%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL562+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 11:21:10 AM UTC 2026
% Result : Theorem 1.72s 1.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : java -jar mcs_scs.jar %d %s
% 0.14/0.39 % Computer : n027.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 6 01:14:29 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.25/0.57 start to proof:theBenchmark.p
% 1.72/1.83 % Version : CSI_E---1.1
% 1.72/1.83 % Problem : theBenchmark.p
% 1.72/1.83 % Proof found!
% 1.72/1.83 % SZS status Theorem for theBenchmark.p
% 1.72/1.83 % SZS output start Proof
% 1.72/1.83 fof(adjunction, axiom, (adjunction<=>![X1, X2]:((is_a_theorem(X1)&is_a_theorem(X2))=>is_a_theorem(and(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', adjunction)).
% 1.72/1.83 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)).
% 1.72/1.83 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)).
% 1.72/1.83 fof(s1_0_adjunction, axiom, adjunction, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_adjunction)).
% 1.72/1.83 fof(s1_0_op_strict_equiv, axiom, op_strict_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_strict_equiv)).
% 1.72/1.83 fof(modus_ponens_strict_implies, axiom, (modus_ponens_strict_implies<=>![X1, X2]:((is_a_theorem(X1)&is_a_theorem(strict_implies(X1,X2)))=>is_a_theorem(X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', modus_ponens_strict_implies)).
% 1.72/1.83 fof(axiom_m5, axiom, (axiom_m5<=>![X1, X2, X3]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m5)).
% 1.72/1.83 fof(s1_0_substitution_strict_equiv, axiom, substitution_strict_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_substitution_strict_equiv)).
% 1.72/1.83 fof(axiom_m1, axiom, (axiom_m1<=>![X1, X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m1)).
% 1.72/1.83 fof(s1_0_modus_ponens_strict_implies, axiom, modus_ponens_strict_implies, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_modus_ponens_strict_implies)).
% 1.72/1.83 fof(s1_0_axiom_m5, axiom, axiom_m5, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m5)).
% 1.72/1.83 fof(axiom_m2, axiom, (axiom_m2<=>![X1, X2]:is_a_theorem(strict_implies(and(X1,X2),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m2)).
% 1.72/1.83 fof(s1_0_axiom_m1, axiom, axiom_m1, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m1)).
% 1.72/1.83 fof(s1_0_axiom_m2, axiom, axiom_m2, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m2)).
% 1.72/1.83 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)).
% 1.72/1.83 fof(axiom_m3, axiom, (axiom_m3<=>![X1, X2, X3]:is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m3)).
% 1.72/1.83 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)).
% 1.72/1.83 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)).
% 1.72/1.83 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_op_implies_and)).
% 1.72/1.83 fof(s1_0_axiom_m3, axiom, axiom_m3, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m3)).
% 1.72/1.83 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_strict_implies)).
% 1.72/1.83 fof(s1_0_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_or)).
% 1.72/1.83 fof(axiom_m4, axiom, (axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m4)).
% 1.72/1.83 fof(s1_0_axiom_m4, axiom, axiom_m4, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m4)).
% 1.72/1.83 fof(op_possibly, axiom, (op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_possibly)).
% 1.72/1.83 fof(s1_0_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_possibly)).
% 1.72/1.83 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)).
% 1.72/1.83 fof(equivalence_2, axiom, (equivalence_2<=>![X1, X2]:is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', equivalence_2)).
% 1.72/1.83 fof(hilbert_equivalence_2, conjecture, equivalence_2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_equivalence_2)).
% 1.72/1.83 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)).
% 1.72/1.83 fof(s1_0_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_equiv)).
% 1.72/1.83 fof(c_0_31, plain, ![X243, X244]:((~adjunction|(~is_a_theorem(X243)|~is_a_theorem(X244)|is_a_theorem(and(X243,X244))))&(((is_a_theorem(esk59_0)|adjunction)&(is_a_theorem(esk60_0)|adjunction))&(~is_a_theorem(and(esk59_0,esk60_0))|adjunction))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])).
% 1.72/1.83 fof(c_0_32, 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])])])).
% 1.72/1.83 fof(c_0_33, 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])])])])])).
% 1.72/1.83 cnf(c_0_34, plain, (is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(split_conjunct,[status(thm)],[c_0_31])).
% 1.72/1.83 cnf(c_0_35, plain, (adjunction), inference(split_conjunct,[status(thm)],[s1_0_adjunction])).
% 1.72/1.83 cnf(c_0_36, plain, (strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv), inference(split_conjunct,[status(thm)],[c_0_32])).
% 1.72/1.83 cnf(c_0_37, plain, (op_strict_equiv), inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv])).
% 1.72/1.83 fof(c_0_38, plain, ![X239, X240]:((~modus_ponens_strict_implies|(~is_a_theorem(X239)|~is_a_theorem(strict_implies(X239,X240))|is_a_theorem(X240)))&(((is_a_theorem(esk57_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk57_0,esk58_0))|modus_ponens_strict_implies))&(~is_a_theorem(esk58_0)|modus_ponens_strict_implies))), 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_strict_implies])])])])])).
% 1.72/1.83 fof(c_0_39, plain, ![X295, X296, X297]:((~axiom_m5|is_a_theorem(strict_implies(and(strict_implies(X295,X296),strict_implies(X296,X297)),strict_implies(X295,X297))))&(~is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0)))|axiom_m5)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])).
% 1.72/1.83 cnf(c_0_40, plain, (X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_33])).
% 1.72/1.83 cnf(c_0_41, plain, (substitution_strict_equiv), inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv])).
% 1.72/1.83 cnf(c_0_42, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 1.72/1.83 cnf(c_0_43, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 1.72/1.83 fof(c_0_44, plain, ![X279, X280]:((~axiom_m1|is_a_theorem(strict_implies(and(X279,X280),and(X280,X279))))&(~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))|axiom_m1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])).
% 1.72/1.83 cnf(c_0_45, plain, (is_a_theorem(X2)|~modus_ponens_strict_implies|~is_a_theorem(X1)|~is_a_theorem(strict_implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 1.72/1.83 cnf(c_0_46, plain, (modus_ponens_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies])).
% 1.72/1.83 cnf(c_0_47, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_m5), inference(split_conjunct,[status(thm)],[c_0_39])).
% 1.72/1.83 cnf(c_0_48, plain, (axiom_m5), inference(split_conjunct,[status(thm)],[s1_0_axiom_m5])).
% 1.72/1.83 fof(c_0_49, plain, ![X283, X284]:((~axiom_m2|is_a_theorem(strict_implies(and(X283,X284),X283)))&(~is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))|axiom_m2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])).
% 1.72/1.83 cnf(c_0_50, plain, (X1=X2|~is_a_theorem(strict_equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 1.72/1.83 cnf(c_0_51, plain, (is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
% 1.72/1.83 cnf(c_0_52, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1), inference(split_conjunct,[status(thm)],[c_0_44])).
% 1.72/1.83 cnf(c_0_53, plain, (axiom_m1), inference(split_conjunct,[status(thm)],[s1_0_axiom_m1])).
% 1.72/1.83 cnf(c_0_54, plain, (is_a_theorem(X1)|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 1.72/1.83 cnf(c_0_55, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 1.72/1.83 cnf(c_0_56, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2), inference(split_conjunct,[status(thm)],[c_0_49])).
% 1.72/1.83 cnf(c_0_57, plain, (axiom_m2), inference(split_conjunct,[status(thm)],[s1_0_axiom_m2])).
% 1.72/1.83 cnf(c_0_58, plain, (X1=X2|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))), inference(spm,[status(thm)],[c_0_50, c_0_51])).
% 1.72/1.83 cnf(c_0_59, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 1.72/1.83 fof(c_0_60, plain, ![X231, X232]:(~op_implies_and|implies(X231,X232)=not(and(X231,not(X232)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])).
% 1.72/1.83 cnf(c_0_61, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 1.72/1.83 cnf(c_0_62, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 1.72/1.83 cnf(c_0_63, plain, (and(X1,X2)=and(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_59])])).
% 1.72/1.83 fof(c_0_64, plain, ![X287, X288, X289]:((~axiom_m3|is_a_theorem(strict_implies(and(and(X287,X288),X289),and(X287,and(X288,X289)))))&(~is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0))))|axiom_m3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])])).
% 1.72/1.83 fof(c_0_65, 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])])])).
% 1.72/1.83 fof(c_0_66, plain, ![X227, X228]:(~op_or|or(X227,X228)=not(and(not(X227),not(X228)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])).
% 1.72/1.83 cnf(c_0_67, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_60])).
% 1.72/1.83 cnf(c_0_68, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 1.72/1.83 cnf(c_0_69, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X3,X2))|~is_a_theorem(strict_implies(X1,X3))), inference(spm,[status(thm)],[c_0_61, c_0_42])).
% 1.72/1.83 cnf(c_0_70, plain, (is_a_theorem(strict_implies(and(X1,X2),X2))), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 1.72/1.83 cnf(c_0_71, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3), inference(split_conjunct,[status(thm)],[c_0_64])).
% 1.72/1.83 cnf(c_0_72, plain, (axiom_m3), inference(split_conjunct,[status(thm)],[s1_0_axiom_m3])).
% 1.72/1.83 cnf(c_0_73, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_65])).
% 1.72/1.83 cnf(c_0_74, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 1.72/1.83 cnf(c_0_75, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_66])).
% 1.72/1.83 cnf(c_0_76, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 1.72/1.83 cnf(c_0_77, plain, (op_or), inference(split_conjunct,[status(thm)],[s1_0_op_or])).
% 1.72/1.83 fof(c_0_78, plain, ![X293]:((~axiom_m4|is_a_theorem(strict_implies(X293,and(X293,X293))))&(~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))|axiom_m4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])).
% 1.72/1.83 cnf(c_0_79, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X3,X2)))), inference(spm,[status(thm)],[c_0_69, c_0_70])).
% 1.72/1.83 cnf(c_0_80, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])).
% 1.72/1.83 cnf(c_0_81, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74])])).
% 1.72/1.83 cnf(c_0_82, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76]), c_0_77])])).
% 1.72/1.83 cnf(c_0_83, plain, (not(and(not(X1),X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_76, c_0_63])).
% 1.72/1.83 cnf(c_0_84, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4), inference(split_conjunct,[status(thm)],[c_0_78])).
% 1.72/1.83 cnf(c_0_85, plain, (axiom_m4), inference(split_conjunct,[status(thm)],[s1_0_axiom_m4])).
% 1.72/1.83 cnf(c_0_86, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X2,X3)))), inference(spm,[status(thm)],[c_0_79, c_0_80])).
% 1.72/1.83 cnf(c_0_87, plain, (necessarily(or(X1,X2))=strict_implies(not(X1),X2)), inference(spm,[status(thm)],[c_0_81, c_0_82])).
% 1.72/1.83 cnf(c_0_88, plain, (or(X1,X2)=or(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_83]), c_0_82]), c_0_82])).
% 1.72/1.83 cnf(c_0_89, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])).
% 1.72/1.83 cnf(c_0_90, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(and(and(X3,X1),X2))), inference(spm,[status(thm)],[c_0_54, c_0_86])).
% 1.72/1.83 cnf(c_0_91, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X2,X3)))), inference(spm,[status(thm)],[c_0_69, c_0_62])).
% 1.72/1.83 cnf(c_0_92, plain, (strict_implies(not(X1),X2)=strict_implies(not(X2),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_87])).
% 1.72/1.83 cnf(c_0_93, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_89]), c_0_62])])).
% 1.72/1.83 cnf(c_0_94, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(and(X3,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_90, c_0_42])).
% 1.72/1.83 cnf(c_0_95, plain, (is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(strict_implies(not(and(X2,X3)),X1))), inference(spm,[status(thm)],[c_0_91, c_0_92])).
% 1.72/1.83 cnf(c_0_96, plain, (is_a_theorem(strict_implies(X1,X1))), inference(rw,[status(thm)],[c_0_89, c_0_93])).
% 1.72/1.83 cnf(c_0_97, plain, (is_a_theorem(and(strict_implies(X1,X2),X3))|~is_a_theorem(strict_equiv(X2,X1))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_94, c_0_43])).
% 1.72/1.83 cnf(c_0_98, plain, (strict_equiv(X1,X1)=strict_implies(X1,X1)), inference(spm,[status(thm)],[c_0_43, c_0_93])).
% 1.72/1.83 cnf(c_0_99, plain, (is_a_theorem(strict_implies(not(X1),not(and(X1,X2))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_92])).
% 1.72/1.83 cnf(c_0_100, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(and(X2,X1))), inference(spm,[status(thm)],[c_0_54, c_0_59])).
% 1.72/1.83 cnf(c_0_101, plain, (is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98]), c_0_96])])).
% 1.72/1.83 cnf(c_0_102, plain, (is_a_theorem(strict_implies(not(X1),implies(X1,X2)))), inference(spm,[status(thm)],[c_0_99, c_0_76])).
% 1.72/1.83 cnf(c_0_103, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_93]), c_0_82])).
% 1.72/1.83 cnf(c_0_104, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,not(X3)),strict_implies(not(X2),X3)))), inference(spm,[status(thm)],[c_0_61, c_0_92])).
% 1.72/1.83 cnf(c_0_105, plain, (is_a_theorem(and(X1,strict_implies(X2,X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_100, c_0_101])).
% 1.72/1.83 cnf(c_0_106, plain, (is_a_theorem(strict_implies(or(X1,X1),or(X1,X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_82])).
% 1.72/1.83 cnf(c_0_107, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))), inference(spm,[status(thm)],[c_0_104, c_0_105])).
% 1.72/1.83 cnf(c_0_108, plain, (is_a_theorem(strict_implies(or(X1,X1),not(not(X1))))), inference(spm,[status(thm)],[c_0_106, c_0_103])).
% 1.72/1.83 cnf(c_0_109, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))), inference(spm,[status(thm)],[c_0_107, c_0_103])).
% 1.72/1.83 cnf(c_0_110, plain, (is_a_theorem(strict_implies(or(X1,X1),X1))), inference(spm,[status(thm)],[c_0_107, c_0_108])).
% 1.72/1.83 cnf(c_0_111, plain, (is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_110]), c_0_103]), c_0_92])).
% 1.72/1.83 cnf(c_0_112, plain, (is_a_theorem(strict_implies(not(not(X1)),or(X1,X2)))), inference(spm,[status(thm)],[c_0_102, c_0_82])).
% 1.72/1.83 cnf(c_0_113, plain, (X1=not(X2)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(strict_implies(X1,not(X2)))), inference(spm,[status(thm)],[c_0_58, c_0_92])).
% 1.72/1.83 cnf(c_0_114, plain, (not(or(X1,X1))=not(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_111]), c_0_92]), c_0_112])])).
% 1.72/1.83 cnf(c_0_115, plain, (and(and(X1,X2),X3)=and(X1,and(X2,X3))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))), inference(spm,[status(thm)],[c_0_58, c_0_80])).
% 1.72/1.83 cnf(c_0_116, plain, (not(not(X1))=X1|~is_a_theorem(strict_implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_113, c_0_96])).
% 1.72/1.83 cnf(c_0_117, plain, (implies(X1,or(X2,X2))=implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_114]), c_0_76])).
% 1.72/1.83 cnf(c_0_118, plain, (and(X1,and(X1,X2))=and(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_93]), c_0_70])])).
% 1.72/1.83 cnf(c_0_119, plain, (or(X1,X1)=X1|~is_a_theorem(strict_implies(X1,or(X1,X1)))), inference(spm,[status(thm)],[c_0_116, c_0_103])).
% 1.72/1.83 cnf(c_0_120, plain, (strict_implies(X1,or(X2,X2))=strict_implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_117]), c_0_81])).
% 1.72/1.83 cnf(c_0_121, plain, (not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_76, c_0_76])).
% 1.72/1.83 cnf(c_0_122, plain, (and(X1,and(X2,X1))=and(X2,X1)), inference(spm,[status(thm)],[c_0_118, c_0_63])).
% 1.72/1.83 cnf(c_0_123, plain, (or(and(X1,not(X2)),X3)=implies(implies(X1,X2),X3)), inference(spm,[status(thm)],[c_0_82, c_0_76])).
% 1.72/1.83 cnf(c_0_124, plain, (or(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_120]), c_0_96])])).
% 1.72/1.83 cnf(c_0_125, plain, (implies(implies(X1,X2),and(X1,not(X2)))=not(implies(X1,X2))), inference(spm,[status(thm)],[c_0_121, c_0_93])).
% 1.72/1.83 cnf(c_0_126, plain, (implies(and(X1,not(X2)),X2)=implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_122]), c_0_76])).
% 1.72/1.83 cnf(c_0_127, plain, (and(X1,not(X2))=not(implies(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124]), c_0_125])).
% 1.72/1.83 cnf(c_0_128, plain, (not(and(X1,or(X2,X2)))=implies(X1,not(X2))), inference(spm,[status(thm)],[c_0_76, c_0_103])).
% 1.72/1.83 cnf(c_0_129, plain, (implies(or(X1,X1),X2)=or(not(X1),X2)), inference(spm,[status(thm)],[c_0_82, c_0_103])).
% 1.72/1.83 cnf(c_0_130, plain, (or(X1,implies(X2,X1))=implies(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126, c_0_127]), c_0_82]), c_0_88])).
% 1.72/1.83 cnf(c_0_131, plain, (or(X1,not(X2))=implies(or(X2,X2),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_128]), c_0_82])).
% 1.72/1.83 cnf(c_0_132, plain, (or(not(X1),X2)=implies(X1,X2)), inference(rw,[status(thm)],[c_0_129, c_0_124])).
% 1.72/1.83 cnf(c_0_133, plain, (or(X1,or(X2,X1))=or(X2,X1)), inference(spm,[status(thm)],[c_0_130, c_0_82])).
% 1.72/1.83 cnf(c_0_134, plain, (or(X1,not(X2))=implies(X2,X1)), inference(rw,[status(thm)],[c_0_131, c_0_124])).
% 1.72/1.83 cnf(c_0_135, plain, (implies(X1,implies(X1,X2))=implies(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134]), c_0_134])).
% 1.72/1.83 cnf(c_0_136, plain, (is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(and(strict_implies(not(X3),X1),strict_implies(X3,X2)))), inference(spm,[status(thm)],[c_0_61, c_0_92])).
% 1.72/1.83 cnf(c_0_137, plain, (is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,not(X2)))), inference(spm,[status(thm)],[c_0_69, c_0_102])).
% 1.72/1.83 cnf(c_0_138, plain, (strict_implies(not(X1),X1)=necessarily(X1)), inference(spm,[status(thm)],[c_0_87, c_0_124])).
% 1.72/1.83 cnf(c_0_139, plain, (not(not(X1))=X1), inference(rw,[status(thm)],[c_0_103, c_0_124])).
% 1.72/1.83 cnf(c_0_140, plain, (strict_implies(X1,implies(X1,X2))=strict_implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_135]), c_0_81])).
% 1.72/1.83 cnf(c_0_141, plain, (is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_54, c_0_92])).
% 1.72/1.83 cnf(c_0_142, plain, (is_a_theorem(strict_implies(not(not(X1)),X2))|~is_a_theorem(strict_implies(X1,X2))), inference(spm,[status(thm)],[c_0_136, c_0_101])).
% 1.72/1.83 cnf(c_0_143, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(necessarily(not(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_139]), c_0_140])).
% 1.72/1.83 cnf(c_0_144, plain, (is_a_theorem(not(X1))|~is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_141, c_0_142])).
% 1.72/1.83 cnf(c_0_145, plain, (is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(necessarily(X1))), inference(spm,[status(thm)],[c_0_143, c_0_139])).
% 1.72/1.83 cnf(c_0_146, plain, (is_a_theorem(X1)|~is_a_theorem(not(X2))|~is_a_theorem(necessarily(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_139])).
% 1.72/1.83 fof(c_0_147, plain, ![X315]:(~op_possibly|possibly(X315)=not(necessarily(not(X315)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])).
% 1.72/1.83 cnf(c_0_148, plain, (is_a_theorem(X1)|~is_a_theorem(necessarily(X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_146, c_0_139])).
% 1.72/1.83 cnf(c_0_149, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_147])).
% 1.72/1.84 cnf(c_0_150, plain, (op_possibly), inference(split_conjunct,[status(thm)],[s1_0_op_possibly])).
% 1.72/1.84 fof(c_0_151, 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])])])])).
% 1.72/1.84 cnf(c_0_152, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_148, c_0_81])).
% 1.72/1.84 cnf(c_0_153, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149, c_0_150])])).
% 1.72/1.84 fof(c_0_154, plain, ![X173, X174]:((~equivalence_2|is_a_theorem(implies(equiv(X173,X174),implies(X174,X173))))&(~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))|equivalence_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])).
% 1.72/1.84 fof(c_0_155, negated_conjecture, ~equivalence_2, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_equivalence_2])])).
% 1.72/1.84 fof(c_0_156, 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])])])).
% 1.72/1.84 cnf(c_0_157, plain, (and_2|~is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))), inference(split_conjunct,[status(thm)],[c_0_151])).
% 1.72/1.84 cnf(c_0_158, plain, (is_a_theorem(implies(and(X1,X2),X1))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_152, c_0_62])).
% 1.72/1.84 cnf(c_0_159, plain, (is_a_theorem(strict_implies(possibly(X1),implies(necessarily(not(X1)),X2)))), inference(spm,[status(thm)],[c_0_102, c_0_153])).
% 1.72/1.84 cnf(c_0_160, plain, (equivalence_2|~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))), inference(split_conjunct,[status(thm)],[c_0_154])).
% 1.72/1.84 cnf(c_0_161, negated_conjecture, (~equivalence_2), inference(split_conjunct,[status(thm)],[c_0_155])).
% 1.72/1.84 cnf(c_0_162, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_156])).
% 1.72/1.84 cnf(c_0_163, plain, (op_equiv), inference(split_conjunct,[status(thm)],[s1_0_op_equiv])).
% 1.72/1.84 cnf(c_0_164, plain, (and_2|~is_a_theorem(implies(and(esk17_0,esk16_0),esk17_0))), inference(rw,[status(thm)],[c_0_157, c_0_63])).
% 1.72/1.84 cnf(c_0_165, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(spm,[status(thm)],[c_0_158, c_0_159])).
% 1.72/1.84 cnf(c_0_166, plain, (~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))), inference(sr,[status(thm)],[c_0_160, c_0_161])).
% 1.72/1.84 cnf(c_0_167, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162, c_0_163])])).
% 1.72/1.84 cnf(c_0_168, plain, (is_a_theorem(implies(and(X1,X2),X2))|~and_2), inference(split_conjunct,[status(thm)],[c_0_151])).
% 1.72/1.84 cnf(c_0_169, plain, (and_2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164, c_0_165])])).
% 1.72/1.84 cnf(c_0_170, plain, (~is_a_theorem(implies(and(implies(esk29_0,esk30_0),implies(esk30_0,esk29_0)),implies(esk30_0,esk29_0)))), inference(rw,[status(thm)],[c_0_166, c_0_167])).
% 1.72/1.84 cnf(c_0_171, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168, c_0_169])])).
% 1.72/1.84 cnf(c_0_172, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170, c_0_171])]), ['proof']).
% 1.72/1.84 % SZS output end Proof
% 1.72/1.84 % User time : 1.140 s
% 1.72/1.84 % System time : 0.063 s
% 1.72/1.84 % Total time : 1.202 s
% 1.72/1.84
%------------------------------------------------------------------------------