0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_epr.jar %d %s 0.09/0.30 % Computer : n029.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Thu Jul 2 08:33:31 EDT 2020 0.09/0.30 % CPUTime : 0.14/0.39 openjdk version "1.8.0_171" 0.14/0.39 OpenJDK Runtime Environment (build 1.8.0_171-b10) 0.14/0.39 OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode) 0.14/0.40 file=/export/starexec/sandbox2/benchmark/theBenchmark.p 0.25/0.54 start to proof:theBenchmark.p 0.60/0.85 % Version : CSE_E---1.2 0.60/0.85 % Problem : theBenchmark.p 0.60/0.85 % Proof found! 0.60/0.85 % SZS status Theorem for theBenchmark.p 0.60/0.85 % SZS output start Proof 0.60/0.85 fof(modus_ponens, axiom, (![X1, X2]:(is_a_theorem(X2)<=(is_a_theorem(X1)&is_a_theorem(implies(X1,X2))))<=>modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_ponens)). 0.60/0.85 fof(and_3, axiom, (![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))<=>and_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', and_3)). 0.60/0.85 fof(substitution_of_equivalents, axiom, (![X1, X2]:(X1=X2<=is_a_theorem(equiv(X1,X2)))<=>substitution_of_equivalents), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)). 0.60/0.85 fof(op_equiv, axiom, (![X1, X2]:and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)<=op_equiv), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_equiv)). 0.60/0.85 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)). 0.60/0.85 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)). 0.60/0.85 fof(implies_2, axiom, (implies_2<=>![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_2)). 0.60/0.85 fof(substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', substitution_of_equivalents)). 0.60/0.85 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)). 0.60/0.85 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)). 0.60/0.85 fof(and_1, axiom, (![X1, X2]:is_a_theorem(implies(and(X1,X2),X1))<=>and_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', and_1)). 0.60/0.85 fof(op_implies_and, axiom, (op_implies_and=>![X1, X2]:not(and(X1,not(X2)))=implies(X1,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_and)). 0.60/0.85 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)). 0.60/0.85 fof(op_or, axiom, (op_or=>![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_or)). 0.60/0.85 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)). 0.60/0.85 fof(or_1, axiom, (![X1, X2]:is_a_theorem(implies(X1,or(X1,X2)))<=>or_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', or_1)). 0.60/0.85 fof(implies_1, axiom, (implies_1<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_1)). 0.60/0.85 fof(op_possibly, axiom, (op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax', op_possibly)). 0.60/0.85 fof(axiom_5, axiom, (![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))<=>axiom_5), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_5)). 0.60/0.85 fof(axiom_M, axiom, (![X1]:is_a_theorem(implies(necessarily(X1),X1))<=>axiom_M), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_M)). 0.60/0.85 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)). 0.60/0.85 fof(modus_tollens, axiom, (![X1, X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))<=>modus_tollens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_tollens)). 0.60/0.85 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)). 0.60/0.85 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)). 0.60/0.85 fof(km5_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_op_possibly)). 0.60/0.85 fof(km5_axiom_5, axiom, axiom_5, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_axiom_5)). 0.60/0.85 fof(km5_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_axiom_M)). 0.60/0.85 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)). 0.60/0.85 fof(s1_0_m6s3m9b_axiom_m9, conjecture, axiom_m9, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', s1_0_m6s3m9b_axiom_m9)). 0.60/0.85 fof(necessitation, axiom, (necessitation<=>![X1]:(is_a_theorem(X1)=>is_a_theorem(necessarily(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', necessitation)). 0.60/0.85 fof(op_strict_implies, axiom, (op_strict_implies=>![X1, X2]:necessarily(implies(X1,X2))=strict_implies(X1,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax', op_strict_implies)). 0.60/0.85 fof(axiom_m9, axiom, (![X1]:is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))<=>axiom_m9), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_m9)). 0.60/0.85 fof(km5_necessitation, axiom, necessitation, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_necessitation)). 0.60/0.85 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', s1_0_op_strict_implies)). 0.60/0.85 fof(c_0_34, plain, ![X105, X106]:((((is_a_theorem(esk49_0)|modus_ponens)&(is_a_theorem(implies(esk49_0,esk50_0))|modus_ponens))&(~is_a_theorem(esk50_0)|modus_ponens))&(~modus_ponens|(~is_a_theorem(X105)|~is_a_theorem(implies(X105,X106))|is_a_theorem(X106)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[modus_ponens])])])])])])). 0.60/0.85 fof(c_0_35, plain, ![X21, X22]:((~is_a_theorem(implies(esk7_0,implies(esk8_0,and(esk7_0,esk8_0))))|and_3)&(~and_3|is_a_theorem(implies(X21,implies(X22,and(X21,X22)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])). 0.60/0.85 fof(c_0_36, plain, ![X51, X52]:(((is_a_theorem(equiv(esk22_0,esk23_0))|substitution_of_equivalents)&(esk22_0!=esk23_0|substitution_of_equivalents))&(~substitution_of_equivalents|(~is_a_theorem(equiv(X51,X52))|X51=X52))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[substitution_of_equivalents])])])])])])). 0.60/0.85 fof(c_0_37, plain, ![X119, X120]:(~op_equiv|and(implies(X119,X120),implies(X120,X119))=equiv(X119,X120)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[op_equiv])])])])). 0.60/0.85 cnf(c_0_38, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_34])). 0.60/0.85 cnf(c_0_39, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])). 0.60/0.85 cnf(c_0_40, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_35])). 0.60/0.85 cnf(c_0_41, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])). 0.60/0.85 fof(c_0_42, plain, ![X107, X108]:((~implies_2|is_a_theorem(implies(implies(X107,implies(X107,X108)),implies(X107,X108))))&(~is_a_theorem(implies(implies(esk51_0,implies(esk51_0,esk52_0)),implies(esk51_0,esk52_0)))|implies_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])). 0.60/0.85 cnf(c_0_43, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_36])). 0.60/0.85 cnf(c_0_44, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[substitution_of_equivalents])). 0.60/0.85 cnf(c_0_45, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_37])). 0.60/0.85 cnf(c_0_46, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])). 0.60/0.85 cnf(c_0_47, 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_38, c_0_39])])). 0.60/0.85 cnf(c_0_48, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])). 0.60/0.85 cnf(c_0_49, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_42])). 0.60/0.85 cnf(c_0_50, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])). 0.60/0.85 cnf(c_0_51, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])). 0.60/0.85 cnf(c_0_52, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])). 0.60/0.85 cnf(c_0_53, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_47, c_0_48])). 0.60/0.85 cnf(c_0_54, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])). 0.60/0.85 fof(c_0_55, plain, ![X91, X92]:((~is_a_theorem(implies(and(esk42_0,esk43_0),esk42_0))|and_1)&(~and_1|is_a_theorem(implies(and(X91,X92),X91)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])). 0.60/0.85 fof(c_0_56, plain, ![X123, X124]:(~op_implies_and|not(and(X123,not(X124)))=implies(X123,X124)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])). 0.60/0.85 cnf(c_0_57, plain, (X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_51, c_0_52])). 0.60/0.85 cnf(c_0_58, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_47, c_0_53])). 0.60/0.85 cnf(c_0_59, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_47, c_0_54])). 0.60/0.85 cnf(c_0_60, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_55])). 0.60/0.85 cnf(c_0_61, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])). 0.60/0.85 fof(c_0_62, plain, ![X121, X122]:(~op_or|or(X121,X122)=not(and(not(X121),not(X122)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])). 0.60/0.85 cnf(c_0_63, plain, (not(and(X1,not(X2)))=implies(X1,X2)|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_56])). 0.60/0.85 cnf(c_0_64, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])). 0.60/0.85 fof(c_0_65, plain, ![X75, X76]:((~is_a_theorem(implies(esk34_0,or(esk34_0,esk35_0)))|or_1)&(~or_1|is_a_theorem(implies(X75,or(X75,X76))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])). 0.60/0.85 fof(c_0_66, plain, ![X45, X46]:((~implies_1|is_a_theorem(implies(X45,implies(X46,X45))))&(~is_a_theorem(implies(esk20_0,implies(esk21_0,esk20_0)))|implies_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])). 0.60/0.85 fof(c_0_67, plain, ![X208]:(~op_possibly|possibly(X208)=not(necessarily(not(X208)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])). 0.60/0.85 fof(c_0_68, plain, ![X200]:((~is_a_theorem(implies(possibly(esk92_0),necessarily(possibly(esk92_0))))|axiom_5)&(~axiom_5|is_a_theorem(implies(possibly(X200),necessarily(possibly(X200)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])). 0.60/0.85 fof(c_0_69, plain, ![X138]:((~is_a_theorem(implies(necessarily(esk61_0),esk61_0))|axiom_M)&(~axiom_M|is_a_theorem(implies(necessarily(X138),X138)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])). 0.60/0.85 cnf(c_0_70, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_57, c_0_58])). 0.60/0.85 cnf(c_0_71, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_59, c_0_48])). 0.60/0.85 cnf(c_0_72, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])). 0.60/0.85 cnf(c_0_73, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_62])). 0.60/0.85 cnf(c_0_74, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])). 0.60/0.85 cnf(c_0_75, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])). 0.60/0.85 fof(c_0_76, plain, ![X33, X34]:((~is_a_theorem(implies(implies(not(esk14_0),not(esk13_0)),implies(esk13_0,esk14_0)))|modus_tollens)&(~modus_tollens|is_a_theorem(implies(implies(not(X34),not(X33)),implies(X33,X34))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])). 0.60/0.85 cnf(c_0_77, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[c_0_65])). 0.60/0.85 cnf(c_0_78, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1])). 0.60/0.85 cnf(c_0_79, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_66])). 0.60/0.85 cnf(c_0_80, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])). 0.60/0.85 cnf(c_0_81, plain, (possibly(X1)=not(necessarily(not(X1)))|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_67])). 0.60/0.85 cnf(c_0_82, plain, (op_possibly), inference(split_conjunct,[status(thm)],[km5_op_possibly])). 0.60/0.85 cnf(c_0_83, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5), inference(split_conjunct,[status(thm)],[c_0_68])). 0.60/0.85 cnf(c_0_84, plain, (axiom_5), inference(split_conjunct,[status(thm)],[km5_axiom_5])). 0.60/0.85 cnf(c_0_85, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_69])). 0.60/0.85 cnf(c_0_86, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km5_axiom_M])). 0.60/0.85 cnf(c_0_87, plain, (and(X1,X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])])). 0.60/0.85 cnf(c_0_88, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74]), c_0_75])])). 0.60/0.85 cnf(c_0_89, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_76])). 0.60/0.85 cnf(c_0_90, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])). 0.60/0.85 cnf(c_0_91, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77, c_0_78])])). 0.60/0.85 cnf(c_0_92, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])])). 0.60/0.85 fof(c_0_93, negated_conjecture, ~(axiom_m9), inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m9])). 0.60/0.85 fof(c_0_94, plain, ![X163]:((~necessitation|(~is_a_theorem(X163)|is_a_theorem(necessarily(X163))))&((is_a_theorem(esk74_0)|necessitation)&(~is_a_theorem(necessarily(esk74_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])])])])])). 0.60/0.85 fof(c_0_95, plain, ![X206, X207]:(~op_strict_implies|necessarily(implies(X206,X207))=strict_implies(X206,X207)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])). 0.60/0.85 cnf(c_0_96, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_82])])). 0.60/0.85 cnf(c_0_97, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])). 0.60/0.85 cnf(c_0_98, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_86])])). 0.60/0.85 cnf(c_0_99, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_87]), c_0_88])). 0.60/0.85 cnf(c_0_100, 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_89, c_0_88]), c_0_90])])). 0.60/0.85 cnf(c_0_101, plain, (is_a_theorem(or(X1,or(not(X1),X2)))), inference(spm,[status(thm)],[c_0_91, c_0_88])). 0.60/0.85 cnf(c_0_102, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_47, c_0_92])). 0.60/0.85 fof(c_0_103, plain, ![X170]:((~is_a_theorem(strict_implies(possibly(possibly(esk77_0)),possibly(esk77_0)))|axiom_m9)&(~axiom_m9|is_a_theorem(strict_implies(possibly(possibly(X170)),possibly(X170))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m9])])])])). 0.60/0.85 fof(c_0_104, negated_conjecture, ~axiom_m9, inference(fof_simplification,[status(thm)],[c_0_93])). 0.60/0.85 cnf(c_0_105, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)), inference(split_conjunct,[status(thm)],[c_0_94])). 0.60/0.85 cnf(c_0_106, plain, (necessitation), inference(split_conjunct,[status(thm)],[km5_necessitation])). 0.60/0.85 cnf(c_0_107, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_95])). 0.60/0.85 cnf(c_0_108, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])). 0.60/0.85 cnf(c_0_109, plain, (not(necessarily(possibly(X1)))=possibly(necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_96, c_0_96])). 0.60/0.85 cnf(c_0_110, plain, (necessarily(possibly(X1))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_97]), c_0_98])])). 0.60/0.85 cnf(c_0_111, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_91, c_0_99])). 0.60/0.85 cnf(c_0_112, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_47, c_0_100])). 0.60/0.85 cnf(c_0_113, plain, (is_a_theorem(or(X1,not(not(not(X1)))))), inference(spm,[status(thm)],[c_0_101, c_0_99])). 0.60/0.85 cnf(c_0_114, plain, (X1=X2|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_70, c_0_102])). 0.60/0.85 cnf(c_0_115, plain, (axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk77_0)),possibly(esk77_0)))), inference(split_conjunct,[status(thm)],[c_0_103])). 0.60/0.85 cnf(c_0_116, negated_conjecture, (~axiom_m9), inference(split_conjunct,[status(thm)],[c_0_104])). 0.60/0.85 cnf(c_0_117, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_106])])). 0.60/0.85 cnf(c_0_118, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_108])])). 0.60/0.85 cnf(c_0_119, plain, (possibly(necessarily(not(X1)))=not(possibly(X1))), inference(rw,[status(thm)],[c_0_109, c_0_110])). 0.60/0.85 cnf(c_0_120, plain, (not(not(X1))=X1|~is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_111]), c_0_88])). 0.60/0.85 cnf(c_0_121, plain, (is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113]), c_0_88])). 0.60/0.85 cnf(c_0_122, plain, (X1=X2|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_114, c_0_102])). 0.60/0.85 cnf(c_0_123, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_59, c_0_92])). 0.60/0.85 cnf(c_0_124, plain, (~is_a_theorem(strict_implies(possibly(possibly(esk77_0)),possibly(esk77_0)))), inference(sr,[status(thm)],[c_0_115, c_0_116])). 0.60/0.85 cnf(c_0_125, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_117, c_0_118])). 0.60/0.85 cnf(c_0_126, plain, (not(not(possibly(X1)))=possibly(possibly(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_96]), c_0_110]), c_0_119])). 0.60/0.85 cnf(c_0_127, plain, (not(not(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120, c_0_121])])). 0.60/0.85 cnf(c_0_128, plain, (implies(X1,X1)=X2|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_122, c_0_123])). 0.60/0.85 cnf(c_0_129, plain, (~is_a_theorem(implies(possibly(possibly(esk77_0)),possibly(esk77_0)))), inference(spm,[status(thm)],[c_0_124, c_0_125])). 0.60/0.85 cnf(c_0_130, plain, (possibly(possibly(X1))=possibly(X1)), inference(rw,[status(thm)],[c_0_126, c_0_127])). 0.60/0.85 cnf(c_0_131, plain, (implies(X1,X1)=implies(X2,X2)), inference(spm,[status(thm)],[c_0_128, c_0_123])). 0.60/0.85 cnf(c_0_132, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129, c_0_130]), c_0_131]), c_0_123])]), ['proof']). 0.60/0.85 % SZS output end Proof 0.60/0.85 % User time : 0.168 s 0.60/0.85 % System time : 0.019 s 0.60/0.85 % Total time : 0.187 s 0.60/0.85 0.83/0.87 EOF