%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n011.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 11:21:08 AM UTC 2026
% Result : Theorem 0.52s 0.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 01:53:28 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.43 start to proof:theBenchmark.p
% 0.52/0.74 % Version : CSI_E---1.1
% 0.52/0.74 % Problem : theBenchmark.p
% 0.52/0.74 % Proof found!
% 0.52/0.74 % SZS status Theorem for theBenchmark.p
% 0.52/0.74 % SZS output start Proof
% 0.52/0.74 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)).
% 0.52/0.74 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)).
% 0.52/0.74 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)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.52/0.74 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.52/0.74 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.52/0.74 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.52/0.74 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)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)).
% 0.52/0.74 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 0.52/0.74 fof(necessitation, axiom, (necessitation<=>![X1]:(is_a_theorem(X1)=>is_a_theorem(necessarily(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', necessitation)).
% 0.52/0.74 fof(op_strict_implies, axiom, (op_strict_implies=>![X1, X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_strict_implies)).
% 0.52/0.74 fof(axiom_m1, axiom, (axiom_m1<=>![X1, X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m1)).
% 0.52/0.74 fof(s1_0_axiom_m1, conjecture, axiom_m1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_axiom_m1)).
% 0.52/0.74 fof(km5_necessitation, axiom, necessitation, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_necessitation)).
% 0.52/0.74 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_op_strict_implies)).
% 0.52/0.74 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)).
% 0.52/0.74 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.52/0.74 fof(c_0_28, 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])])])])])).
% 0.52/0.74 fof(c_0_29, 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])])])])).
% 0.52/0.74 fof(c_0_30, 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])])])])])).
% 0.52/0.74 fof(c_0_31, 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])])])).
% 0.52/0.74 cnf(c_0_32, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.52/0.74 cnf(c_0_33, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.52/0.74 cnf(c_0_34, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_29])).
% 0.52/0.74 cnf(c_0_35, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.52/0.74 fof(c_0_36, 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])])])])).
% 0.52/0.74 cnf(c_0_37, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_30])).
% 0.52/0.74 cnf(c_0_38, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.52/0.74 cnf(c_0_39, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.52/0.74 cnf(c_0_40, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.52/0.74 cnf(c_0_41, 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_32, c_0_33])])).
% 0.52/0.74 cnf(c_0_42, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 0.52/0.74 cnf(c_0_43, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_36])).
% 0.52/0.74 cnf(c_0_44, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.52/0.74 cnf(c_0_45, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 0.52/0.74 cnf(c_0_46, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 0.52/0.74 cnf(c_0_47, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 0.52/0.74 cnf(c_0_48, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 0.52/0.74 fof(c_0_49, 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])])])])).
% 0.52/0.74 fof(c_0_50, 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])])])).
% 0.52/0.74 cnf(c_0_51, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 0.52/0.74 cnf(c_0_52, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_41, c_0_47])).
% 0.52/0.74 cnf(c_0_53, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_41, c_0_48])).
% 0.52/0.74 cnf(c_0_54, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_49])).
% 0.52/0.74 cnf(c_0_55, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])).
% 0.52/0.74 fof(c_0_56, 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])])])).
% 0.52/0.74 cnf(c_0_57, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_50])).
% 0.52/0.74 cnf(c_0_58, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.52/0.74 fof(c_0_59, 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])])])])).
% 0.52/0.74 cnf(c_0_60, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 0.52/0.74 cnf(c_0_61, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_53, c_0_42])).
% 0.52/0.74 cnf(c_0_62, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 0.52/0.74 cnf(c_0_63, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_56])).
% 0.52/0.74 cnf(c_0_64, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 0.52/0.74 cnf(c_0_65, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.52/0.74 fof(c_0_66, 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])])])])).
% 0.52/0.74 cnf(c_0_67, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[c_0_59])).
% 0.52/0.74 cnf(c_0_68, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1])).
% 0.52/0.74 cnf(c_0_69, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_62])])).
% 0.52/0.74 cnf(c_0_70, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64]), c_0_65])])).
% 0.52/0.74 cnf(c_0_71, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.52/0.74 cnf(c_0_72, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])).
% 0.52/0.74 cnf(c_0_73, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 0.52/0.74 cnf(c_0_74, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_69]), c_0_70])).
% 0.52/0.74 cnf(c_0_75, 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_71, c_0_70]), c_0_72])])).
% 0.52/0.74 cnf(c_0_76, plain, (is_a_theorem(or(X1,or(not(X1),X2)))), inference(spm,[status(thm)],[c_0_73, c_0_70])).
% 0.52/0.74 cnf(c_0_77, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_73, c_0_74])).
% 0.52/0.74 cnf(c_0_78, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_41, c_0_75])).
% 0.52/0.74 cnf(c_0_79, plain, (is_a_theorem(or(X1,not(not(not(X1)))))), inference(spm,[status(thm)],[c_0_76, c_0_74])).
% 0.52/0.74 cnf(c_0_80, plain, (not(not(X1))=X1|~is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_77]), c_0_70])).
% 0.52/0.74 cnf(c_0_81, plain, (is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_70])).
% 0.52/0.74 cnf(c_0_82, plain, (is_a_theorem(implies(or(X1,not(not(X2))),or(X2,X1)))), inference(spm,[status(thm)],[c_0_75, c_0_70])).
% 0.52/0.74 cnf(c_0_83, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 0.52/0.74 fof(c_0_84, plain, ![X237]:((~necessitation|(~is_a_theorem(X237)|is_a_theorem(necessarily(X237))))&((is_a_theorem(esk56_0)|necessitation)&(~is_a_theorem(necessarily(esk56_0))|necessitation))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])).
% 0.52/0.74 fof(c_0_85, plain, ![X317, X318]:(~op_strict_implies|strict_implies(X317,X318)=necessarily(implies(X317,X318))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])).
% 0.52/0.74 cnf(c_0_86, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(rw,[status(thm)],[c_0_82, c_0_83])).
% 0.52/0.74 fof(c_0_87, plain, ![X279, X280]:((~axiom_m1|is_a_theorem(strict_implies(and(X279,X280),and(X280,X279))))&(~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))|axiom_m1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])).
% 0.52/0.74 fof(c_0_88, negated_conjecture, ~axiom_m1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_axiom_m1])])).
% 0.52/0.74 cnf(c_0_89, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)), inference(split_conjunct,[status(thm)],[c_0_84])).
% 0.52/0.74 cnf(c_0_90, plain, (necessitation), inference(split_conjunct,[status(thm)],[km5_necessitation])).
% 0.52/0.74 cnf(c_0_91, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.52/0.74 cnf(c_0_92, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 0.52/0.74 cnf(c_0_93, plain, (not(and(X1,X2))=implies(X1,not(X2))), inference(spm,[status(thm)],[c_0_64, c_0_83])).
% 0.52/0.74 cnf(c_0_94, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_70, c_0_83])).
% 0.52/0.74 cnf(c_0_95, plain, (or(X1,X2)=or(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_86]), c_0_86])])).
% 0.52/0.74 fof(c_0_96, 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])])])])).
% 0.52/0.74 cnf(c_0_97, plain, (axiom_m1|~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.52/0.74 cnf(c_0_98, negated_conjecture, (~axiom_m1), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.52/0.74 cnf(c_0_99, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])).
% 0.52/0.74 cnf(c_0_100, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91, c_0_92])])).
% 0.52/0.74 cnf(c_0_101, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(spm,[status(thm)],[c_0_83, c_0_93])).
% 0.52/0.74 cnf(c_0_102, plain, (or(X1,not(X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_94, c_0_95])).
% 0.52/0.74 cnf(c_0_103, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_96])).
% 0.52/0.74 cnf(c_0_104, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 0.52/0.74 cnf(c_0_105, plain, (~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))), inference(sr,[status(thm)],[c_0_97, c_0_98])).
% 0.52/0.74 cnf(c_0_106, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_99, c_0_100])).
% 0.52/0.74 cnf(c_0_107, plain, (and(not(X1),X2)=not(implies(X2,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_70]), c_0_102])).
% 0.52/0.74 cnf(c_0_108, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_104])])).
% 0.52/0.74 cnf(c_0_109, plain, (~is_a_theorem(implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))), inference(spm,[status(thm)],[c_0_105, c_0_106])).
% 0.52/0.74 cnf(c_0_110, plain, (and(X1,X2)=and(X2,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_83]), c_0_101])).
% 0.52/0.74 cnf(c_0_111, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_53, c_0_108])).
% 0.52/0.74 cnf(c_0_112, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110]), c_0_111])]), ['proof']).
% 0.52/0.74 % SZS output end Proof
% 0.52/0.74 % User time : 0.273 s
% 0.52/0.74 % System time : 0.020 s
% 0.52/0.74 % Total time : 0.293 s
% 0.52/0.74
%------------------------------------------------------------------------------