%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL451+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:25 PM UTC 2026
% Result : Theorem 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL451+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n023.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 22:36:53 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Theorem for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% 0.28/1.61 fof(kn3, axiom, (kn3<=>![X4, X5, X6]:is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn3)).
% 0.28/1.61 fof(or_3, axiom, (or_3<=>![X1, X2, X3]:is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_3)).
% 0.28/1.61 fof(r4, axiom, (r4<=>![X4, X5, X6]:is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r4)).
% 0.28/1.61 fof(r5, axiom, (r5<=>![X4, X5, X6]:is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r5)).
% 0.28/1.61 fof(cn1, axiom, (cn1<=>![X4, X5, X6]:is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', cn1)).
% 0.28/1.61 fof(equivalence_3, axiom, (equivalence_3<=>![X1, X2]:is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', equivalence_3)).
% 0.28/1.61 fof(implies_3, axiom, (implies_3<=>![X1, X2, X3]:is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_3)).
% 0.28/1.61 fof(implies_2, axiom, (implies_2<=>![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_2)).
% 0.28/1.61 fof(and_3, axiom, (and_3<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_3)).
% 0.28/1.61 fof(modus_tollens, axiom, (modus_tollens<=>![X1, X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_tollens)).
% 0.28/1.61 fof(r3, axiom, (r3<=>![X4, X5]:is_a_theorem(implies(or(X4,X5),or(X5,X4)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r3)).
% 0.28/1.61 fof(equivalence_2, axiom, (equivalence_2<=>![X1, X2]:is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', equivalence_2)).
% 0.28/1.61 fof(equivalence_1, axiom, (equivalence_1<=>![X1, X2]:is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', equivalence_1)).
% 0.28/1.61 fof(cn3, axiom, (cn3<=>![X4]:is_a_theorem(implies(implies(not(X4),X4),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', cn3)).
% 0.28/1.61 fof(cn2, axiom, (cn2<=>![X4, X5]:is_a_theorem(implies(X4,implies(not(X4),X5)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', cn2)).
% 0.28/1.61 fof(r1, axiom, (r1<=>![X4]:is_a_theorem(implies(or(X4,X4),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r1)).
% 0.28/1.61 fof(kn2, axiom, (kn2<=>![X4, X5]:is_a_theorem(implies(and(X4,X5),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn2)).
% 0.28/1.61 fof(and_2, axiom, (and_2<=>![X1, X2]:is_a_theorem(implies(and(X1,X2),X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_2)).
% 0.28/1.61 fof(and_1, axiom, (and_1<=>![X1, X2]:is_a_theorem(implies(and(X1,X2),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_1)).
% 0.28/1.61 fof(r2, axiom, (r2<=>![X4, X5]:is_a_theorem(implies(X5,or(X4,X5)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r2)).
% 0.28/1.61 fof(kn1, axiom, (kn1<=>![X4]:is_a_theorem(implies(X4,and(X4,X4)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn1)).
% 0.28/1.61 fof(or_2, axiom, (or_2<=>![X1, X2]:is_a_theorem(implies(X2,or(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_2)).
% 0.28/1.61 fof(or_1, axiom, (or_1<=>![X1, X2]:is_a_theorem(implies(X1,or(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_1)).
% 0.28/1.61 fof(implies_1, axiom, (implies_1<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_1)).
% 0.28/1.61 fof(op_equiv, axiom, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_equiv)).
% 0.28/1.61 fof(op_or, axiom, (op_or=>![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_or)).
% 0.28/1.61 fof(op_and, axiom, (op_and=>![X1, X2]:and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_and)).
% 0.28/1.61 fof(modus_ponens, axiom, (modus_ponens<=>![X1, X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))=>is_a_theorem(X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_ponens)).
% 0.28/1.61 fof(op_implies_and, axiom, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_and)).
% 0.28/1.61 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X1=X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)).
% 0.28/1.61 fof(op_implies_or, axiom, (op_implies_or=>![X1, X2]:implies(X1,X2)=or(not(X1),X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_or)).
% 0.28/1.61 fof(luka_cn1, conjecture, cn1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', luka_cn1)).
% 0.28/1.61 fof(luka_op_implies, axiom, op_implies, file('/export/starexec/sandbox/benchmark/theBenchmark.p', luka_op_implies)).
% 0.28/1.61 fof(luka_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/theBenchmark.p', luka_op_equiv)).
% 0.28/1.61 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.28/1.61 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.28/1.61 fof(luka_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/theBenchmark.p', luka_op_or)).
% 0.28/1.61 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.28/1.61 fof(hilbert_equivalence_3, axiom, equivalence_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_equivalence_3)).
% 0.28/1.61 fof(hilbert_equivalence_2, axiom, equivalence_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_equivalence_2)).
% 0.28/1.61 fof(hilbert_equivalence_1, axiom, equivalence_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_equivalence_1)).
% 0.28/1.61 fof(hilbert_or_3, axiom, or_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_3)).
% 0.28/1.61 fof(hilbert_or_2, axiom, or_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_2)).
% 0.28/1.61 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)).
% 0.28/1.61 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.28/1.61 fof(hilbert_and_2, axiom, and_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_2)).
% 0.28/1.61 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.28/1.61 fof(hilbert_implies_3, axiom, implies_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_3)).
% 0.28/1.61 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.28/1.61 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.28/1.61 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 0.28/1.61 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.28/1.61 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.28/1.61 fof(i_0_53, plain, ![X142, X143, X144]:((~kn3|is_a_theorem(implies(implies(X142,X143),implies(not(and(X143,X144)),not(and(X144,X142))))))&(~is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))|kn3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])).
% 0.28/1.61 fof(i_0_54, plain, ![X118, X119, X120]:((~or_3|is_a_theorem(implies(implies(X118,X120),implies(implies(X119,X120),implies(or(X118,X119),X120)))))&(~is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0))))|or_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])])).
% 0.28/1.61 fof(i_0_55, plain, ![X170, X171, X172]:((~r4|is_a_theorem(implies(or(X170,or(X171,X172)),or(X171,or(X170,X172)))))&(~is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))|r4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])).
% 0.28/1.61 fof(i_0_56, plain, ![X176, X177, X178]:((~r5|is_a_theorem(implies(implies(X177,X178),implies(or(X176,X177),or(X176,X178)))))&(~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))|r5)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])).
% 0.28/1.61 fof(i_0_57, plain, ![X148, X149, X150]:((~cn1|is_a_theorem(implies(implies(X148,X149),implies(implies(X149,X150),implies(X148,X150)))))&(~is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))|cn1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])])).
% 0.28/1.61 fof(i_0_58, plain, ![X132, X133]:((~equivalence_3|is_a_theorem(implies(implies(X132,X133),implies(implies(X133,X132),equiv(X132,X133)))))&(~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))|equivalence_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_3])])])])).
% 0.28/1.61 fof(i_0_59, plain, ![X92, X93, X94]:((~implies_3|is_a_theorem(implies(implies(X92,X93),implies(implies(X93,X94),implies(X92,X94)))))&(~is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))|implies_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])).
% 0.28/1.61 fof(i_0_60, plain, ![X88, X89]:((~implies_2|is_a_theorem(implies(implies(X88,implies(X88,X89)),implies(X88,X89))))&(~is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))|implies_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])).
% 0.28/1.61 fof(i_0_61, plain, ![X106, X107]:((~and_3|is_a_theorem(implies(X106,implies(X107,and(X106,X107)))))&(~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))|and_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])).
% 0.28/1.61 fof(i_0_62, plain, ![X80, X81]:((~modus_tollens|is_a_theorem(implies(implies(not(X81),not(X80)),implies(X80,X81))))&(~is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))|modus_tollens)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])).
% 0.28/1.61 fof(i_0_63, plain, ![X166, X167]:((~r3|is_a_theorem(implies(or(X166,X167),or(X167,X166))))&(~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))|r3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])).
% 0.28/1.61 fof(i_0_64, plain, ![X128, X129]:((~equivalence_2|is_a_theorem(implies(equiv(X128,X129),implies(X129,X128))))&(~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))|equivalence_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])).
% 0.28/1.61 fof(i_0_65, plain, ![X124, X125]:((~equivalence_1|is_a_theorem(implies(equiv(X124,X125),implies(X124,X125))))&(~is_a_theorem(implies(equiv(esk27_0,esk28_0),implies(esk27_0,esk28_0)))|equivalence_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_1])])])])).
% 0.28/1.61 fof(i_0_66, plain, ![X158]:((~cn3|is_a_theorem(implies(implies(not(X158),X158),X158)))&(~is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))|cn3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])])).
% 0.28/1.61 fof(i_0_67, plain, ![X154, X155]:((~cn2|is_a_theorem(implies(X154,implies(not(X154),X155))))&(~is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))|cn2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])])).
% 0.28/1.61 fof(i_0_68, plain, ![X160]:((~r1|is_a_theorem(implies(or(X160,X160),X160)))&(~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))|r1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])).
% 0.28/1.61 fof(i_0_69, plain, ![X138, X139]:((~kn2|is_a_theorem(implies(and(X138,X139),X138)))&(~is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))|kn2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])).
% 0.28/1.61 fof(i_0_70, plain, ![X102, X103]:((~and_2|is_a_theorem(implies(and(X102,X103),X103)))&(~is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))|and_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])).
% 0.28/1.61 fof(i_0_71, plain, ![X98, X99]:((~and_1|is_a_theorem(implies(and(X98,X99),X98)))&(~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))|and_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])).
% 0.28/1.61 fof(i_0_72, plain, ![X162, X163]:((~r2|is_a_theorem(implies(X163,or(X162,X163))))&(~is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))|r2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])).
% 0.28/1.61 fof(i_0_73, plain, ![X136]:((~kn1|is_a_theorem(implies(X136,and(X136,X136))))&(~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))|kn1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])).
% 0.28/1.61 fof(i_0_74, plain, ![X114, X115]:((~or_2|is_a_theorem(implies(X115,or(X114,X115))))&(~is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0)))|or_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_2])])])])).
% 0.28/1.61 fof(i_0_75, plain, ![X110, X111]:((~or_1|is_a_theorem(implies(X110,or(X110,X111))))&(~is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))|or_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])).
% 0.28/1.61 fof(i_0_76, plain, ![X84, X85]:((~implies_1|is_a_theorem(implies(X84,implies(X85,X84))))&(~is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))|implies_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])).
% 0.28/1.61 fof(i_0_77, plain, ![X190, X191]:(~op_equiv|equiv(X190,X191)=and(implies(X190,X191),implies(X191,X190))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])).
% 0.28/1.61 fof(i_0_78, plain, ![X182, X183]:(~op_or|or(X182,X183)=not(and(not(X182),not(X183)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])).
% 0.28/1.61 fof(i_0_79, plain, ![X184, X185]:(~op_and|and(X184,X185)=not(or(not(X184),not(X185)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])).
% 0.28/1.61 fof(i_0_80, plain, ![X72, X73]:((~modus_ponens|(~is_a_theorem(X72)|~is_a_theorem(implies(X72,X73))|is_a_theorem(X73)))&(((is_a_theorem(esk1_0)|modus_ponens)&(is_a_theorem(implies(esk1_0,esk2_0))|modus_ponens))&(~is_a_theorem(esk2_0)|modus_ponens))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])).
% 0.28/1.61 fof(i_0_81, plain, ![X186, X187]:(~op_implies_and|implies(X186,X187)=not(and(X186,not(X187)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])).
% 0.28/1.61 fof(i_0_82, plain, ![X76, X77]:((~substitution_of_equivalents|(~is_a_theorem(equiv(X76,X77))|X76=X77))&((is_a_theorem(equiv(esk3_0,esk4_0))|substitution_of_equivalents)&(esk3_0!=esk4_0|substitution_of_equivalents))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])).
% 0.28/1.61 fof(i_0_83, plain, ![X188, X189]:(~op_implies_or|implies(X188,X189)=or(not(X188),X189)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])).
% 0.28/1.61 fof(i_0_84, negated_conjecture, ~cn1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[luka_cn1])])).
% 0.28/1.61 cnf(i_0_85, plain, (kn3|~is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))), inference(split_conjunct,[status(thm)],[i_0_53]), ['final']).
% 0.28/1.61 cnf(i_0_86, plain, (or_3|~is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0))))), inference(split_conjunct,[status(thm)],[i_0_54]), ['final']).
% 0.28/1.61 cnf(i_0_87, plain, (is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))|~kn3), inference(split_conjunct,[status(thm)],[i_0_53]), ['final']).
% 0.28/1.61 cnf(i_0_88, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))|~or_3), inference(split_conjunct,[status(thm)],[i_0_54]), ['final']).
% 0.28/1.61 cnf(i_0_89, plain, (r4|~is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))), inference(split_conjunct,[status(thm)],[i_0_55]), ['final']).
% 0.28/1.61 cnf(i_0_90, plain, (r5|~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))), inference(split_conjunct,[status(thm)],[i_0_56]), ['final']).
% 0.28/1.61 cnf(i_0_91, plain, (cn1|~is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))), inference(split_conjunct,[status(thm)],[i_0_57]), ['final']).
% 0.28/1.61 cnf(i_0_92, plain, (equivalence_3|~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))), inference(split_conjunct,[status(thm)],[i_0_58]), ['final']).
% 0.28/1.61 cnf(i_0_93, plain, (implies_3|~is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))), inference(split_conjunct,[status(thm)],[i_0_59]), ['final']).
% 0.28/1.61 cnf(i_0_94, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4), inference(split_conjunct,[status(thm)],[i_0_55]), ['final']).
% 0.28/1.61 cnf(i_0_95, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5), inference(split_conjunct,[status(thm)],[i_0_56]), ['final']).
% 0.28/1.61 cnf(i_0_96, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))|~equivalence_3), inference(split_conjunct,[status(thm)],[i_0_58]), ['final']).
% 0.28/1.61 cnf(i_0_97, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~cn1), inference(split_conjunct,[status(thm)],[i_0_57]), ['final']).
% 0.28/1.61 cnf(i_0_98, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~implies_3), inference(split_conjunct,[status(thm)],[i_0_59]), ['final']).
% 0.28/1.61 cnf(i_0_99, plain, (implies_2|~is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))), inference(split_conjunct,[status(thm)],[i_0_60]), ['final']).
% 0.28/1.61 cnf(i_0_100, plain, (and_3|~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))), inference(split_conjunct,[status(thm)],[i_0_61]), ['final']).
% 0.28/1.61 cnf(i_0_101, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[i_0_60]), ['final']).
% 0.28/1.61 cnf(i_0_102, plain, (modus_tollens|~is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))), inference(split_conjunct,[status(thm)],[i_0_62]), ['final']).
% 0.28/1.61 cnf(i_0_103, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[i_0_61]), ['final']).
% 0.28/1.61 cnf(i_0_104, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[i_0_62]), ['final']).
% 0.28/1.61 cnf(i_0_105, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))), inference(split_conjunct,[status(thm)],[i_0_63]), ['final']).
% 0.28/1.61 cnf(i_0_106, plain, (equivalence_2|~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))), inference(split_conjunct,[status(thm)],[i_0_64]), ['final']).
% 0.28/1.61 cnf(i_0_107, plain, (equivalence_1|~is_a_theorem(implies(equiv(esk27_0,esk28_0),implies(esk27_0,esk28_0)))), inference(split_conjunct,[status(thm)],[i_0_65]), ['final']).
% 0.28/1.61 cnf(i_0_108, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3), inference(split_conjunct,[status(thm)],[i_0_63]), ['final']).
% 0.28/1.61 cnf(i_0_109, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))|~equivalence_1), inference(split_conjunct,[status(thm)],[i_0_65]), ['final']).
% 0.28/1.61 cnf(i_0_110, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))|~equivalence_2), inference(split_conjunct,[status(thm)],[i_0_64]), ['final']).
% 0.28/1.61 cnf(i_0_111, plain, (cn3|~is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))), inference(split_conjunct,[status(thm)],[i_0_66]), ['final']).
% 0.28/1.61 cnf(i_0_112, plain, (cn2|~is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))), inference(split_conjunct,[status(thm)],[i_0_67]), ['final']).
% 0.28/1.61 cnf(i_0_113, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))|~cn3), inference(split_conjunct,[status(thm)],[i_0_66]), ['final']).
% 0.28/1.61 cnf(i_0_114, plain, (is_a_theorem(implies(X1,implies(not(X1),X2)))|~cn2), inference(split_conjunct,[status(thm)],[i_0_67]), ['final']).
% 0.28/1.61 cnf(i_0_115, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(split_conjunct,[status(thm)],[i_0_68]), ['final']).
% 0.28/1.61 cnf(i_0_116, plain, (kn2|~is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))), inference(split_conjunct,[status(thm)],[i_0_69]), ['final']).
% 0.28/1.61 cnf(i_0_117, plain, (and_2|~is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))), inference(split_conjunct,[status(thm)],[i_0_70]), ['final']).
% 0.28/1.61 cnf(i_0_118, plain, (and_1|~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))), inference(split_conjunct,[status(thm)],[i_0_71]), ['final']).
% 0.28/1.61 cnf(i_0_119, plain, (r2|~is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))), inference(split_conjunct,[status(thm)],[i_0_72]), ['final']).
% 0.28/1.61 cnf(i_0_120, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))), inference(split_conjunct,[status(thm)],[i_0_73]), ['final']).
% 0.28/1.61 cnf(i_0_121, plain, (or_2|~is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0)))), inference(split_conjunct,[status(thm)],[i_0_74]), ['final']).
% 0.28/1.61 cnf(i_0_122, plain, (or_1|~is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))), inference(split_conjunct,[status(thm)],[i_0_75]), ['final']).
% 0.28/1.61 cnf(i_0_123, plain, (implies_1|~is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))), inference(split_conjunct,[status(thm)],[i_0_76]), ['final']).
% 0.28/1.61 cnf(i_0_124, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1), inference(split_conjunct,[status(thm)],[i_0_68]), ['final']).
% 0.28/1.61 cnf(i_0_125, plain, (is_a_theorem(implies(and(X1,X2),X1))|~kn2), inference(split_conjunct,[status(thm)],[i_0_69]), ['final']).
% 0.28/1.61 cnf(i_0_126, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[i_0_71]), ['final']).
% 0.28/1.61 cnf(i_0_127, plain, (is_a_theorem(implies(and(X1,X2),X2))|~and_2), inference(split_conjunct,[status(thm)],[i_0_70]), ['final']).
% 0.28/1.61 cnf(i_0_128, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[i_0_75]), ['final']).
% 0.28/1.61 cnf(i_0_129, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~r2), inference(split_conjunct,[status(thm)],[i_0_72]), ['final']).
% 0.28/1.61 cnf(i_0_130, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~or_2), inference(split_conjunct,[status(thm)],[i_0_74]), ['final']).
% 0.28/1.61 cnf(i_0_131, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1), inference(split_conjunct,[status(thm)],[i_0_73]), ['final']).
% 0.28/1.61 cnf(i_0_132, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[i_0_76]), ['final']).
% 0.28/1.61 cnf(i_0_133, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[i_0_77]), ['final']).
% 0.28/1.61 cnf(i_0_134, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[i_0_78]), ['final']).
% 0.28/1.61 cnf(i_0_135, plain, (and(X1,X2)=not(or(not(X1),not(X2)))|~op_and), inference(split_conjunct,[status(thm)],[i_0_79]), ['final']).
% 0.28/1.61 cnf(i_0_136, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[i_0_80]), ['final']).
% 0.28/1.61 cnf(i_0_137, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[i_0_81]), ['final']).
% 0.28/1.61 cnf(i_0_138, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[i_0_82]), ['final']).
% 0.28/1.61 cnf(i_0_139, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[i_0_83]), ['final']).
% 0.28/1.61 cnf(i_0_140, plain, (is_a_theorem(equiv(esk3_0,esk4_0))|substitution_of_equivalents), inference(split_conjunct,[status(thm)],[i_0_82]), ['final']).
% 0.28/1.61 cnf(i_0_141, plain, (is_a_theorem(implies(esk1_0,esk2_0))|modus_ponens), inference(split_conjunct,[status(thm)],[i_0_80]), ['final']).
% 0.28/1.61 cnf(i_0_142, plain, (modus_ponens|~is_a_theorem(esk2_0)), inference(split_conjunct,[status(thm)],[i_0_80]), ['final']).
% 0.28/1.61 cnf(i_0_143, plain, (is_a_theorem(esk1_0)|modus_ponens), inference(split_conjunct,[status(thm)],[i_0_80]), ['final']).
% 0.28/1.61 cnf(i_0_144, plain, (substitution_of_equivalents|esk3_0!=esk4_0), inference(split_conjunct,[status(thm)],[i_0_82]), ['final']).
% 0.28/1.61 cnf(i_0_145, negated_conjecture, (~cn1), inference(split_conjunct,[status(thm)],[i_0_84]), ['final']).
% 0.28/1.61 cnf(i_0_146, plain, (op_implies), inference(split_conjunct,[status(thm)],[luka_op_implies]), ['final']).
% 0.28/1.61 cnf(i_0_147, plain, (op_equiv), inference(split_conjunct,[status(thm)],[luka_op_equiv]), ['final']).
% 0.28/1.61 cnf(i_0_148, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv]), ['final']).
% 0.28/1.61 cnf(i_0_149, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]), ['final']).
% 0.28/1.61 cnf(i_0_150, plain, (op_or), inference(split_conjunct,[status(thm)],[luka_op_or]), ['final']).
% 0.28/1.61 cnf(i_0_151, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or]), ['final']).
% 0.28/1.61 cnf(i_0_152, plain, (equivalence_3), inference(split_conjunct,[status(thm)],[hilbert_equivalence_3]), ['final']).
% 0.28/1.61 cnf(i_0_153, plain, (equivalence_2), inference(split_conjunct,[status(thm)],[hilbert_equivalence_2]), ['final']).
% 0.28/1.61 cnf(i_0_154, plain, (equivalence_1), inference(split_conjunct,[status(thm)],[hilbert_equivalence_1]), ['final']).
% 0.28/1.61 cnf(i_0_155, plain, (or_3), inference(split_conjunct,[status(thm)],[hilbert_or_3]), ['final']).
% 0.28/1.61 cnf(i_0_156, plain, (or_2), inference(split_conjunct,[status(thm)],[hilbert_or_2]), ['final']).
% 0.28/1.61 cnf(i_0_157, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1]), ['final']).
% 0.28/1.61 cnf(i_0_158, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3]), ['final']).
% 0.28/1.61 cnf(i_0_159, plain, (and_2), inference(split_conjunct,[status(thm)],[hilbert_and_2]), ['final']).
% 0.28/1.61 cnf(i_0_160, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1]), ['final']).
% 0.28/1.61 cnf(i_0_161, plain, (implies_3), inference(split_conjunct,[status(thm)],[hilbert_implies_3]), ['final']).
% 0.28/1.61 cnf(i_0_162, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2]), ['final']).
% 0.28/1.61 cnf(i_0_163, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1]), ['final']).
% 0.28/1.61 cnf(i_0_164, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]), ['final']).
% 0.28/1.61 cnf(i_0_165, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]), ['final']).
% 0.28/1.61 cnf(i_0_166, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]), ['final']).
% 0.28/1.61 cnf(i_0_167, axiom, (X1=X1)).
% 0.28/1.61 cnf(i_0_168, axiom, (X1=X2|X2!=X1)).
% 0.28/1.61 cnf(i_0_169, axiom, (X1=X2|X1!=X3|X3!=X2)).
% 0.28/1.61 cnf(i_0_170, axiom, (X1!=X2|implies(X1,X3)=implies(X2,X3))).
% 0.28/1.61 cnf(i_0_171, axiom, (X1!=X2|implies(X3,X1)=implies(X3,X2))).
% 0.28/1.61 cnf(i_0_172, axiom, (X1!=X2|not(X1)=not(X2))).
% 0.28/1.61 cnf(i_0_173, axiom, (X1!=X2|and(X1,X3)=and(X2,X3))).
% 0.28/1.61 cnf(i_0_174, axiom, (X1!=X2|and(X3,X1)=and(X3,X2))).
% 0.28/1.61 cnf(i_0_175, axiom, (X1!=X2|or(X1,X3)=or(X2,X3))).
% 0.28/1.61 cnf(i_0_176, axiom, (X1!=X2|or(X3,X1)=or(X3,X2))).
% 0.28/1.61 cnf(i_0_177, axiom, (X1!=X2|equiv(X1,X3)=equiv(X2,X3))).
% 0.28/1.61 cnf(i_0_178, axiom, (X1!=X2|equiv(X3,X1)=equiv(X3,X2))).
% 0.28/1.61 cnf(i_0_179, axiom, (X1!=X2|~is_a_theorem(X1)|is_a_theorem(X2))).
% 0.28/1.64 cnf(i_0_167, axiom, (X1=X1)).
% 0.28/1.64 cnf(i_0_168, axiom, (X1=X2|X2!=X1)).
% 0.28/1.64 cnf(i_0_169, axiom, (X1=X2|X1!=X3|X3!=X2)).
% 0.28/1.64 cnf(i_0_170, axiom, (X1!=X2|implies(X1,X3)=implies(X2,X3))).
% 0.28/1.64 cnf(i_0_171, axiom, (X1!=X2|implies(X3,X1)=implies(X3,X2))).
% 0.28/1.64 cnf(i_0_172, axiom, (X1!=X2|not(X1)=not(X2))).
% 0.28/1.64 cnf(i_0_173, axiom, (X1!=X2|and(X1,X3)=and(X2,X3))).
% 0.28/1.64 cnf(i_0_174, axiom, (X1!=X2|and(X3,X1)=and(X3,X2))).
% 0.28/1.64 cnf(i_0_175, axiom, (X1!=X2|or(X1,X3)=or(X2,X3))).
% 0.28/1.64 cnf(i_0_176, axiom, (X1!=X2|or(X3,X1)=or(X3,X2))).
% 0.28/1.64 cnf(i_0_177, axiom, (X1!=X2|equiv(X1,X3)=equiv(X2,X3))).
% 0.28/1.64 cnf(i_0_178, axiom, (X1!=X2|equiv(X3,X1)=equiv(X3,X2))).
% 0.28/1.64 cnf(i_0_179, axiom, (X1!=X2|~is_a_theorem(X1)|is_a_theorem(X2))).
% 0.28/1.64 cnf(i_0_180, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))), inference(scs_inference,[],[i_0_155,i_0_88])).
% 0.28/1.64 cnf(i_0_181, plain, (~is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))), inference(scs_inference,[],[i_0_145,i_0_91])).
% 0.28/1.64 cnf(i_0_182, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))), inference(scs_inference,[],[i_0_152,i_0_96])).
% 0.28/1.64 cnf(i_0_183, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))), inference(scs_inference,[],[i_0_161,i_0_98])).
% 0.28/1.64 cnf(i_0_184, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(scs_inference,[],[i_0_162,i_0_101])).
% 0.28/1.64 cnf(i_0_185, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(scs_inference,[],[i_0_158,i_0_103])).
% 0.28/1.64 cnf(i_0_186, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))), inference(scs_inference,[],[i_0_164,i_0_104])).
% 0.28/1.64 cnf(i_0_187, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))), inference(scs_inference,[],[i_0_154,i_0_109])).
% 0.28/1.64 cnf(i_0_188, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))), inference(scs_inference,[],[i_0_153,i_0_110])).
% 0.28/1.64 cnf(i_0_189, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(scs_inference,[],[i_0_160,i_0_126])).
% 0.28/1.64 cnf(i_0_190, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(scs_inference,[],[i_0_159,i_0_127])).
% 0.28/1.64 cnf(i_0_191, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(scs_inference,[],[i_0_157,i_0_128])).
% 0.28/1.64 cnf(i_0_192, plain, (is_a_theorem(implies(X1,or(X2,X1)))), inference(scs_inference,[],[i_0_156,i_0_130])).
% 0.28/1.64 cnf(i_0_193, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(scs_inference,[],[i_0_163,i_0_132])).
% 0.28/1.64 cnf(i_0_194, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(scs_inference,[],[i_0_148,i_0_133])).
% 0.28/1.64 cnf(i_0_195, plain, (or(X1,X2)=not(and(not(X1),not(X2)))), inference(scs_inference,[],[i_0_151,i_0_134])).
% 0.28/1.64 cnf(i_0_196, plain, (is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))), inference(scs_inference,[],[i_0_166,i_0_136])).
% 0.28/1.64 cnf(i_0_197, plain, (implies(X1,X2)=not(and(X1,not(X2)))), inference(scs_inference,[],[i_0_149,i_0_137])).
% 0.28/1.64 cnf(i_0_198, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(scs_inference,[],[i_0_165,i_0_138])).
% 0.28/1.64 cnf(i_0_199,plain, ($false), inference(scs_inference,[],[i_0+181, i_0_183]), ['proof']).
% 0.28/1.64 % SZS output end CNFRefutation
% 0.28/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------