%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n029.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 11:21:09 AM UTC 2026
% Result : Theorem 0.76s 0.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n029.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 15:52:24 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.76/0.94 % Version : CSI_E---1.1
% 0.76/0.94 % Problem : theBenchmark.p
% 0.76/0.94 % Proof found!
% 0.76/0.94 % SZS status Theorem for theBenchmark.p
% 0.76/0.94 % SZS output start Proof
% 0.76/0.94 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)).
% 0.76/0.94 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)).
% 0.76/0.94 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)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.76/0.94 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', use_substitution_of_equivalents)).
% 0.76/0.94 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)).
% 0.76/0.94 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.76/0.94 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)).
% 0.76/0.94 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)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)).
% 0.76/0.94 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)).
% 0.76/0.94 fof(modus_tollens, axiom, (modus_tollens<=>![X1, X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_tollens)).
% 0.76/0.94 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)).
% 0.76/0.94 fof(or_1, axiom, (or_1<=>![X1, X2]:is_a_theorem(implies(X1,or(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_1)).
% 0.76/0.94 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)).
% 0.76/0.94 fof(or_2, axiom, (or_2<=>![X1, X2]:is_a_theorem(implies(X2,or(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', or_2)).
% 0.76/0.94 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)).
% 0.76/0.94 fof(hilbert_or_2, axiom, or_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_2)).
% 0.76/0.94 fof(necessitation, axiom, (necessitation<=>![X1]:(is_a_theorem(X1)=>is_a_theorem(necessarily(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', necessitation)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(op_possibly, axiom, (op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_possibly)).
% 0.76/0.94 fof(axiom_4, axiom, (axiom_4<=>![X1]:is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_4)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(axiom_m9, axiom, (axiom_m9<=>![X1]:is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m9)).
% 0.76/0.94 fof(s1_0_m6s3m9b_axiom_m9, conjecture, axiom_m9, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_m6s3m9b_axiom_m9)).
% 0.76/0.94 fof(km4b_necessitation, axiom, necessitation, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax', km4b_necessitation)).
% 0.76/0.94 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_op_strict_implies)).
% 0.76/0.94 fof(km4b_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax', km4b_op_possibly)).
% 0.76/0.94 fof(km4b_axiom_4, axiom, axiom_4, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax', km4b_axiom_4)).
% 0.76/0.94 fof(km4b_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax', km4b_axiom_M)).
% 0.76/0.94 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)).
% 0.76/0.94 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)).
% 0.76/0.94 fof(c_0_36, 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])])])])])).
% 0.76/0.94 fof(c_0_37, 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])])])])).
% 0.76/0.94 fof(c_0_38, 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])])])])])).
% 0.76/0.94 fof(c_0_39, 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])])])).
% 0.76/0.94 cnf(c_0_40, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_36])).
% 0.76/0.94 cnf(c_0_41, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.76/0.94 cnf(c_0_42, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.76/0.94 cnf(c_0_43, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.76/0.94 fof(c_0_44, plain, ![X133, X134]:((~implies_2|is_a_theorem(implies(implies(X133,implies(X133,X134)),implies(X133,X134))))&(~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])])])])).
% 0.76/0.94 cnf(c_0_45, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.76/0.94 cnf(c_0_46, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 0.76/0.94 cnf(c_0_47, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.76/0.94 cnf(c_0_48, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])).
% 0.76/0.94 cnf(c_0_49, 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_40, c_0_41])])).
% 0.76/0.94 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_42, c_0_43])])).
% 0.76/0.94 cnf(c_0_51, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_44])).
% 0.76/0.94 cnf(c_0_52, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.76/0.94 fof(c_0_53, 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])])])).
% 0.76/0.94 cnf(c_0_54, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 0.76/0.94 cnf(c_0_55, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 0.76/0.94 cnf(c_0_56, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_49, c_0_50])).
% 0.76/0.94 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_51, c_0_52])])).
% 0.76/0.94 fof(c_0_58, 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])])])])).
% 0.76/0.94 fof(c_0_59, 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])])])).
% 0.76/0.94 cnf(c_0_60, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.76/0.94 cnf(c_0_61, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.76/0.94 cnf(c_0_62, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 0.76/0.94 cnf(c_0_63, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_49, c_0_56])).
% 0.76/0.94 cnf(c_0_64, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_49, c_0_57])).
% 0.76/0.94 cnf(c_0_65, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_58])).
% 0.76/0.94 cnf(c_0_66, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])).
% 0.76/0.94 fof(c_0_67, plain, ![X125, X126]:((~modus_tollens|is_a_theorem(implies(implies(not(X126),not(X125)),implies(X125,X126))))&(~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])])])])).
% 0.76/0.94 cnf(c_0_68, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_59])).
% 0.76/0.94 cnf(c_0_69, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 0.76/0.94 cnf(c_0_70, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.76/0.94 fof(c_0_71, plain, ![X155, X156]:((~or_1|is_a_theorem(implies(X155,or(X155,X156))))&(~is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))|or_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])).
% 0.76/0.94 cnf(c_0_72, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 0.76/0.94 cnf(c_0_73, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_64, c_0_50])).
% 0.76/0.94 cnf(c_0_74, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 0.76/0.94 cnf(c_0_75, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_67])).
% 0.76/0.94 cnf(c_0_76, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68, c_0_69]), c_0_70])])).
% 0.76/0.94 cnf(c_0_77, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])).
% 0.76/0.94 fof(c_0_78, plain, ![X159, X160]:((~or_2|is_a_theorem(implies(X160,or(X159,X160))))&(~is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0)))|or_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_2])])])])).
% 0.76/0.94 cnf(c_0_79, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[c_0_71])).
% 0.76/0.94 cnf(c_0_80, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1])).
% 0.76/0.94 cnf(c_0_81, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_74])])).
% 0.76/0.94 cnf(c_0_82, 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_75, c_0_76]), c_0_77])])).
% 0.76/0.94 cnf(c_0_83, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~or_2), inference(split_conjunct,[status(thm)],[c_0_78])).
% 0.76/0.94 cnf(c_0_84, plain, (or_2), inference(split_conjunct,[status(thm)],[hilbert_or_2])).
% 0.76/0.94 cnf(c_0_85, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])])).
% 0.76/0.94 cnf(c_0_86, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_81]), c_0_76])).
% 0.76/0.94 cnf(c_0_87, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_49, c_0_82])).
% 0.76/0.94 cnf(c_0_88, plain, (is_a_theorem(implies(X1,or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])).
% 0.76/0.94 fof(c_0_89, plain, ![X237]:((~necessitation|(~is_a_theorem(X237)|is_a_theorem(necessarily(X237))))&((is_a_theorem(esk56_0)|necessitation)&(~is_a_theorem(necessarily(esk56_0))|necessitation))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])).
% 0.76/0.94 fof(c_0_90, 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])])])).
% 0.76/0.94 fof(c_0_91, 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])])])).
% 0.76/0.94 cnf(c_0_92, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_85, c_0_86])).
% 0.76/0.94 cnf(c_0_93, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,or(X1,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_86]), c_0_76])).
% 0.76/0.94 cnf(c_0_94, plain, (is_a_theorem(or(X1,or(X2,not(X1))))), inference(spm,[status(thm)],[c_0_88, c_0_76])).
% 0.76/0.94 fof(c_0_95, plain, ![X257]:((~axiom_4|is_a_theorem(implies(necessarily(X257),necessarily(necessarily(X257)))))&(~is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0))))|axiom_4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])).
% 0.76/0.94 fof(c_0_96, 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])])])])).
% 0.76/0.94 fof(c_0_97, plain, ![X311]:((~axiom_m9|is_a_theorem(strict_implies(possibly(possibly(X311)),possibly(X311))))&(~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0)))|axiom_m9)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m9])])])])).
% 0.76/0.94 fof(c_0_98, negated_conjecture, ~axiom_m9, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m9])])).
% 0.76/0.94 cnf(c_0_99, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)), inference(split_conjunct,[status(thm)],[c_0_89])).
% 0.76/0.94 cnf(c_0_100, plain, (necessitation), inference(split_conjunct,[status(thm)],[km4b_necessitation])).
% 0.76/0.94 cnf(c_0_101, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_90])).
% 0.76/0.94 cnf(c_0_102, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 0.76/0.94 cnf(c_0_103, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_91])).
% 0.76/0.94 cnf(c_0_104, plain, (op_possibly), inference(split_conjunct,[status(thm)],[km4b_op_possibly])).
% 0.76/0.94 cnf(c_0_105, plain, (not(not(X1))=X1|~is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_92]), c_0_76])).
% 0.76/0.94 cnf(c_0_106, plain, (is_a_theorem(or(not(X1),X1))), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 0.76/0.94 cnf(c_0_107, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4), inference(split_conjunct,[status(thm)],[c_0_95])).
% 0.76/0.94 cnf(c_0_108, plain, (axiom_4), inference(split_conjunct,[status(thm)],[km4b_axiom_4])).
% 0.76/0.94 cnf(c_0_109, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_96])).
% 0.76/0.94 cnf(c_0_110, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km4b_axiom_M])).
% 0.76/0.94 fof(c_0_111, plain, ![X129, X130]:((~implies_1|is_a_theorem(implies(X129,implies(X130,X129))))&(~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])])])])).
% 0.76/0.94 cnf(c_0_112, plain, (axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0)))), inference(split_conjunct,[status(thm)],[c_0_97])).
% 0.76/0.94 cnf(c_0_113, negated_conjecture, (~axiom_m9), inference(split_conjunct,[status(thm)],[c_0_98])).
% 0.76/0.94 cnf(c_0_114, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99, c_0_100])])).
% 0.76/0.94 cnf(c_0_115, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101, c_0_102])])).
% 0.76/0.94 cnf(c_0_116, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_104])])).
% 0.76/0.94 cnf(c_0_117, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_106])])).
% 0.76/0.94 cnf(c_0_118, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_108])])).
% 0.76/0.94 cnf(c_0_119, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110])])).
% 0.76/0.94 cnf(c_0_120, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_111])).
% 0.76/0.94 cnf(c_0_121, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])).
% 0.76/0.94 cnf(c_0_122, plain, (~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0)))), inference(sr,[status(thm)],[c_0_112, c_0_113])).
% 0.76/0.94 cnf(c_0_123, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_114, c_0_115])).
% 0.76/0.94 cnf(c_0_124, plain, (possibly(not(X1))=not(necessarily(X1))), inference(spm,[status(thm)],[c_0_116, c_0_117])).
% 0.76/0.94 cnf(c_0_125, plain, (necessarily(necessarily(X1))=necessarily(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_118]), c_0_119])])).
% 0.76/0.94 cnf(c_0_126, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120, c_0_121])])).
% 0.76/0.94 cnf(c_0_127, plain, (~is_a_theorem(implies(possibly(possibly(esk93_0)),possibly(esk93_0)))), inference(spm,[status(thm)],[c_0_122, c_0_123])).
% 0.76/0.94 cnf(c_0_128, plain, (possibly(possibly(X1))=possibly(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_116]), c_0_125]), c_0_116])).
% 0.76/0.94 cnf(c_0_129, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_64, c_0_126])).
% 0.76/0.94 cnf(c_0_130, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127, c_0_128]), c_0_129])]), ['proof']).
% 0.76/0.94 % SZS output end Proof
% 0.76/0.94 % User time : 0.416 s
% 0.76/0.94 % System time : 0.032 s
% 0.76/0.94 % Total time : 0.448 s
% 0.76/0.94
%------------------------------------------------------------------------------