%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL526+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 11:21:08 AM UTC 2026
% Result : Theorem 0.41s 0.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL526+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n027.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 19:28:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.23/0.48 start to proof:theBenchmark.p
% 0.41/0.59 % Version : CSI_E---1.1
% 0.41/0.59 % Problem : theBenchmark.p
% 0.41/0.59 % Proof found!
% 0.41/0.59 % SZS status Theorem for theBenchmark.p
% 0.41/0.59 % SZS output start Proof
% 0.41/0.59 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)).
% 0.41/0.59 fof(and_2, axiom, (and_2<=>![X1, X2]:is_a_theorem(implies(and(X1,X2),X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_2)).
% 0.41/0.59 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)).
% 0.41/0.59 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)).
% 0.41/0.59 fof(axiom_M, axiom, (axiom_M<=>![X1]:is_a_theorem(implies(necessarily(X1),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_M)).
% 0.41/0.59 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.41/0.59 fof(hilbert_and_2, axiom, and_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_2)).
% 0.41/0.59 fof(op_strict_equiv, axiom, (op_strict_equiv=>![X1, X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_strict_equiv)).
% 0.41/0.59 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.41/0.59 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)).
% 0.41/0.59 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)).
% 0.41/0.59 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.41/0.59 fof(km5_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_axiom_M)).
% 0.41/0.59 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)).
% 0.41/0.59 fof(s1_0_op_strict_equiv, axiom, op_strict_equiv, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_op_strict_equiv)).
% 0.41/0.59 fof(substitution_strict_equiv, axiom, (substitution_strict_equiv<=>![X1, X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', substitution_strict_equiv)).
% 0.41/0.59 fof(s1_0_substitution_strict_equiv, conjecture, substitution_strict_equiv, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_substitution_strict_equiv)).
% 0.41/0.59 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.41/0.59 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.41/0.59 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_op_strict_implies)).
% 0.41/0.59 fof(c_0_20, 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])])])])])).
% 0.41/0.59 fof(c_0_21, plain, ![X147, X148]:((~and_2|is_a_theorem(implies(and(X147,X148),X148)))&(~is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))|and_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])).
% 0.41/0.59 fof(c_0_22, 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])])])])).
% 0.41/0.59 fof(c_0_23, 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])])])])).
% 0.41/0.59 fof(c_0_24, plain, ![X255]:((~axiom_M|is_a_theorem(implies(necessarily(X255),X255)))&(~is_a_theorem(implies(necessarily(esk65_0),esk65_0))|axiom_M)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])).
% 0.41/0.59 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_20])).
% 0.41/0.59 cnf(c_0_26, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.41/0.59 cnf(c_0_27, plain, (is_a_theorem(implies(and(X1,X2),X2))|~and_2), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.41/0.59 cnf(c_0_28, plain, (and_2), inference(split_conjunct,[status(thm)],[hilbert_and_2])).
% 0.41/0.59 fof(c_0_29, plain, ![X319, X320]:(~op_strict_equiv|strict_equiv(X319,X320)=and(strict_implies(X319,X320),strict_implies(X320,X319))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])).
% 0.41/0.59 cnf(c_0_30, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.41/0.59 cnf(c_0_31, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])).
% 0.41/0.59 fof(c_0_32, 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])])])])])).
% 0.41/0.59 fof(c_0_33, 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])])])).
% 0.41/0.59 cnf(c_0_34, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_23])).
% 0.41/0.59 cnf(c_0_35, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.41/0.59 cnf(c_0_36, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_24])).
% 0.41/0.59 cnf(c_0_37, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km5_axiom_M])).
% 0.41/0.59 fof(c_0_38, 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])])])).
% 0.41/0.59 cnf(c_0_39, 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])])).
% 0.41/0.59 cnf(c_0_40, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 0.41/0.59 cnf(c_0_41, plain, (strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv), inference(split_conjunct,[status(thm)],[c_0_29])).
% 0.41/0.59 cnf(c_0_42, plain, (op_strict_equiv), inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv])).
% 0.41/0.59 fof(c_0_43, plain, ![X247, X248]:((~substitution_strict_equiv|(~is_a_theorem(strict_equiv(X247,X248))|X247=X248))&((is_a_theorem(strict_equiv(esk61_0,esk62_0))|substitution_strict_equiv)&(esk61_0!=esk62_0|substitution_strict_equiv))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])])).
% 0.41/0.59 fof(c_0_44, negated_conjecture, ~substitution_strict_equiv, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_substitution_strict_equiv])])).
% 0.41/0.59 cnf(c_0_45, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 0.41/0.59 cnf(c_0_46, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.41/0.59 cnf(c_0_47, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.41/0.59 cnf(c_0_48, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.41/0.59 cnf(c_0_49, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.41/0.59 cnf(c_0_50, 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])])).
% 0.41/0.59 cnf(c_0_51, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 0.41/0.59 cnf(c_0_52, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.41/0.59 cnf(c_0_53, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 0.41/0.59 cnf(c_0_54, plain, (is_a_theorem(X1)|~is_a_theorem(and(X2,X1))), inference(spm,[status(thm)],[c_0_39, c_0_40])).
% 0.41/0.59 cnf(c_0_55, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 0.41/0.59 cnf(c_0_56, plain, (is_a_theorem(strict_equiv(esk61_0,esk62_0))|substitution_strict_equiv), inference(split_conjunct,[status(thm)],[c_0_43])).
% 0.41/0.59 cnf(c_0_57, negated_conjecture, (~substitution_strict_equiv), inference(split_conjunct,[status(thm)],[c_0_44])).
% 0.41/0.59 cnf(c_0_58, plain, (is_a_theorem(X1)|~is_a_theorem(and(X1,X2))), inference(spm,[status(thm)],[c_0_39, c_0_45])).
% 0.41/0.59 cnf(c_0_59, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])).
% 0.41/0.59 cnf(c_0_60, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49])])).
% 0.41/0.59 cnf(c_0_61, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_39, c_0_50])).
% 0.41/0.59 cnf(c_0_62, plain, (is_a_theorem(X1)|~is_a_theorem(necessarily(X1))), inference(spm,[status(thm)],[c_0_39, c_0_51])).
% 0.41/0.59 cnf(c_0_63, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 0.41/0.59 cnf(c_0_64, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X2,X1))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 0.41/0.59 cnf(c_0_65, plain, (is_a_theorem(strict_equiv(esk61_0,esk62_0))), inference(sr,[status(thm)],[c_0_56, c_0_57])).
% 0.41/0.59 cnf(c_0_66, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))), inference(spm,[status(thm)],[c_0_58, c_0_55])).
% 0.41/0.59 cnf(c_0_67, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 0.41/0.59 cnf(c_0_68, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_39, c_0_61])).
% 0.41/0.59 cnf(c_0_69, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(strict_implies(X1,X2))), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 0.41/0.59 cnf(c_0_70, plain, (is_a_theorem(strict_implies(esk62_0,esk61_0))), inference(spm,[status(thm)],[c_0_64, c_0_65])).
% 0.41/0.59 cnf(c_0_71, plain, (is_a_theorem(strict_implies(esk61_0,esk62_0))), inference(spm,[status(thm)],[c_0_66, c_0_65])).
% 0.41/0.59 cnf(c_0_72, plain, (substitution_strict_equiv|esk61_0!=esk62_0), inference(split_conjunct,[status(thm)],[c_0_43])).
% 0.41/0.59 cnf(c_0_73, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 0.41/0.59 cnf(c_0_74, plain, (is_a_theorem(implies(esk62_0,esk61_0))), inference(spm,[status(thm)],[c_0_69, c_0_70])).
% 0.41/0.59 cnf(c_0_75, plain, (is_a_theorem(implies(esk61_0,esk62_0))), inference(spm,[status(thm)],[c_0_69, c_0_71])).
% 0.41/0.59 cnf(c_0_76, plain, (esk62_0!=esk61_0), inference(sr,[status(thm)],[c_0_72, c_0_57])).
% 0.41/0.59 cnf(c_0_77, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_75])]), c_0_76]), ['proof']).
% 0.41/0.59 % SZS output end Proof
% 0.41/0.59 % User time : 0.085 s
% 0.41/0.59 % System time : 0.007 s
% 0.41/0.59 % Total time : 0.092 s
% 0.41/0.59
%------------------------------------------------------------------------------