%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL573+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n001.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 11:21:11 AM UTC 2026
% Result : Theorem 2.66s 0.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL573+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 02:15:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.48 start to proof:theBenchmark.p
% 2.66/0.94 % Version : CSI_E---1.1
% 2.66/0.94 % Problem : theBenchmark.p
% 2.66/0.94 % Proof found!
% 2.66/0.94 % SZS status Theorem for theBenchmark.p
% 2.66/0.94 % SZS output start Proof
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_adjunction, axiom, adjunction, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_adjunction)).
% 2.66/0.94 fof(s1_0_op_strict_equiv, axiom, op_strict_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_strict_equiv)).
% 2.66/0.94 fof(s1_0_substitution_strict_equiv, axiom, substitution_strict_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_substitution_strict_equiv)).
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_axiom_m1, axiom, axiom_m1, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m1)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_axiom_m5, axiom, axiom_m5, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m5)).
% 2.66/0.94 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)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_op_implies_and)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_strict_implies)).
% 2.66/0.94 fof(s1_0_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_or)).
% 2.66/0.94 fof(s1_0_axiom_m2, axiom, axiom_m2, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m2)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_axiom_m4, axiom, axiom_m4, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m4)).
% 2.66/0.94 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)).
% 2.66/0.94 fof(s1_0_axiom_m3, axiom, axiom_m3, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_axiom_m3)).
% 2.66/0.94 fof(op_possibly, axiom, (op_possibly=>![X1]:(possibly(X1)=not(necessarily(not(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_possibly)).
% 2.66/0.94 fof(s1_0_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax', s1_0_op_possibly)).
% 2.66/0.94 fof(axiom_m10, axiom, (axiom_m10<=>![X1]:(is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m10)).
% 2.66/0.94 fof(s1_0_m10_axiom_m10, axiom, axiom_m10, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+6.ax', s1_0_m10_axiom_m10)).
% 2.66/0.94 fof(km5_axiom_5, conjecture, axiom_5, file('/export/starexec/sandbox/benchmark/theBenchmark.p', km5_axiom_5)).
% 2.66/0.94 fof(axiom_5, axiom, (axiom_5<=>![X1]:(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_5)).
% 2.66/0.94 fof(c_0_30, plain, ![X22, X23]:(((~adjunction|(~is_a_theorem(X22)|~is_a_theorem(X23)|is_a_theorem(and(X22,X23))))&(((is_a_theorem(esk4_0)|adjunction)&(is_a_theorem(esk5_0)|adjunction))&(~is_a_theorem(and(esk4_0,esk5_0))|adjunction)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])])).
% 2.66/0.94 fof(c_0_31, plain, ![X98, X99]:((~op_strict_equiv|strict_equiv(X98,X99)=and(strict_implies(X98,X99),strict_implies(X99,X98)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])])).
% 2.66/0.94 fof(c_0_32, plain, ![X26, X27]:(((~substitution_strict_equiv|(~is_a_theorem(strict_equiv(X26,X27))|X26=X27))&((is_a_theorem(strict_equiv(esk6_0,esk7_0))|substitution_strict_equiv)&(esk6_0!=esk7_0|substitution_strict_equiv)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])])])).
% 2.66/0.94 cnf(c_0_33, plain, (is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(split_conjunct,[status(thm)],[c_0_30])).
% 2.66/0.94 cnf(c_0_34, plain, (adjunction), inference(split_conjunct,[status(thm)],[s1_0_adjunction])).
% 2.66/0.94 cnf(c_0_35, plain, (strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv), inference(split_conjunct,[status(thm)],[c_0_31])).
% 2.66/0.94 cnf(c_0_36, plain, (op_strict_equiv), inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv])).
% 2.66/0.94 cnf(c_0_37, plain, (X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 2.66/0.94 cnf(c_0_38, plain, (substitution_strict_equiv), inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv])).
% 2.66/0.94 cnf(c_0_39, 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_33, c_0_34])])).
% 2.66/0.94 cnf(c_0_40, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 2.66/0.94 fof(c_0_41, plain, ![X58, X59]:(((~axiom_m1|is_a_theorem(strict_implies(and(X58,X59),and(X59,X58))))&(~is_a_theorem(strict_implies(and(esk22_0,esk23_0),and(esk23_0,esk22_0)))|axiom_m1))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])])).
% 2.66/0.94 fof(c_0_42, plain, ![X18, X19]:(((~modus_ponens_strict_implies|(~is_a_theorem(X18)|~is_a_theorem(strict_implies(X18,X19))|is_a_theorem(X19)))&(((is_a_theorem(esk2_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk2_0,esk3_0))|modus_ponens_strict_implies))&(~is_a_theorem(esk3_0)|modus_ponens_strict_implies)))), inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])).
% 2.66/0.94 fof(c_0_43, plain, ![X74, X75, X76]:(((~axiom_m5|is_a_theorem(strict_implies(and(strict_implies(X74,X75),strict_implies(X75,X76)),strict_implies(X74,X76))))&(~is_a_theorem(strict_implies(and(strict_implies(esk30_0,esk31_0),strict_implies(esk31_0,esk32_0)),strict_implies(esk30_0,esk32_0)))|axiom_m5))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])])).
% 2.66/0.94 fof(c_0_44, plain, ![X10, X11]:((~op_implies_and|implies(X10,X11)=not(and(X10,not(X11))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])).
% 2.66/0.94 cnf(c_0_45, plain, (X1=X2|~is_a_theorem(strict_equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 2.66/0.94 cnf(c_0_46, 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_39, c_0_40])).
% 2.66/0.94 cnf(c_0_47, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1), inference(split_conjunct,[status(thm)],[c_0_41])).
% 2.66/0.94 cnf(c_0_48, plain, (axiom_m1), inference(split_conjunct,[status(thm)],[s1_0_axiom_m1])).
% 2.66/0.94 cnf(c_0_49, 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_42])).
% 2.66/0.94 cnf(c_0_50, plain, (modus_ponens_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies])).
% 2.66/0.94 cnf(c_0_51, 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_43])).
% 2.66/0.94 cnf(c_0_52, plain, (axiom_m5), inference(split_conjunct,[status(thm)],[s1_0_axiom_m5])).
% 2.66/0.94 fof(c_0_53, plain, ![X96, X97]:((~op_strict_implies|strict_implies(X96,X97)=necessarily(implies(X96,X97)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])])).
% 2.66/0.94 fof(c_0_54, plain, ![X6, X7]:((~op_or|or(X6,X7)=not(and(not(X6),not(X7))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])])).
% 2.66/0.94 cnf(c_0_55, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_44])).
% 2.66/0.94 cnf(c_0_56, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 2.66/0.94 cnf(c_0_57, plain, (X1=X2|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 2.66/0.94 cnf(c_0_58, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 2.66/0.94 cnf(c_0_59, 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_49, c_0_50])])).
% 2.66/0.94 cnf(c_0_60, 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_51, c_0_52])])).
% 2.66/0.94 fof(c_0_61, plain, ![X62, X63]:(((~axiom_m2|is_a_theorem(strict_implies(and(X62,X63),X62)))&(~is_a_theorem(strict_implies(and(esk24_0,esk25_0),esk24_0))|axiom_m2))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])])).
% 2.66/0.94 cnf(c_0_62, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_53])).
% 2.66/0.94 cnf(c_0_63, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 2.66/0.94 cnf(c_0_64, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_54])).
% 2.66/0.94 cnf(c_0_65, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56])])).
% 2.66/0.94 cnf(c_0_66, plain, (op_or), inference(split_conjunct,[status(thm)],[s1_0_op_or])).
% 2.66/0.94 cnf(c_0_67, plain, (and(X1,X2)=and(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_58])])).
% 2.66/0.94 cnf(c_0_68, 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_59, c_0_60])).
% 2.66/0.94 cnf(c_0_69, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2), inference(split_conjunct,[status(thm)],[c_0_61])).
% 2.66/0.94 cnf(c_0_70, plain, (axiom_m2), inference(split_conjunct,[status(thm)],[s1_0_axiom_m2])).
% 2.66/0.94 cnf(c_0_71, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 2.66/0.94 cnf(c_0_72, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65]), c_0_66])])).
% 2.66/0.94 cnf(c_0_73, plain, (not(and(not(X1),X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_65, c_0_67])).
% 2.66/0.94 fof(c_0_74, plain, ![X72]:(((~axiom_m4|is_a_theorem(strict_implies(X72,and(X72,X72))))&(~is_a_theorem(strict_implies(esk29_0,and(esk29_0,esk29_0)))|axiom_m4))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])])).
% 2.66/0.94 cnf(c_0_75, 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_68, c_0_39])).
% 2.66/0.94 cnf(c_0_76, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])).
% 2.66/0.94 cnf(c_0_77, plain, (necessarily(or(X1,X2))=strict_implies(not(X1),X2)), inference(spm,[status(thm)],[c_0_71, c_0_72])).
% 2.66/0.94 cnf(c_0_78, plain, (or(X1,X2)=or(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_73]), c_0_72]), c_0_72])).
% 2.66/0.94 cnf(c_0_79, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4), inference(split_conjunct,[status(thm)],[c_0_74])).
% 2.66/0.94 cnf(c_0_80, plain, (axiom_m4), inference(split_conjunct,[status(thm)],[s1_0_axiom_m4])).
% 2.66/0.94 cnf(c_0_81, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X2,X3)))), inference(spm,[status(thm)],[c_0_75, c_0_76])).
% 2.66/0.94 cnf(c_0_82, plain, (strict_implies(not(X1),X2)=strict_implies(not(X2),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_77])).
% 2.66/0.94 cnf(c_0_83, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])])).
% 2.66/0.94 cnf(c_0_84, 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_81, c_0_82])).
% 2.66/0.94 cnf(c_0_85, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_83]), c_0_76])])).
% 2.66/0.94 cnf(c_0_86, plain, (is_a_theorem(strict_implies(not(X1),not(and(X1,X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_83]), c_0_85]), c_0_82])).
% 2.66/0.94 cnf(c_0_87, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(not(X2),X3))|~is_a_theorem(strict_implies(X1,not(X3)))), inference(spm,[status(thm)],[c_0_75, c_0_82])).
% 2.66/0.94 cnf(c_0_88, plain, (is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(strict_implies(not(X2),X1))), inference(spm,[status(thm)],[c_0_84, c_0_85])).
% 2.66/0.94 cnf(c_0_89, plain, (is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_86, c_0_73])).
% 2.66/0.94 cnf(c_0_90, 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_57, c_0_82])).
% 2.66/0.94 cnf(c_0_91, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_83]), c_0_85])).
% 2.66/0.94 cnf(c_0_92, plain, (is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2)))), inference(spm,[status(thm)],[c_0_88, c_0_89])).
% 2.66/0.94 cnf(c_0_93, plain, (not(not(X1))=X1|~is_a_theorem(strict_implies(X1,not(not(X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_83]), c_0_85]), c_0_85])).
% 2.66/0.94 cnf(c_0_94, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_85]), c_0_72])).
% 2.66/0.94 cnf(c_0_95, plain, (is_a_theorem(strict_implies(not(X1),implies(X2,not(X1))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92]), c_0_82])).
% 2.66/0.94 fof(c_0_96, plain, ![X66, X67, X68]:(((~axiom_m3|is_a_theorem(strict_implies(and(and(X66,X67),X68),and(X66,and(X67,X68)))))&(~is_a_theorem(strict_implies(and(and(esk26_0,esk27_0),esk28_0),and(esk26_0,and(esk27_0,esk28_0))))|axiom_m3))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])])])).
% 2.66/0.94 cnf(c_0_97, plain, (or(X1,X1)=X1|~is_a_theorem(strict_implies(X1,or(X1,X1)))), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 2.66/0.94 cnf(c_0_98, plain, (is_a_theorem(strict_implies(not(X1),or(X2,not(X1))))), inference(spm,[status(thm)],[c_0_95, c_0_72])).
% 2.66/0.94 cnf(c_0_99, 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_96])).
% 2.66/0.94 cnf(c_0_100, plain, (axiom_m3), inference(split_conjunct,[status(thm)],[s1_0_axiom_m3])).
% 2.66/0.94 cnf(c_0_101, plain, (not(not(not(X1)))=not(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98]), c_0_94])).
% 2.66/0.94 cnf(c_0_102, 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_99, c_0_100])])).
% 2.66/0.94 cnf(c_0_103, plain, (implies(X1,not(not(X2)))=implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_101]), c_0_73])).
% 2.66/0.94 cnf(c_0_104, 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_57, c_0_102])).
% 2.66/0.94 cnf(c_0_105, plain, (is_a_theorem(strict_implies(and(X1,X2),X2))), inference(spm,[status(thm)],[c_0_76, c_0_67])).
% 2.66/0.94 cnf(c_0_106, plain, (strict_implies(X1,not(not(X2)))=strict_implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_103]), c_0_71])).
% 2.66/0.94 cnf(c_0_107, plain, (is_a_theorem(strict_implies(X1,X1))), inference(spm,[status(thm)],[c_0_76, c_0_85])).
% 2.66/0.94 cnf(c_0_108, plain, (and(X1,and(X1,X2))=and(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_85]), c_0_105])])).
% 2.66/0.94 cnf(c_0_109, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93, c_0_106]), c_0_107])])).
% 2.66/0.94 cnf(c_0_110, plain, (and(X1,and(X2,X1))=and(X2,X1)), inference(spm,[status(thm)],[c_0_108, c_0_67])).
% 2.66/0.94 cnf(c_0_111, plain, (not(implies(X1,X2))=and(not(X2),X1)), inference(spm,[status(thm)],[c_0_109, c_0_73])).
% 2.66/0.94 cnf(c_0_112, plain, (implies(and(X1,not(X2)),X2)=implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_110]), c_0_65])).
% 2.66/0.94 cnf(c_0_113, plain, (and(not(X1),not(X2))=not(or(X2,X1))), inference(spm,[status(thm)],[c_0_111, c_0_72])).
% 2.66/0.94 cnf(c_0_114, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_72, c_0_109])).
% 2.66/0.94 cnf(c_0_115, plain, (or(X1,or(X1,X2))=or(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113]), c_0_72]), c_0_72]), c_0_78])).
% 2.66/0.94 cnf(c_0_116, plain, (or(X1,not(X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_78, c_0_114])).
% 2.66/0.94 cnf(c_0_117, plain, (is_a_theorem(strict_implies(not(X1),implies(X1,X2)))), inference(spm,[status(thm)],[c_0_86, c_0_65])).
% 2.66/0.94 cnf(c_0_118, plain, (necessarily(not(not(X1)))=strict_implies(not(X1),X1)), inference(spm,[status(thm)],[c_0_77, c_0_94])).
% 2.66/0.94 cnf(c_0_119, plain, (implies(X1,implies(X1,X2))=implies(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_116]), c_0_114])).
% 2.66/0.94 fof(c_0_120, plain, ![X94]:((~op_possibly|possibly(X94)=not(necessarily(not(X94))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])])).
% 2.66/0.94 cnf(c_0_121, plain, (strict_implies(not(X1),not(X2))=strict_implies(X2,X1)), inference(spm,[status(thm)],[c_0_82, c_0_109])).
% 2.66/0.94 cnf(c_0_122, plain, (is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,not(X2)))), inference(spm,[status(thm)],[c_0_75, c_0_117])).
% 2.66/0.94 cnf(c_0_123, plain, (strict_implies(not(X1),X1)=necessarily(X1)), inference(rw,[status(thm)],[c_0_118, c_0_109])).
% 2.66/0.94 cnf(c_0_124, plain, (strict_implies(X1,implies(X1,X2))=strict_implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_119]), c_0_71])).
% 2.66/0.94 cnf(c_0_125, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_120])).
% 2.66/0.94 cnf(c_0_126, plain, (op_possibly), inference(split_conjunct,[status(thm)],[s1_0_op_possibly])).
% 2.66/0.94 cnf(c_0_127, plain, (strict_implies(X1,not(X2))=strict_implies(X2,not(X1))), inference(spm,[status(thm)],[c_0_121, c_0_109])).
% 2.66/0.94 cnf(c_0_128, 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_122, c_0_123]), c_0_109]), c_0_124])).
% 2.66/0.94 fof(c_0_129, plain, ![X92]:(((~axiom_m10|is_a_theorem(strict_implies(possibly(X92),necessarily(possibly(X92)))))&(~is_a_theorem(strict_implies(possibly(esk39_0),necessarily(possibly(esk39_0))))|axiom_m10))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m10])])])])])).
% 2.66/0.94 cnf(c_0_130, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125, c_0_126])])).
% 2.66/0.94 cnf(c_0_131, plain, (is_a_theorem(not(X1))|~is_a_theorem(strict_implies(X1,not(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_59, c_0_127])).
% 2.66/0.94 cnf(c_0_132, plain, (is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(necessarily(X1))), inference(spm,[status(thm)],[c_0_128, c_0_109])).
% 2.66/0.94 cnf(c_0_133, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|~axiom_m10), inference(split_conjunct,[status(thm)],[c_0_129])).
% 2.66/0.94 cnf(c_0_134, plain, (axiom_m10), inference(split_conjunct,[status(thm)],[s1_0_m10_axiom_m10])).
% 2.66/0.94 cnf(c_0_135, plain, (not(and(X1,possibly(X2)))=implies(X1,necessarily(not(X2)))), inference(spm,[status(thm)],[c_0_65, c_0_130])).
% 2.66/0.94 fof(c_0_136, negated_conjecture, ~axiom_5, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[km5_axiom_5])])).
% 2.66/0.94 cnf(c_0_137, plain, (is_a_theorem(X1)|~is_a_theorem(necessarily(X1))|~is_a_theorem(X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_109])).
% 2.66/0.94 cnf(c_0_138, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133, c_0_134])])).
% 2.66/0.94 cnf(c_0_139, plain, (possibly(and(X1,not(X2)))=not(strict_implies(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_65]), c_0_71])).
% 2.66/0.94 cnf(c_0_140, plain, (or(X1,necessarily(not(X2)))=implies(possibly(X2),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_73]), c_0_72])).
% 2.66/0.94 fof(c_0_141, plain, ![X40]:(((~axiom_5|is_a_theorem(implies(possibly(X40),necessarily(possibly(X40)))))&(~is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))|axiom_5))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])])).
% 2.66/0.94 fof(c_0_142, negated_conjecture, ~axiom_5, inference(fof_nnf,[status(thm)],[c_0_136])).
% 2.66/0.94 cnf(c_0_143, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_137, c_0_71])).
% 2.66/0.94 cnf(c_0_144, plain, (is_a_theorem(strict_implies(not(strict_implies(X1,X2)),necessarily(not(strict_implies(X1,X2)))))), inference(spm,[status(thm)],[c_0_138, c_0_139])).
% 2.66/0.94 cnf(c_0_145, plain, (strict_implies(not(X1),necessarily(not(X2)))=strict_implies(possibly(X2),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_140]), c_0_71])).
% 2.66/0.94 cnf(c_0_146, plain, (axiom_5|~is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))), inference(split_conjunct,[status(thm)],[c_0_141])).
% 2.66/0.94 cnf(c_0_147, negated_conjecture, (~axiom_5), inference(split_conjunct,[status(thm)],[c_0_142])).
% 2.66/0.94 cnf(c_0_148, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_143, c_0_138])).
% 2.66/0.94 cnf(c_0_149, plain, (is_a_theorem(strict_implies(possibly(strict_implies(X1,X2)),strict_implies(X1,X2)))), inference(rw,[status(thm)],[c_0_144, c_0_145])).
% 2.66/0.94 cnf(c_0_150, plain, (~is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))), inference(sr,[status(thm)],[c_0_146, c_0_147])).
% 2.66/0.94 cnf(c_0_151, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), inference(spm,[status(thm)],[c_0_148, c_0_149])).
% 2.66/0.94 cnf(c_0_152, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150, c_0_151])]), ['proof']).
% 2.66/0.94 % SZS output end Proof
% 2.66/0.94 % User time : 0.373 s
% 2.66/0.94 % System time : 0.030 s
% 2.66/0.94 % Total time : 0.403 s
% 2.66/0.94 % User time : 1.502 s
% 2.66/0.94 % System time : 0.104 s
% 2.66/0.94 % Total time : 1.606 s
% 2.66/0.94
%------------------------------------------------------------------------------