AG (EXY_1 ) 3 0.04% 1 0.04% Cluster 103 T198: Y1EFY_1 ↝ (Y1)AG (AFY_1 ) 3 0.04% 1 0.04% Cluster 104 T221: (¬Y1)EF ( Y_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 105 T236: (Y1)EG (AGY_1 ) ↝ (Y1)AG (EFY_1 ) 3 0.04% 1 0.04% Cluster 106 T238: (Y1)EG (AXY_1 ) ↝ (Y1)AG (EXY_1 ) 3 0.04% 1 0.04% Cluster 107 T242: (Y1)EG (EFY_1 ) ↝ (Y1)EF (AGY_1 ) 3 0.04% 1 0.04% Cluster 108 T248: (¬(Y1))EG ( (AGY_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 109 T264: Y1EXY_1 ↝ (¬Y1)AX ( Y_1 ) 3 0.04% 1 0.04% Cluster 110 T292: Y1→Y2Y_1→ Y_2 ↝ (Y1→Y2)AG (Y_1 _2 ) 3 0.04% 1 0.04% Cluster 111 T318: ¬(Y1) (EFY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 3 0.04% 1 0.04% Cluster 112 T32: (Y1)AF (AXY_1 ) ↝ (Y1)AG (EFY_1 ) 2 0.03% 2 0.07% Cluster 113 T65: (Y1)AG (AFY_1 ) ↝ Y1EFY_1 2 0.03% 2 0.07% Cluster 114 T194: (Y1∨Y2)AX (Y_1 Y_2 ) ↝ Y1AGY_1 2 0.03% 2 0.07% Cluster 115 T202: Y1EFY_1 ↝ Y1EXY_1 2 0.03% 2 0.07% T94: (Y1)AG (EFY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 116 T203: (Y1)EF (AFY_1 ) ↝ (Y1)AG (EFY_1 ) 2 0.03% 2 0.07% Cluster 117 T256: (Y1Y2)E (Y_1UY_2 ) ↝ (Y1→Y2)AG (Y_1→ Y_2 ) 2 0.03% 2 0.07% Cluster 118 T3: Y1Y_1 ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 119 T26: (Y1∧Y2)AF (Y_1 Y_2 ) ↝ (Y1∨Y2)AG (Y_1 Y_2 ) 2 0.03% 1 0.04% Cluster 120 T30: (Y1∧Y2)AF (EFY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 2 0.03% 1 0.04% Cluster 121 T31: (Y1)AF (AXY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 122 T39: (Y1)AF (EGY_1 ) ↝ (Y1)AG (EXY_1 ) 2 0.03% 1 0.04% Cluster 123 T48: (¬(Y1))AF ( (EFY_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 124 T55: Y1AGY_1 ↝ (¬Y1)AG ( Y_1 ) 2 0.03% 1 0.04% Cluster 125 T60: (Y1)AG (AFY_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 126 T64: (Y1)AG (AFY_1 ) ↝ Y1AXY_1 2 0.03% 1 0.04% Cluster 127 T69: ((Y1→Y2))AG (AF (Y_1→ Y_2 ) ) ↝ (Y1→Y2)AG (Y_1 _2 ) 2 0.03% 1 0.04% Cluster 128 T78: (Y1∧Y1)AG (EFY_1 Y_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 129 T79: (Y1∧Y2)AG (EFY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 2 0.03% 1 0.04% Cluster 130 T81: (¬Y1∧Y1)AG ( Y_1 _1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 2 0.03% 1 0.04% Cluster 131 T82: (¬Y1∧Y1)AG ( Y_1 _1 ) ↝ (Y1)AG (EXY_1 ) 2 0.03% 1 0.04% Cluster 132 T95: (Y1)AG (EFY_1 ) ↝ Y1AXY_1 2 0.03% 1 0.04% Cluster 133 T134: ¬Y1∧(¬Y1) Y_1 ( Y_1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 2 0.03% 1 0.04% Cluster 134 T155: ((¬Y1))AX (AF ( Y_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 135 T157: (Y1)AX (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 136 T164: (Y1∧Y2)AX (EXY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 2 0.03% 1 0.04% Cluster 137 T175: (Y1)AX (EFY_1 ) ↝ (Y1)AG (EXY_1 ) 2 0.03% 1 0.04% Cluster 138 ⌈ == T182: (Y1)AX (EXY_1 ) ↝ Y1AGY_1 2 0.03% 1 0.04% ⌊ == T186: ((Y1))AX (EX (EXY_1 ) ) ↝ (Y1)AG (EXY_1 ) 2 0.03% 1 0.04% Cluster 139 T183: (Y1)AX (EXY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 140 T187: (Y1→Y2)AX (Y_1→ Y_2 ) ↝ (Y2∧Y1)EF (Y_2 Y_1 ) 2 0.03% 1 0.04% Cluster 141 T191: (Y1→Y2)AX (EXY_1 _2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 2 0.03% 1 0.04% Cluster 142 T200: Y1EFY_1 ↝ (Y1)AG (EXY_1 ) 2 0.03% 1 0.04% Cluster 143 T207: (Y1)EF (AGY_1 ) ↝ (Y1)AG (EFY_1 ) 2 0.03% 1 0.04% Cluster 144 T216: ((Y2Y1))EF (E (Y_2UY_1 ) ) ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 2 0.03% 1 0.04% Cluster 145 T240: (Y1)EG (EFY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 146 T250: (¬(Y1))EG ( (EFY_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 147 T253: Y1↔Y2Y_1 _2 ↝ (Y1→Y2)AG (Y_1 _2 ) 2 0.03% 1 0.04% Cluster 148 T267: (Y1)EX (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 149 T268: (Y1)EX (AGY_1 ) ↝ (Y1)AG (EFY_1 ) 2 0.03% 1 0.04% Cluster 150 T278: ((¬Y1))EX (AX ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 151 T279: (Y1)EX (EGY_1 ) ↝ (Y1)EF (AGY_1 ) 2 0.03% 1 0.04% Cluster 152 T291: (Y1∨Y2)EX (Y_1 Y_2 ) ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 2 0.03% 1 0.04% Cluster 153 T296: Y1→Y2Y_1 _2 ↝ (Y1→Y2)AG (Y_1 _2 ) 2 0.03% 1 0.04% Cluster 154 T297: Y1→Y2Y_1 _2 ↝ Y1→Y2Y_1 _2 2 0.03% 1 0.04% Cluster 155 T309: ¬(Y1) (AGY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 2 0.03% 1 0.04% Cluster 156 T317: ¬(Y1) (EFY_1 ) ↝ (¬Y1)AX ( Y_1 ) 2 0.03% 1 0.04% Cluster 157 T320: ¬((¬Y1)) (EG ( Y_1 ) ) ↝ (Y1)AG (AFY_1 ) 2 0.03% 1 0.04% Cluster 158 T324: (¬Y1∧¬Y2)∨(¬Y1∧Y2)∨(¬Y2∧Y1) ( Y_1 Y_2 ) ( Y_1 Y_2 ) ( Y_2 Y_1 ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 2 0.03% 1 0.04% Cluster 159 T5: Y1Y_1 ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 160 T10: Y1AFY_1 ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 161 T19: ((Y1→Y2))AF (AF (Y_1→ Y_2 ) ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 162 T23: (Y1)AF (AGY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 163 T25: ((Y1→Y2))AF (AG (Y_1→ Y_2 ) ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 164 T28: (Y1∧Y1)AF (AGY_1 Y_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 165 T34: (Y1)AF (AXY_1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 166 T35: (Y1)AF (EFY_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 167 T37: (Y1)AF (EFY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% Cluster 168 T40: ((Y1))AF (EG (AXY_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 169 T41: (Y1)AF (EXY_1 ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 170 T44: (¬Y1→Y2)AF ( Y_1→ Y_2 ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 171 T45: (¬Y1)AF ( Y_1 ) ↝ Y1AGY_1 1 0.01% 1 0.04% Cluster 172 T47: (¬(Y1∧Y2))AF ( (Y_1 Y_2 ) ) ↝ ((Y1∨Y2))AG (EF (Y_1 Y_2 ) ) 1 0.01% 1 0.04% Cluster 173 T58: Y1AGY_1 ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 174 T63: (Y1)AG (AFY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 175 ⌈ == T66: (Y1)AG (AFY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% ⌊ == T71: ((¬Y1))AG (AF ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 176 T67: ((Y1))AG (AF (AFY_1 ) ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 177 T68: ((Y1))AG (AF (AXY_1 ) ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 178 T70: ((¬Y1))AG (AF ( Y_1 ) ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 179 T73: (Y1)AG (AGY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 180 T74: ((Y1))AG (AG (EFY_1 ) ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 181 T77: (Y1∧Y2)AG (AFY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 182 T80: (Y1∧Y2)AG (EGY_1 Y_2 ) ↝ (Y1∧Y2)AX (EFY_1 Y_2 ) 1 0.01% 1 0.04% Cluster 183 T98: (Y1)AG (EFY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 184 T99: ((Y1))AG (EF (AFY_1 ) ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 185 T100: ((Y1))AG (EF (AXY_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 186 T104: ((¬(Y1)))AG (EF ( (EXY_1 ) ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 187 T105: (((¬Y1∧Y2)∨(¬Y2∧Y1)))AG (EF ( ( Y_1 Y_2 ) ( Y_2 Y_1 ) ) ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 188 T108: (Y1)AG (EGY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% Cluster 189 T113: (Y1)AG (EXY_1 ) ↝ Y1AXY_1 1 0.01% 1 0.04% Cluster 190 T116: (Y1→Y1)AG (Y_1 _1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 191 T117: (Y1→Y2)AG (EFY_1→ Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 192 T118: (Y1→Y2)AG (EFY_1 _2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 193 T119: (Y1→Y2)AG (EGY_1→ Y_2 ) ↝ Y1→Y2EFY_1→ Y_2 1 0.01% 1 0.04% Cluster 194 T120: (Y1→Y2)AG (EXY_1→ Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 195 T126: (¬(Y1))AG ( (AGY_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 196 T128: (¬Y1∨Y1)AG ( Y_1 Y_1 ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 197 T132: ¬Y1∧Y2 Y_1 Y_2 ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 198 T133: ¬Y1∧Y1∧(¬Y1) Y_1 _1 ( Y_1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 199 T136: ¬(Y1∧Y2)∧(¬(Y1∧Y2)) (Y_1 Y_2 ) ( (Y_1 Y_2 ) ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 200 T137: ¬(Y1)∧Y2 (EFY_1 ) _2 ↝ (Y1∧Y2)AX (EFY_1 Y_2 ) 1 0.01% 1 0.04% Cluster 201 T140: ¬((Y1))∧¬(Y1)∧Y1 (EX (EXY_1 ) ) (EXY_1 ) _1 ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 202 T149: Y1AXY_1 ↝ (¬Y1)AX ( Y_1 ) 1 0.01% 1 0.04% Cluster 203 T153: (Y1)AX (AFY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 204 T154: (Y1)AX (AFY_1 ) ↝ Y1EFY_1 1 0.01% 1 0.04% Cluster 205 T161: ((Y1))AX (AG (AFY_1 ) ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 206 T165: (¬Y1∧Y1)AX ( Y_1 _1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 207 T166: (¬Y1∧Y1)AX ( Y_1 _1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 208 T167: (Y1)AX (AXY_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 209 T170: ((Y1))AX (AX (AGY_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 210 T171: ((Y1))AX (AX (AXY_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 211 T172: (Y1)AX (EFY_1 ) ↝ Y1AFY_1 1 0.01% 1 0.04% Cluster 212 T173: (Y1)AX (EFY_1 ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 213 T177: ((Y1↔¬Y2))AX (EF (Y_1 Y_2 ) ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 214 T178: (Y1)AX (EGY_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 215 T179: (Y1)AX (EGY_1 ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 216 T180: (Y1)AX (EGY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 217 T181: (Y1)AX (EXY_1 ) ↝ (Y1)AF (AGY_1 ) 1 0.01% 1 0.04% Cluster 218 T184: (Y1)AX (EXY_1 ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 219 T185: ((Y1))AX (EX (EGY_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 220 T188: (Y1→Y2)AX (Y_1 _2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 221 T189: (Y1→Y2)AX (Y_1 _2 ) ↝ (Y2∧Y1)AX (EFY_2 Y_1 ) 1 0.01% 1 0.04% Cluster 222 T190: (Y1→¬Y2)AX (Y_1→ Y_2 ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 223 T193: (¬Y1)AX ( Y_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 224 T204: (Y1)EF (AFY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 225 T208: (Y1∧Y2)EF (Y_1 Y_2 ) ↝ ((Y1∨Y2))AG (EF (Y_1 Y_2 ) ) 1 0.01% 1 0.04% Cluster 226 T209: (Y1∧Y2)EF (Y_1 Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 227 T211: (Y1∧Y1)EF (EFY_1 Y_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 228 T212: (¬Y1∧Y1)EF ( Y_1 _1 ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 229 T214: ((Y1))EF (EF (EFY_1 ) ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 230 T215: (Y1)EF (EGY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 231 T220: (¬Y1→Y2)EF ( Y_1→ Y_2 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 232 T224: (¬((¬Y1)))EF ( (EF ( Y_1 ) ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 233 T232: (Y1)EG (AFY_1 ) ↝ (Y1)AG (EFY_1 ) 1 0.01% 1 0.04% Cluster 234 T233: (Y1)EG (AFY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 235 T235: (Y1)EG (AGY_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 236 T237: (Y1)EG (AGY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 237 T239: ((¬Y1))EG (AX ( Y_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 238 T243: (Y1)EG (EGY_1 ) ↝ (Y1)EF (AGY_1 ) 1 0.01% 1 0.04% Cluster 239 T244: (Y1→Y2)EG (Y_1 _2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 240 T245: (¬Y1)EG ( Y_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 241 T247: (¬(Y1))EG ( (AFY_1 ) ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 242 T249: (¬((¬Y1)))EG ( (AG ( Y_1 ) ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 243 T251: (Y1∨Y2)EG (EFY_1 _2 ) ↝ ((Y1∨Y2))AG (EF (Y_1 Y_2 ) ) 1 0.01% 1 0.04% Cluster 244 T254: Y1↔Y2Y_1 _2 ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 245 T257: (Y1Y2)E (Y_1UEFY_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 246 T260: Y1EXY_1 ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 247 T269: (Y1)EX (AGY_1 ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 248 T271: (Y1∧Y2)EX (AFY_1 Y_2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 249 T272: (Y1∧Y1)EX (EFY_1 Y_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 250 T273: (Y1∧Y2)EX (EXY_1 Y_2 ) ↝ (Y1∧Y2)AX (EFY_1 Y_2 ) 1 0.01% 1 0.04% Cluster 251 T274: ((Y1)∧Y1)EX (EX (EFY_1 ) Y_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 252 T275: (¬Y1∧Y1)EX ( Y_1 _1 ) ↝ Y1EFY_1 1 0.01% 1 0.04% Cluster 253 T277: ((Y1))EX (AX (EFY_1 ) ) ↝ ¬(Y1)∧¬Y1∧Y1 (EXY_1 ) Y_1 _1 1 0.01% 1 0.04% Cluster 254 T280: (Y1↔Y2)EX (Y_1 Y_2 ) ↝ (Y1∧Y2)EF (Y_1 Y_2 ) 1 0.01% 1 0.04% Cluster 255 T281: (Y1)EX (EXY_1 ) ↝ (Y1)AG (AFY_1 ) 1 0.01% 1 0.04% Cluster 256 T286: (Y1→Y2)EX (Y_1→ Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 257 T287: (Y1→Y2)EX (Y_1 _2 ) ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 258 T288: (Y1→Y2)EX (EXY_1→ Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 259 T290: (¬(Y1))EX ( (AGY_1 ) ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 260 T294: Y1→(¬Y1∧Y2)Y_1 ( Y_1 Y_2 ) ↝ (Y1→Y2)AG (Y_1 _2 ) 1 0.01% 1 0.04% Cluster 261 T295: Y1→(¬Y2∧¬Y1∧Y3)Y_1 ( Y_2 Y_1 Y_3 ) ↝ (Y1→Y3)AG (Y_1 _3 ) 1 0.01% 1 0.04% Cluster 262 T298: (¬Y1∧Y2)→Y1 ( Y_1 Y_2 ) _1 ↝ (Y2→Y1)AG (Y_2 _1 ) 1 0.01% 1 0.04% Cluster 263 T301: (Y1→Y2)→(Y1→Y3) (Y_1 _2 )→ (Y_1 _3 ) ↝ Y2→Y3EFY_2 _3 1 0.01% 1 0.04% Cluster 264 T305: ¬(Y1) (AFY_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 265 T307: ¬(Y1) (AFY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 266 T310: ¬((Y1)) (AG (EXY_1 ) ) ↝ (¬Y1)AX ( Y_1 ) 1 0.01% 1 0.04% Cluster 267 T313: ¬(Y1) (AXY_1 ) ↝ ((¬Y1))EF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 268 T315: ¬((¬Y1)) (AX ( Y_1 ) ) ↝ (Y1)AG (EXY_1 ) 1 0.01% 1 0.04% Cluster 269 T316: ¬(Y1) (EFY_1 ) ↝ ((¬Y1))AF (AG ( Y_1 ) ) 1 0.01% 1 0.04% Cluster 270 T319: ¬(Y1) (EGY_1 ) ↝ (¬Y1)AG ( Y_1 ) 1 0.01% 1 0.04% Cluster 271 T325: (¬Y1∧Y2)∨(¬Y2∧Y1)AX ( Y_1 Y_2 ) ( Y_2 Y_1 ) ↝ (¬Y1∨¬Y2)AG ( Y_1 Y_2 ) 1 0.01% 1 0.04%