%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL458+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n003.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 11:21:02 AM UTC 2026
% Result : Theorem 5.45s 5.64s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL458+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 4 15:57:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.23/0.47 start to proof:theBenchmark.p
% 5.45/5.64 % Version : CSI_E---1.1
% 5.45/5.64 % Problem : theBenchmark.p
% 5.45/5.64 % Proof found!
% 5.45/5.64 % SZS status Theorem for theBenchmark.p
% 5.45/5.64 % SZS output start Proof
% 5.45/5.64 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)).
% 5.45/5.64 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)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 5.45/5.64 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 5.45/5.64 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 5.45/5.64 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)).
% 5.45/5.64 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)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 5.45/5.64 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 5.45/5.64 fof(op_implies_or, axiom, (op_implies_or=>![X1, X2]:implies(X1,X2)=or(not(X1),X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_or)).
% 5.45/5.64 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 5.45/5.64 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', principia_op_implies_or)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 5.45/5.64 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)).
% 5.45/5.64 fof(r5, axiom, (r5<=>![X4, X5, X6]:is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r5)).
% 5.45/5.64 fof(principia_r5, conjecture, r5, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', principia_r5)).
% 5.45/5.64 fof(hilbert_implies_3, axiom, implies_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_3)).
% 5.45/5.64 fof(c_0_24, 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])])])])])).
% 5.45/5.64 fof(c_0_25, 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])])])])).
% 5.45/5.64 fof(c_0_26, 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])])])])).
% 5.45/5.64 cnf(c_0_27, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_24])).
% 5.45/5.64 cnf(c_0_28, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 5.45/5.64 cnf(c_0_29, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_25])).
% 5.45/5.64 cnf(c_0_30, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 5.45/5.64 cnf(c_0_31, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_26])).
% 5.45/5.64 cnf(c_0_32, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 5.45/5.64 fof(c_0_33, 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])])])])).
% 5.45/5.64 fof(c_0_34, 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])])])).
% 5.45/5.64 cnf(c_0_35, 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_27, c_0_28])])).
% 5.45/5.64 cnf(c_0_36, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 5.45/5.64 fof(c_0_37, 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])])])).
% 5.45/5.64 cnf(c_0_38, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 5.45/5.64 cnf(c_0_39, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_33])).
% 5.45/5.64 cnf(c_0_40, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 5.45/5.64 fof(c_0_41, 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])])])).
% 5.45/5.64 cnf(c_0_42, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_34])).
% 5.45/5.64 cnf(c_0_43, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 5.45/5.64 fof(c_0_44, 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])])])])])).
% 5.45/5.64 cnf(c_0_45, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_35, c_0_36])).
% 5.45/5.64 cnf(c_0_46, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_37])).
% 5.45/5.64 cnf(c_0_47, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 5.45/5.64 cnf(c_0_48, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_35, c_0_38])).
% 5.45/5.64 cnf(c_0_49, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 5.45/5.64 cnf(c_0_50, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_41])).
% 5.45/5.64 cnf(c_0_51, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 5.45/5.64 cnf(c_0_52, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 5.45/5.64 fof(c_0_53, 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])])])).
% 5.45/5.64 cnf(c_0_54, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_44])).
% 5.45/5.64 cnf(c_0_55, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 5.45/5.64 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_35, c_0_45])).
% 5.45/5.64 cnf(c_0_57, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])).
% 5.45/5.64 cnf(c_0_58, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_48, c_0_49])).
% 5.45/5.64 cnf(c_0_59, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51]), c_0_52])])).
% 5.45/5.64 cnf(c_0_60, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_53])).
% 5.45/5.64 cnf(c_0_61, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])).
% 5.45/5.64 fof(c_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])])])])).
% 5.45/5.64 cnf(c_0_63, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 5.45/5.64 cnf(c_0_64, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_56, c_0_57])).
% 5.45/5.64 cnf(c_0_65, plain, (is_a_theorem(or(X1,not(X1)))), inference(spm,[status(thm)],[c_0_58, c_0_59])).
% 5.45/5.64 cnf(c_0_66, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 5.45/5.64 cnf(c_0_67, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_62])).
% 5.45/5.64 cnf(c_0_68, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])).
% 5.45/5.64 cnf(c_0_69, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_63, c_0_64])).
% 5.45/5.64 cnf(c_0_70, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_65, c_0_66])).
% 5.45/5.64 fof(c_0_71, 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])])])])).
% 5.45/5.64 cnf(c_0_72, 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_67, c_0_59]), c_0_68])])).
% 5.45/5.64 cnf(c_0_73, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_59]), c_0_66]), c_0_58])])).
% 5.45/5.64 fof(c_0_74, 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])])])])).
% 5.45/5.64 fof(c_0_75, negated_conjecture, ~r5, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r5])])).
% 5.45/5.64 cnf(c_0_76, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~implies_3), inference(split_conjunct,[status(thm)],[c_0_71])).
% 5.45/5.64 cnf(c_0_77, plain, (implies_3), inference(split_conjunct,[status(thm)],[hilbert_implies_3])).
% 5.45/5.64 cnf(c_0_78, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_59]), c_0_73])).
% 5.45/5.64 cnf(c_0_79, 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)],[c_0_74])).
% 5.45/5.64 cnf(c_0_80, negated_conjecture, (~r5), inference(split_conjunct,[status(thm)],[c_0_75])).
% 5.45/5.64 cnf(c_0_81, 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_76, c_0_77])])).
% 5.45/5.64 cnf(c_0_82, plain, (or(X1,X2)=or(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_78]), c_0_78])])).
% 5.45/5.64 cnf(c_0_83, plain, (~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))), inference(sr,[status(thm)],[c_0_79, c_0_80])).
% 5.45/5.64 cnf(c_0_84, 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_81, c_0_59]), c_0_59])).
% 5.45/5.64 cnf(c_0_85, plain, (or(X1,not(X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_66, c_0_82])).
% 5.45/5.64 cnf(c_0_86, plain, (~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk54_0,esk53_0),or(esk55_0,esk53_0))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_82]), c_0_82])).
% 5.45/5.64 cnf(c_0_87, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X1,X3),or(X2,X3))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_59]), c_0_85])).
% 5.45/5.64 cnf(c_0_88, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])]), ['proof']).
% 5.45/5.64 % SZS output end Proof
% 5.45/5.64 % User time : 4.913 s
% 5.45/5.64 % System time : 0.233 s
% 5.45/5.64 % Total time : 5.146 s
% 5.45/5.64
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