%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL456+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 11:21:01 AM UTC 2026
% Result : Theorem 0.49s 0.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n011.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 18:42:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.49/0.69 % Version : CSI_E---1.1
% 0.49/0.69 % Problem : theBenchmark.p
% 0.49/0.69 % Proof found!
% 0.49/0.69 % SZS status Theorem for theBenchmark.p
% 0.49/0.69 % SZS output start Proof
% 0.49/0.69 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)).
% 0.49/0.69 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)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.49/0.69 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.49/0.69 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.49/0.69 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)).
% 0.49/0.69 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)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.49/0.69 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.49/0.69 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', principia_op_implies_or)).
% 0.49/0.69 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)).
% 0.49/0.69 fof(r3, axiom, (r3<=>![X4, X5]:is_a_theorem(implies(or(X4,X5),or(X5,X4)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r3)).
% 0.49/0.69 fof(principia_r3, conjecture, r3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', principia_r3)).
% 0.49/0.69 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 0.49/0.69 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])])])])])).
% 0.49/0.69 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])])])])).
% 0.49/0.69 fof(c_0_24, 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])])])])).
% 0.49/0.69 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])).
% 0.49/0.69 cnf(c_0_26, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.49/0.69 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])).
% 0.49/0.69 cnf(c_0_28, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.49/0.69 cnf(c_0_29, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_24])).
% 0.49/0.69 cnf(c_0_30, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.49/0.69 fof(c_0_31, 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])])])])).
% 0.49/0.69 fof(c_0_32, 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])])])).
% 0.49/0.69 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])])).
% 0.49/0.69 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])])).
% 0.49/0.69 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])])])).
% 0.49/0.69 cnf(c_0_36, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 0.49/0.69 cnf(c_0_37, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.49/0.69 cnf(c_0_38, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 0.49/0.69 fof(c_0_39, 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])])])).
% 0.49/0.69 cnf(c_0_40, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.49/0.69 cnf(c_0_41, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.49/0.69 fof(c_0_42, 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])])])])])).
% 0.49/0.69 cnf(c_0_43, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_33, c_0_34])).
% 0.49/0.69 cnf(c_0_44, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.49/0.69 cnf(c_0_45, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.49/0.69 cnf(c_0_46, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_33, c_0_36])).
% 0.49/0.69 cnf(c_0_47, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 0.49/0.69 cnf(c_0_48, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.49/0.69 cnf(c_0_49, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 0.49/0.69 cnf(c_0_50, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.49/0.69 fof(c_0_51, 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])])])).
% 0.49/0.69 cnf(c_0_52, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_42])).
% 0.49/0.69 cnf(c_0_53, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.49/0.69 cnf(c_0_54, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_33, c_0_43])).
% 0.49/0.69 cnf(c_0_55, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45])])).
% 0.49/0.69 cnf(c_0_56, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_46, c_0_47])).
% 0.49/0.69 cnf(c_0_57, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49]), c_0_50])])).
% 0.49/0.69 cnf(c_0_58, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_51])).
% 0.49/0.69 cnf(c_0_59, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])).
% 0.49/0.69 fof(c_0_60, 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])])])])).
% 0.49/0.69 cnf(c_0_61, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 0.49/0.69 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_54, c_0_55])).
% 0.49/0.69 cnf(c_0_63, plain, (is_a_theorem(or(X1,not(X1)))), inference(spm,[status(thm)],[c_0_56, c_0_57])).
% 0.49/0.69 cnf(c_0_64, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_59])])).
% 0.49/0.69 fof(c_0_65, plain, ![X166, X167]:((~r3|is_a_theorem(implies(or(X166,X167),or(X167,X166))))&(~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))|r3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])).
% 0.49/0.69 fof(c_0_66, negated_conjecture, ~r3, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r3])])).
% 0.49/0.69 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_60])).
% 0.49/0.69 cnf(c_0_68, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])).
% 0.49/0.69 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])).
% 0.49/0.69 cnf(c_0_70, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_63, c_0_64])).
% 0.49/0.69 cnf(c_0_71, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.49/0.69 cnf(c_0_72, negated_conjecture, (~r3), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.49/0.69 cnf(c_0_73, 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_57]), c_0_68])])).
% 0.49/0.69 cnf(c_0_74, 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_57]), c_0_64]), c_0_56])])).
% 0.49/0.69 cnf(c_0_75, plain, (~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))), inference(sr,[status(thm)],[c_0_71, c_0_72])).
% 0.49/0.69 cnf(c_0_76, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_57]), c_0_74])).
% 0.49/0.69 cnf(c_0_77, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76])]), ['proof']).
% 0.49/0.69 % SZS output end Proof
% 0.49/0.69 % User time : 0.185 s
% 0.49/0.69 % System time : 0.007 s
% 0.49/0.69 % Total time : 0.192 s
% 0.49/0.69
%------------------------------------------------------------------------------