%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL524+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:21:07 AM UTC 2026
% Result : Theorem 0.64s 0.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL524+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 07:41:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.64/0.84 % Version : CSI_E---1.1
% 0.64/0.84 % Problem : theBenchmark.p
% 0.64/0.84 % Proof found!
% 0.64/0.84 % SZS status Theorem for theBenchmark.p
% 0.64/0.84 % SZS output start Proof
% 0.64/0.84 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/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_ponens)).
% 0.64/0.84 fof(and_3, axiom, (and_3<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', and_3)).
% 0.64/0.84 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X1=X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)).
% 0.64/0.84 fof(op_equiv, axiom, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_equiv)).
% 0.64/0.84 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.64/0.84 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.64/0.84 fof(implies_2, axiom, (implies_2<=>![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_2)).
% 0.64/0.84 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.64/0.84 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.64/0.84 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.64/0.84 fof(and_1, axiom, (and_1<=>![X1, X2]:is_a_theorem(implies(and(X1,X2),X1))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', and_1)).
% 0.64/0.84 fof(op_implies_and, axiom, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_and)).
% 0.64/0.84 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.64/0.84 fof(op_or, axiom, (op_or=>![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_or)).
% 0.64/0.84 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.64/0.84 fof(or_1, axiom, (or_1<=>![X1, X2]:is_a_theorem(implies(X1,or(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', or_1)).
% 0.64/0.84 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.64/0.84 fof(modus_tollens, axiom, (modus_tollens<=>![X1, X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_tollens)).
% 0.64/0.84 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)).
% 0.64/0.84 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 0.64/0.84 fof(implies_1, axiom, (implies_1<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_1)).
% 0.64/0.84 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.64/0.84 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/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_3)).
% 0.64/0.84 fof(axiom_M, axiom, (axiom_M<=>![X1]:is_a_theorem(implies(necessarily(X1),X1))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_M)).
% 0.64/0.84 fof(hilbert_implies_3, axiom, implies_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_3)).
% 0.64/0.84 fof(km5_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_axiom_M)).
% 0.64/0.84 fof(op_possibly, axiom, (op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax', op_possibly)).
% 0.64/0.84 fof(axiom_5, axiom, (axiom_5<=>![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_5)).
% 0.64/0.84 fof(km5_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_op_possibly)).
% 0.64/0.84 fof(axiom_B, axiom, (axiom_B<=>![X1]:is_a_theorem(implies(X1,necessarily(possibly(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_B)).
% 0.64/0.84 fof(km4b_axiom_B, conjecture, axiom_B, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', km4b_axiom_B)).
% 0.64/0.84 fof(km5_axiom_5, axiom, axiom_5, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_axiom_5)).
% 0.64/0.84 fof(c_0_32, plain, ![X117, X118]:((~modus_ponens|(~is_a_theorem(X117)|~is_a_theorem(implies(X117,X118))|is_a_theorem(X118)))&(((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])])])])])).
% 0.64/0.84 fof(c_0_33, plain, ![X151, X152]:((~and_3|is_a_theorem(implies(X151,implies(X152,and(X151,X152)))))&(~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])])])])).
% 0.64/0.84 fof(c_0_34, plain, ![X121, X122]:((~substitution_of_equivalents|(~is_a_theorem(equiv(X121,X122))|X121=X122))&((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])])])])])).
% 0.64/0.84 fof(c_0_35, plain, ![X235, X236]:(~op_equiv|equiv(X235,X236)=and(implies(X235,X236),implies(X236,X235))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])).
% 0.64/0.84 cnf(c_0_36, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.64/0.84 cnf(c_0_37, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.64/0.84 cnf(c_0_38, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.64/0.84 cnf(c_0_39, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.64/0.84 fof(c_0_40, plain, ![X133, X134]:((~implies_2|is_a_theorem(implies(implies(X133,implies(X133,X134)),implies(X133,X134))))&(~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])])])])).
% 0.64/0.84 cnf(c_0_41, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_34])).
% 0.64/0.84 cnf(c_0_42, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.64/0.84 cnf(c_0_43, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.64/0.84 cnf(c_0_44, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.64/0.84 cnf(c_0_45, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 0.64/0.84 cnf(c_0_46, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 0.64/0.84 cnf(c_0_47, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.64/0.84 cnf(c_0_48, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.64/0.84 cnf(c_0_49, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 0.64/0.84 cnf(c_0_50, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 0.64/0.84 cnf(c_0_51, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 0.64/0.84 cnf(c_0_52, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 0.64/0.84 fof(c_0_53, plain, ![X143, X144]:((~and_1|is_a_theorem(implies(and(X143,X144),X143)))&(~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])])])])).
% 0.64/0.84 fof(c_0_54, plain, ![X231, X232]:(~op_implies_and|implies(X231,X232)=not(and(X231,not(X232)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])).
% 0.64/0.84 cnf(c_0_55, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_49, c_0_50])).
% 0.64/0.84 cnf(c_0_56, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_45, c_0_51])).
% 0.64/0.84 cnf(c_0_57, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_45, c_0_52])).
% 0.64/0.84 cnf(c_0_58, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.64/0.84 cnf(c_0_59, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])).
% 0.64/0.84 fof(c_0_60, plain, ![X227, X228]:(~op_or|or(X227,X228)=not(and(not(X227),not(X228)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])).
% 0.64/0.84 cnf(c_0_61, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_54])).
% 0.64/0.84 cnf(c_0_62, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.64/0.84 fof(c_0_63, plain, ![X155, X156]:((~or_1|is_a_theorem(implies(X155,or(X155,X156))))&(~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])])])])).
% 0.64/0.84 cnf(c_0_64, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_55, c_0_56])).
% 0.64/0.84 cnf(c_0_65, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_57, c_0_46])).
% 0.64/0.84 cnf(c_0_66, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_59])])).
% 0.64/0.84 cnf(c_0_67, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_60])).
% 0.64/0.84 cnf(c_0_68, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 0.64/0.84 cnf(c_0_69, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.64/0.84 fof(c_0_70, plain, ![X125, X126]:((~modus_tollens|is_a_theorem(implies(implies(not(X126),not(X125)),implies(X125,X126))))&(~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])])])])).
% 0.64/0.84 cnf(c_0_71, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[c_0_63])).
% 0.64/0.84 cnf(c_0_72, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1])).
% 0.64/0.84 cnf(c_0_73, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66])])).
% 0.64/0.84 cnf(c_0_74, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68]), c_0_69])])).
% 0.64/0.84 cnf(c_0_75, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_70])).
% 0.64/0.84 cnf(c_0_76, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])).
% 0.64/0.84 cnf(c_0_77, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])).
% 0.64/0.84 cnf(c_0_78, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_73]), c_0_74])).
% 0.64/0.84 cnf(c_0_79, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_74]), c_0_76])])).
% 0.64/0.84 cnf(c_0_80, plain, (is_a_theorem(or(X1,or(not(X1),X2)))), inference(spm,[status(thm)],[c_0_77, c_0_74])).
% 0.64/0.84 cnf(c_0_81, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_77, c_0_78])).
% 0.64/0.84 cnf(c_0_82, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_45, c_0_79])).
% 0.64/0.84 cnf(c_0_83, plain, (is_a_theorem(or(X1,not(not(not(X1)))))), inference(spm,[status(thm)],[c_0_80, c_0_78])).
% 0.64/0.84 cnf(c_0_84, plain, (not(not(X1))=X1|~is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_81]), c_0_74])).
% 0.64/0.84 cnf(c_0_85, plain, (is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_74])).
% 0.64/0.84 fof(c_0_86, plain, ![X129, X130]:((~implies_1|is_a_theorem(implies(X129,implies(X130,X129))))&(~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])])])])).
% 0.64/0.84 cnf(c_0_87, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])).
% 0.64/0.84 cnf(c_0_88, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_86])).
% 0.64/0.84 cnf(c_0_89, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 0.64/0.84 cnf(c_0_90, plain, (not(and(X1,X2))=implies(X1,not(X2))), inference(spm,[status(thm)],[c_0_68, c_0_87])).
% 0.64/0.84 cnf(c_0_91, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88, c_0_89])])).
% 0.64/0.84 cnf(c_0_92, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(spm,[status(thm)],[c_0_87, c_0_90])).
% 0.64/0.84 cnf(c_0_93, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_74]), c_0_87])).
% 0.64/0.84 cnf(c_0_94, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_45, c_0_91])).
% 0.64/0.84 cnf(c_0_95, plain, (is_a_theorem(or(X1,and(X2,not(X1))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_51, c_0_74])).
% 0.64/0.84 cnf(c_0_96, plain, (and(X1,not(X2))=not(implies(X1,X2))), inference(spm,[status(thm)],[c_0_92, c_0_87])).
% 0.64/0.84 cnf(c_0_97, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_74, c_0_87])).
% 0.64/0.84 cnf(c_0_98, plain, (or(X1,X2)=or(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_93]), c_0_93])])).
% 0.64/0.84 fof(c_0_99, plain, ![X137, X138, X139]:((~implies_3|is_a_theorem(implies(implies(X137,X138),implies(implies(X138,X139),implies(X137,X139)))))&(~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])])])])).
% 0.64/0.84 cnf(c_0_100, plain, (X1=X2|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_64, c_0_94])).
% 0.64/0.84 fof(c_0_101, plain, ![X255]:((~axiom_M|is_a_theorem(implies(necessarily(X255),X255)))&(~is_a_theorem(implies(necessarily(esk65_0),esk65_0))|axiom_M)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])).
% 0.64/0.84 cnf(c_0_102, plain, (is_a_theorem(or(X1,not(implies(X2,X1))))|~is_a_theorem(X2)), inference(rw,[status(thm)],[c_0_95, c_0_96])).
% 0.64/0.84 cnf(c_0_103, plain, (or(X1,not(X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_97, c_0_98])).
% 0.64/0.84 cnf(c_0_104, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~implies_3), inference(split_conjunct,[status(thm)],[c_0_99])).
% 0.64/0.84 cnf(c_0_105, plain, (implies_3), inference(split_conjunct,[status(thm)],[hilbert_implies_3])).
% 0.64/0.84 cnf(c_0_106, plain, (X1=X2|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_100, c_0_94])).
% 0.64/0.84 cnf(c_0_107, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_57, c_0_91])).
% 0.64/0.84 cnf(c_0_108, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_101])).
% 0.64/0.84 cnf(c_0_109, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km5_axiom_M])).
% 0.64/0.84 cnf(c_0_110, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(rw,[status(thm)],[c_0_102, c_0_103])).
% 0.64/0.84 cnf(c_0_111, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105])])).
% 0.64/0.84 cnf(c_0_112, plain, (implies(X1,X1)=X2|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_106, c_0_107])).
% 0.64/0.84 cnf(c_0_113, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_109])])).
% 0.64/0.84 cnf(c_0_114, plain, (implies(X1,X2)=X2|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_110]), c_0_91])])).
% 0.64/0.84 cnf(c_0_115, plain, (is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_45, c_0_111])).
% 0.64/0.84 cnf(c_0_116, plain, (implies(X1,X1)=implies(necessarily(X2),X2)), inference(spm,[status(thm)],[c_0_112, c_0_113])).
% 0.64/0.84 cnf(c_0_117, plain, (implies(implies(X1,X1),X2)=X2), inference(spm,[status(thm)],[c_0_114, c_0_107])).
% 0.64/0.84 fof(c_0_118, plain, ![X315]:(~op_possibly|possibly(X315)=not(necessarily(not(X315)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])).
% 0.64/0.84 fof(c_0_119, plain, ![X261]:((~axiom_5|is_a_theorem(implies(possibly(X261),necessarily(possibly(X261)))))&(~is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0))))|axiom_5)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])).
% 0.64/0.84 cnf(c_0_120, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,necessarily(X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_117])).
% 0.64/0.84 cnf(c_0_121, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_118])).
% 0.64/0.84 cnf(c_0_122, plain, (op_possibly), inference(split_conjunct,[status(thm)],[km5_op_possibly])).
% 0.64/0.84 fof(c_0_123, plain, ![X259]:((~axiom_B|is_a_theorem(implies(X259,necessarily(possibly(X259)))))&(~is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0))))|axiom_B)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_B])])])])).
% 0.64/0.84 fof(c_0_124, negated_conjecture, ~axiom_B, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[km4b_axiom_B])])).
% 0.64/0.84 cnf(c_0_125, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5), inference(split_conjunct,[status(thm)],[c_0_119])).
% 0.64/0.84 cnf(c_0_126, plain, (axiom_5), inference(split_conjunct,[status(thm)],[km5_axiom_5])).
% 0.64/0.84 cnf(c_0_127, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,necessarily(X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_74]), c_0_74])).
% 0.64/0.84 cnf(c_0_128, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121, c_0_122])])).
% 0.64/0.84 cnf(c_0_129, plain, (axiom_B|~is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0))))), inference(split_conjunct,[status(thm)],[c_0_123])).
% 0.64/0.84 cnf(c_0_130, negated_conjecture, (~axiom_B), inference(split_conjunct,[status(thm)],[c_0_124])).
% 0.64/0.84 cnf(c_0_131, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125, c_0_126])])).
% 0.64/0.84 cnf(c_0_132, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(necessarily(X2),X1))), inference(spm,[status(thm)],[c_0_127, c_0_98])).
% 0.64/0.84 cnf(c_0_133, plain, (or(necessarily(not(X1)),X2)=implies(possibly(X1),X2)), inference(spm,[status(thm)],[c_0_74, c_0_128])).
% 0.64/0.84 cnf(c_0_134, plain, (~is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0))))), inference(sr,[status(thm)],[c_0_129, c_0_130])).
% 0.64/0.84 cnf(c_0_135, plain, (necessarily(possibly(X1))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_131]), c_0_113])])).
% 0.64/0.84 cnf(c_0_136, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(possibly(X1),X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_103])).
% 0.64/0.84 cnf(c_0_137, plain, (implies(X1,X1)=implies(X2,X2)), inference(spm,[status(thm)],[c_0_112, c_0_107])).
% 0.64/0.84 cnf(c_0_138, plain, (~is_a_theorem(implies(esk67_0,possibly(esk67_0)))), inference(rw,[status(thm)],[c_0_134, c_0_135])).
% 0.64/0.84 cnf(c_0_139, plain, (is_a_theorem(implies(X1,possibly(X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_107])])).
% 0.64/0.84 cnf(c_0_140, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_139])]), ['proof']).
% 0.64/0.84 % SZS output end Proof
% 0.64/0.84 % User time : 0.307 s
% 0.64/0.84 % System time : 0.031 s
% 0.64/0.84 % Total time : 0.338 s
% 0.64/0.84
%------------------------------------------------------------------------------