%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n027.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 11:21:01 AM UTC 2026
% Result : Theorem 0.40s 0.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.10/0.35 % Computer : n027.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 21:43:43 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.40/0.63 % Version : CSI_E---1.1
% 0.40/0.63 % Problem : theBenchmark.p
% 0.40/0.63 % Proof found!
% 0.40/0.63 % SZS status Theorem for theBenchmark.p
% 0.40/0.63 % SZS output start Proof
% 0.40/0.63 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)).
% 0.40/0.63 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)).
% 0.40/0.63 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)).
% 0.40/0.63 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.40/0.63 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.40/0.63 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)).
% 0.40/0.63 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)).
% 0.40/0.63 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.40/0.63 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)).
% 0.40/0.63 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)).
% 0.40/0.63 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.40/0.63 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.40/0.63 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)).
% 0.40/0.63 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)).
% 0.40/0.63 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.40/0.63 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.40/0.63 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox/benchmark/theBenchmark.p', principia_op_implies_or)).
% 0.40/0.63 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.40/0.63 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)).
% 0.40/0.63 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.40/0.63 fof(r1, axiom, (r1<=>![X4]:is_a_theorem(implies(or(X4,X4),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r1)).
% 0.40/0.63 fof(principia_r1, conjecture, r1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', principia_r1)).
% 0.40/0.63 fof(c_0_22, 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])])])])])).
% 0.40/0.63 fof(c_0_23, 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])])])])).
% 0.40/0.63 fof(c_0_24, 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])])])).
% 0.40/0.63 cnf(c_0_25, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.40/0.63 cnf(c_0_26, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.40/0.63 cnf(c_0_27, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_23])).
% 0.40/0.63 cnf(c_0_28, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.40/0.63 fof(c_0_29, 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])])])])).
% 0.40/0.63 fof(c_0_30, 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])])])).
% 0.40/0.63 cnf(c_0_31, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_24])).
% 0.40/0.63 cnf(c_0_32, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.40/0.63 cnf(c_0_33, 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_25, c_0_26])])).
% 0.40/0.63 cnf(c_0_34, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 0.40/0.63 fof(c_0_35, 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])])])).
% 0.40/0.63 fof(c_0_36, 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])])])])).
% 0.40/0.63 cnf(c_0_37, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_29])).
% 0.40/0.63 cnf(c_0_38, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 0.40/0.63 cnf(c_0_39, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_30])).
% 0.40/0.63 cnf(c_0_40, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 0.40/0.63 cnf(c_0_41, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.40/0.63 fof(c_0_42, 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])])])).
% 0.40/0.63 fof(c_0_43, 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])])])])])).
% 0.40/0.63 cnf(c_0_44, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_33, c_0_34])).
% 0.40/0.63 cnf(c_0_45, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.40/0.63 cnf(c_0_46, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.40/0.63 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_36])).
% 0.40/0.63 cnf(c_0_48, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.40/0.63 cnf(c_0_49, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 0.40/0.63 cnf(c_0_50, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40]), c_0_41])])).
% 0.40/0.63 cnf(c_0_51, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_42])).
% 0.40/0.63 cnf(c_0_52, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])).
% 0.40/0.63 cnf(c_0_53, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_43])).
% 0.40/0.63 cnf(c_0_54, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.40/0.63 cnf(c_0_55, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_33, c_0_44])).
% 0.40/0.63 cnf(c_0_56, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 0.40/0.63 cnf(c_0_57, 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])])).
% 0.40/0.63 fof(c_0_58, 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])])])])).
% 0.40/0.63 cnf(c_0_59, plain, (is_a_theorem(or(X1,implies(X2,not(X1))))), inference(spm,[status(thm)],[c_0_49, c_0_50])).
% 0.40/0.63 cnf(c_0_60, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 0.40/0.63 cnf(c_0_61, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 0.40/0.63 cnf(c_0_62, 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_55, c_0_56])).
% 0.40/0.63 cnf(c_0_63, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_33, c_0_57])).
% 0.40/0.63 cnf(c_0_64, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_58])).
% 0.40/0.63 cnf(c_0_65, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])).
% 0.40/0.63 cnf(c_0_66, plain, (is_a_theorem(implies(X1,implies(X2,not(not(X1)))))), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 0.40/0.63 fof(c_0_67, 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])])])])).
% 0.40/0.63 fof(c_0_68, negated_conjecture, ~r1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r1])])).
% 0.40/0.63 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_61, c_0_62])).
% 0.40/0.63 cnf(c_0_70, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_63, c_0_34])).
% 0.40/0.63 cnf(c_0_71, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 0.40/0.63 cnf(c_0_72, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_63, c_0_66])).
% 0.40/0.63 cnf(c_0_73, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_63, c_0_49])).
% 0.40/0.63 cnf(c_0_74, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(split_conjunct,[status(thm)],[c_0_67])).
% 0.40/0.63 cnf(c_0_75, negated_conjecture, (~r1), inference(split_conjunct,[status(thm)],[c_0_68])).
% 0.40/0.63 cnf(c_0_76, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_71])])).
% 0.40/0.63 cnf(c_0_77, 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_72]), c_0_50]), c_0_60]), c_0_73])])).
% 0.40/0.63 cnf(c_0_78, plain, (~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(sr,[status(thm)],[c_0_74, c_0_75])).
% 0.40/0.63 cnf(c_0_79, plain, (or(X1,X1)=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_76]), c_0_50]), c_0_77])).
% 0.40/0.63 cnf(c_0_80, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_79]), c_0_73])]), ['proof']).
% 0.40/0.63 % SZS output end Proof
% 0.40/0.63 % User time : 0.120 s
% 0.40/0.63 % System time : 0.014 s
% 0.40/0.63 % Total time : 0.134 s
% 0.40/0.63
%------------------------------------------------------------------------------