%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL466+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n017.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 11:21:03 AM UTC 2026
% Result : Theorem 0.70s 57.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL466+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : java -jar mcs_scs.jar %d %s
% 0.16/0.43 % Computer : n017.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 5 05:03:21 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.42/0.62 start to proof:theBenchmark.p
% 0.70/57.72 % Version : CSI_E---1.1
% 0.70/57.72 % Problem : theBenchmark.p
% 0.70/57.72 % Proof found!
% 0.70/57.72 % SZS status Theorem for theBenchmark.p
% 0.70/57.72 % SZS output start Proof
% 0.70/57.72 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)).
% 0.70/57.72 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)).
% 0.70/57.72 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)).
% 0.70/57.72 fof(luka_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_modus_ponens)).
% 0.70/57.72 fof(luka_cn1, axiom, cn1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_cn1)).
% 0.70/57.72 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)).
% 0.70/57.72 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)).
% 0.70/57.72 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_op_implies_and)).
% 0.70/57.72 fof(luka_cn2, axiom, cn2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_cn2)).
% 0.70/57.72 fof(luka_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_op_or)).
% 0.70/57.72 fof(cn3, axiom, (cn3<=>![X4]:is_a_theorem(implies(implies(not(X4),X4),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', cn3)).
% 0.70/57.72 fof(luka_cn3, axiom, cn3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_cn3)).
% 0.70/57.72 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)).
% 0.70/57.72 fof(luka_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', luka_op_equiv)).
% 0.70/57.72 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)).
% 0.70/57.72 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax', use_substitution_of_equivalents)).
% 0.70/57.72 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)).
% 0.70/57.72 fof(hilbert_and_1, conjecture, and_1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_and_1)).
% 0.70/57.72 fof(c_0_18, 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])])])])])).
% 0.70/57.72 fof(c_0_19, 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])])])])).
% 0.70/57.72 fof(c_0_20, 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])])])).
% 0.70/57.72 cnf(c_0_21, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.70/57.72 cnf(c_0_22, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[luka_modus_ponens])).
% 0.70/57.72 cnf(c_0_23, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~cn1), inference(split_conjunct,[status(thm)],[c_0_19])).
% 0.70/57.72 cnf(c_0_24, plain, (cn1), inference(split_conjunct,[status(thm)],[luka_cn1])).
% 0.70/57.72 fof(c_0_25, 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])])])])).
% 0.70/57.72 fof(c_0_26, 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])])])).
% 0.70/57.72 cnf(c_0_27, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.70/57.72 cnf(c_0_28, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.70/57.72 cnf(c_0_29, 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_21, c_0_22])])).
% 0.70/57.72 cnf(c_0_30, 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_23, c_0_24])])).
% 0.70/57.72 cnf(c_0_31, plain, (is_a_theorem(implies(X1,implies(not(X1),X2)))|~cn2), inference(split_conjunct,[status(thm)],[c_0_25])).
% 0.70/57.72 cnf(c_0_32, plain, (cn2), inference(split_conjunct,[status(thm)],[luka_cn2])).
% 0.70/57.72 cnf(c_0_33, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.70/57.72 cnf(c_0_34, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 0.70/57.72 cnf(c_0_35, plain, (op_or), inference(split_conjunct,[status(thm)],[luka_op_or])).
% 0.70/57.72 fof(c_0_36, 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])])])])).
% 0.70/57.72 cnf(c_0_37, plain, (is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_29, c_0_30])).
% 0.70/57.72 cnf(c_0_38, plain, (is_a_theorem(implies(X1,implies(not(X1),X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 0.70/57.72 cnf(c_0_39, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34]), c_0_35])])).
% 0.70/57.72 cnf(c_0_40, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))|~cn3), inference(split_conjunct,[status(thm)],[c_0_36])).
% 0.70/57.72 cnf(c_0_41, plain, (cn3), inference(split_conjunct,[status(thm)],[luka_cn3])).
% 0.70/57.72 cnf(c_0_42, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X3,X2))|~is_a_theorem(implies(X1,X3))), inference(spm,[status(thm)],[c_0_29, c_0_37])).
% 0.70/57.72 cnf(c_0_43, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(rw,[status(thm)],[c_0_38, c_0_39])).
% 0.70/57.72 cnf(c_0_44, plain, (is_a_theorem(implies(implies(not(X1),X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 0.70/57.72 cnf(c_0_45, plain, (is_a_theorem(implies(X1,or(X2,X3)))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
% 0.70/57.72 cnf(c_0_46, plain, (is_a_theorem(implies(or(X1,X1),X1))), inference(rw,[status(thm)],[c_0_44, c_0_39])).
% 0.70/57.72 cnf(c_0_47, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,not(X3)))|~is_a_theorem(or(X3,X2))), inference(spm,[status(thm)],[c_0_42, c_0_39])).
% 0.70/57.72 cnf(c_0_48, plain, (is_a_theorem(implies(X1,or(X2,X3)))|~is_a_theorem(implies(X1,X4))|~is_a_theorem(implies(X4,X2))), inference(spm,[status(thm)],[c_0_42, c_0_45])).
% 0.70/57.72 cnf(c_0_49, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,or(X2,X2)))), inference(spm,[status(thm)],[c_0_42, c_0_46])).
% 0.70/57.72 cnf(c_0_50, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,not(X3)))|~is_a_theorem(or(X3,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_39]), c_0_39])).
% 0.70/57.72 cnf(c_0_51, plain, (or(and(X1,not(X2)),X3)=implies(implies(X1,X2),X3)), inference(spm,[status(thm)],[c_0_39, c_0_34])).
% 0.70/57.72 cnf(c_0_52, plain, (is_a_theorem(implies(X1,or(X2,X3)))|~is_a_theorem(implies(or(X1,X4),X2))), inference(spm,[status(thm)],[c_0_48, c_0_43])).
% 0.70/57.72 cnf(c_0_53, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_49, c_0_43])).
% 0.70/57.72 cnf(c_0_54, plain, (is_a_theorem(implies(implies(X1,X2),or(X3,X2)))|~is_a_theorem(or(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_39]), c_0_39])).
% 0.70/57.72 cnf(c_0_55, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,implies(X3,X4)))|~is_a_theorem(implies(implies(X3,X4),X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_34]), c_0_51])).
% 0.70/57.72 cnf(c_0_56, plain, (is_a_theorem(implies(X1,or(or(X1,X2),X3)))), inference(spm,[status(thm)],[c_0_52, c_0_53])).
% 0.70/57.72 cnf(c_0_57, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_49, c_0_54])).
% 0.70/57.72 cnf(c_0_58, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_29, c_0_43])).
% 0.70/57.72 cnf(c_0_59, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,or(X3,X4)))|~is_a_theorem(implies(or(X3,X4),X2))), inference(spm,[status(thm)],[c_0_55, c_0_39])).
% 0.70/57.72 cnf(c_0_60, plain, (is_a_theorem(or(X1,or(or(not(X1),X2),X3)))), inference(spm,[status(thm)],[c_0_56, c_0_39])).
% 0.70/57.72 cnf(c_0_61, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_57, c_0_58])).
% 0.70/57.72 cnf(c_0_62, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(or(or(not(X1),X3),X4),X2))), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 0.70/57.72 cnf(c_0_63, plain, (is_a_theorem(implies(or(X1,X2),X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_61, c_0_39])).
% 0.70/57.72 cnf(c_0_64, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 0.70/57.72 cnf(c_0_65, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_57, c_0_64])).
% 0.70/57.72 cnf(c_0_66, plain, (is_a_theorem(implies(implies(X1,or(X2,X2)),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_49, c_0_65])).
% 0.70/57.72 fof(c_0_67, 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])])])).
% 0.70/57.72 cnf(c_0_68, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,or(X1,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_29, c_0_66])).
% 0.70/57.72 cnf(c_0_69, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_67])).
% 0.70/57.72 cnf(c_0_70, plain, (op_equiv), inference(split_conjunct,[status(thm)],[luka_op_equiv])).
% 0.70/57.72 cnf(c_0_71, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(or(X1,X2))), inference(spm,[status(thm)],[c_0_68, c_0_54])).
% 0.70/57.72 cnf(c_0_72, plain, (is_a_theorem(or(X1,or(X2,X3)))|~is_a_theorem(or(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_39]), c_0_39])).
% 0.70/57.72 cnf(c_0_73, plain, (not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_34, c_0_34])).
% 0.70/57.72 cnf(c_0_74, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])).
% 0.70/57.72 fof(c_0_75, 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])])])])])).
% 0.70/57.72 cnf(c_0_76, plain, (is_a_theorem(X1)|~is_a_theorem(implies(or(X2,X3),X1))|~is_a_theorem(or(X1,X2))), inference(spm,[status(thm)],[c_0_71, c_0_72])).
% 0.70/57.72 cnf(c_0_77, plain, (is_a_theorem(implies(or(X1,X2),X2))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_65, c_0_39])).
% 0.70/57.72 cnf(c_0_78, plain, (implies(implies(X1,X2),and(X2,not(X1)))=not(equiv(X1,X2))), inference(spm,[status(thm)],[c_0_73, c_0_74])).
% 0.70/57.72 cnf(c_0_79, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X1))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_29, c_0_45])).
% 0.70/57.72 cnf(c_0_80, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_75])).
% 0.70/57.72 cnf(c_0_81, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.70/57.72 cnf(c_0_82, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_76, c_0_77])).
% 0.70/57.72 cnf(c_0_83, plain, (is_a_theorem(or(equiv(X1,X2),and(X2,not(X1))))|~is_a_theorem(implies(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_78]), c_0_39])).
% 0.70/57.72 cnf(c_0_84, plain, (is_a_theorem(implies(or(or(X1,X1),or(X1,X1)),X1))), inference(spm,[status(thm)],[c_0_49, c_0_46])).
% 0.70/57.72 cnf(c_0_85, plain, (is_a_theorem(or(implies(X1,X2),X3))|~is_a_theorem(implies(X4,X2))|~is_a_theorem(implies(X1,X4))), inference(spm,[status(thm)],[c_0_79, c_0_37])).
% 0.70/57.72 cnf(c_0_86, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 0.70/57.72 cnf(c_0_87, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_34])).
% 0.70/57.72 cnf(c_0_88, plain, (is_a_theorem(implies(X1,or(X2,X3)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_52, c_0_63])).
% 0.70/57.72 cnf(c_0_89, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,or(or(X2,X2),or(X2,X2))))), inference(spm,[status(thm)],[c_0_42, c_0_84])).
% 0.70/57.72 cnf(c_0_90, plain, (is_a_theorem(or(implies(X1,X2),X3))|~is_a_theorem(implies(X1,or(X2,X2)))), inference(spm,[status(thm)],[c_0_85, c_0_46])).
% 0.70/57.72 cnf(c_0_91, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_86, c_0_87])).
% 0.70/57.72 cnf(c_0_92, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_49, c_0_88])).
% 0.70/57.72 cnf(c_0_93, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,X2))), inference(spm,[status(thm)],[c_0_89, c_0_88])).
% 0.70/57.72 cnf(c_0_94, plain, (is_a_theorem(or(implies(X1,X1),X2))), inference(spm,[status(thm)],[c_0_90, c_0_43])).
% 0.70/57.72 cnf(c_0_95, plain, (implies(X1,X2)=X2|~is_a_theorem(implies(X2,implies(X1,X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_91, c_0_65])).
% 0.70/57.72 cnf(c_0_96, plain, (is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X1,X3))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_39]), c_0_39])).
% 0.70/57.72 cnf(c_0_97, plain, (X1=X2|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_91, c_0_92])).
% 0.70/57.72 cnf(c_0_98, plain, (is_a_theorem(implies(X1,implies(X2,X2)))), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 0.70/57.72 cnf(c_0_99, plain, (implies(implies(X1,X1),or(X2,X1))=or(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_53])])).
% 0.70/57.72 cnf(c_0_100, plain, (or(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_46]), c_0_43])])).
% 0.70/57.72 cnf(c_0_101, plain, (X1=implies(X2,X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_97, c_0_98])).
% 0.70/57.72 cnf(c_0_102, plain, (implies(implies(X1,X1),X1)=X1), inference(spm,[status(thm)],[c_0_99, c_0_100])).
% 0.70/57.72 cnf(c_0_103, plain, (implies(X1,X1)=implies(X2,X2)), inference(spm,[status(thm)],[c_0_101, c_0_53])).
% 0.70/57.72 cnf(c_0_104, plain, (implies(implies(X1,X1),X2)=X2), inference(spm,[status(thm)],[c_0_102, c_0_103])).
% 0.70/57.72 cnf(c_0_105, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_104]), c_0_98])])).
% 0.70/57.72 cnf(c_0_106, plain, (is_a_theorem(or(X1,or(not(X1),X2)))), inference(spm,[status(thm)],[c_0_43, c_0_39])).
% 0.70/57.72 cnf(c_0_107, plain, (is_a_theorem(implies(implies(X1,not(X2)),implies(or(X2,X3),implies(X1,X3))))), inference(spm,[status(thm)],[c_0_30, c_0_39])).
% 0.70/57.72 cnf(c_0_108, plain, (implies(X1,X2)=X2|~is_a_theorem(implies(implies(X1,X2),X2))), inference(spm,[status(thm)],[c_0_91, c_0_105])).
% 0.70/57.72 cnf(c_0_109, plain, (is_a_theorem(implies(implies(or(not(X1),X2),X1),X1))), inference(spm,[status(thm)],[c_0_57, c_0_106])).
% 0.70/57.72 cnf(c_0_110, plain, (is_a_theorem(implies(implies(or(X1,X2),X3),X3))|~is_a_theorem(or(X3,X1))), inference(spm,[status(thm)],[c_0_57, c_0_72])).
% 0.70/57.72 cnf(c_0_111, plain, (is_a_theorem(or(X1,implies(or(X1,X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_104]), c_0_104]), c_0_39])).
% 0.70/57.72 cnf(c_0_112, plain, (implies(or(not(X1),X2),X1)=X1), inference(spm,[status(thm)],[c_0_108, c_0_109])).
% 0.70/57.72 cnf(c_0_113, plain, (implies(or(X1,X2),X3)=X3|~is_a_theorem(or(X3,X1))), inference(spm,[status(thm)],[c_0_108, c_0_110])).
% 0.70/57.72 cnf(c_0_114, plain, (is_a_theorem(or(not(X1),X1))), inference(spm,[status(thm)],[c_0_111, c_0_112])).
% 0.70/57.72 cnf(c_0_115, plain, (implies(or(X1,X2),not(X1))=not(X1)), inference(spm,[status(thm)],[c_0_113, c_0_114])).
% 0.70/57.72 cnf(c_0_116, plain, (implies(X1,not(X1))=not(X1)), inference(spm,[status(thm)],[c_0_115, c_0_100])).
% 0.70/57.72 cnf(c_0_117, plain, (or(X1,X2)=X1|~is_a_theorem(implies(or(X1,X2),X1))), inference(spm,[status(thm)],[c_0_91, c_0_43])).
% 0.70/57.72 cnf(c_0_118, plain, (or(X1,not(not(X1)))=not(not(X1))), inference(spm,[status(thm)],[c_0_39, c_0_116])).
% 0.70/57.72 cnf(c_0_119, plain, (is_a_theorem(implies(and(X1,not(X2)),implies(implies(X1,X2),X3)))), inference(spm,[status(thm)],[c_0_43, c_0_51])).
% 0.70/57.72 cnf(c_0_120, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_39]), c_0_114])])).
% 0.70/57.72 cnf(c_0_121, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(or(not(X2),X3),X2)))), inference(spm,[status(thm)],[c_0_42, c_0_109])).
% 0.70/57.72 cnf(c_0_122, plain, (is_a_theorem(implies(and(not(X1),not(X2)),implies(or(X1,X2),X3)))), inference(spm,[status(thm)],[c_0_119, c_0_39])).
% 0.70/57.72 cnf(c_0_123, plain, (not(and(X1,X2))=implies(X1,not(X2))), inference(spm,[status(thm)],[c_0_34, c_0_120])).
% 0.70/57.72 cnf(c_0_124, plain, (is_a_theorem(implies(and(not(not(X1)),not(X2)),X1))), inference(spm,[status(thm)],[c_0_121, c_0_122])).
% 0.70/57.72 cnf(c_0_125, plain, (implies(X1,and(not(X2),not(X3)))=not(and(X1,or(X2,X3)))), inference(spm,[status(thm)],[c_0_73, c_0_39])).
% 0.70/57.72 cnf(c_0_126, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(spm,[status(thm)],[c_0_120, c_0_123])).
% 0.70/57.72 cnf(c_0_127, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(and(X1,or(not(X2),X3))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_124]), c_0_125])).
% 0.70/57.72 cnf(c_0_128, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_39, c_0_120])).
% 0.70/57.72 cnf(c_0_129, plain, (and(X1,not(X2))=not(implies(X1,X2))), inference(spm,[status(thm)],[c_0_126, c_0_120])).
% 0.70/57.72 fof(c_0_130, 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])])])])).
% 0.70/57.72 fof(c_0_131, negated_conjecture, ~and_1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_1])])).
% 0.70/57.72 cnf(c_0_132, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,not(implies(X2,X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127, c_0_128]), c_0_73]), c_0_129])).
% 0.70/57.72 cnf(c_0_133, plain, (is_a_theorem(or(X1,not(X1)))), inference(spm,[status(thm)],[c_0_53, c_0_39])).
% 0.70/57.72 cnf(c_0_134, plain, (and_1|~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))), inference(split_conjunct,[status(thm)],[c_0_130])).
% 0.70/57.72 cnf(c_0_135, negated_conjecture, (~and_1), inference(split_conjunct,[status(thm)],[c_0_131])).
% 0.70/57.72 cnf(c_0_136, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,and(X2,X3)))), inference(spm,[status(thm)],[c_0_132, c_0_126])).
% 0.70/57.72 cnf(c_0_137, plain, (or(X1,not(X1))=implies(X2,X2)), inference(spm,[status(thm)],[c_0_101, c_0_133])).
% 0.70/57.72 cnf(c_0_138, plain, (~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))), inference(sr,[status(thm)],[c_0_134, c_0_135])).
% 0.70/57.72 cnf(c_0_139, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_133])])).
% 0.70/57.72 cnf(c_0_140, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_139])]), ['proof']).
% 0.70/57.72 % SZS output end Proof
% 0.70/57.72 % User time : 55.045 s
% 0.70/57.72 % System time : 1.987 s
% 0.70/57.72 % Total time : 57.033 s
% 0.70/57.72
%------------------------------------------------------------------------------