0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s 0.13/0.34 % Computer : n015.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 05:13:56 EDT 2022 0.13/0.34 % CPUTime : 0.21/0.45 openjdk version "1.8.0_171" 0.21/0.45 OpenJDK Runtime Environment (build 1.8.0_171-b10) 0.21/0.45 OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode) 0.21/0.46 file=/export/starexec/sandbox/benchmark/theBenchmark.p 0.64/0.71 start to proof: theBenchmark 0.69/0.86 % Version : CSE_E---1.4 0.69/0.86 % Problem : theBenchmark.p 0.69/0.86 % Proof found 0.69/0.86 % SZS status Theorem for theBenchmark.p 0.69/0.86 % SZS output start Proof 0.69/0.86 fof(op_implies_and, axiom, (![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))<=op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_and)). 0.69/0.86 fof(op_or, axiom, (![X1, X2]:not(and(not(X1),not(X2)))=or(X1,X2)<=op_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_or)). 0.69/0.86 fof(rosser_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_implies_and)). 0.69/0.86 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)). 0.69/0.86 fof(kn3, axiom, (kn3<=>![X4, X5, X6]:is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn3)). 0.69/0.86 fof(rosser_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_or)). 0.69/0.86 fof(rosser_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_modus_ponens)). 0.69/0.86 fof(rosser_kn3, axiom, kn3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn3)). 0.69/0.86 fof(kn2, axiom, (kn2<=>![X4, X5]:is_a_theorem(implies(and(X4,X5),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn2)). 0.69/0.86 fof(rosser_kn2, axiom, kn2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn2)). 0.69/0.86 fof(kn1, axiom, (![X4]:is_a_theorem(implies(X4,and(X4,X4)))<=>kn1), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn1)). 0.69/0.86 fof(rosser_kn1, axiom, kn1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn1)). 0.69/0.86 fof(op_equiv, axiom, (![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))<=op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_equiv)). 0.69/0.86 fof(rosser_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_equiv)). 0.69/0.86 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(X2=X1<=is_a_theorem(equiv(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)). 0.69/0.86 fof(substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', substitution_of_equivalents)). 0.69/0.86 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)). 0.69/0.86 fof(hilbert_or_1, conjecture, or_1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_or_1)). 0.69/0.86 fof(c_0_18, plain, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), inference(fof_simplification,[status(thm)],[op_implies_and])). 0.69/0.86 fof(c_0_19, plain, (op_or=>![X1, X2]:not(and(not(X1),not(X2)))=or(X1,X2)), inference(fof_simplification,[status(thm)],[op_or])). 0.69/0.86 fof(c_0_20, plain, ![X182, X183]:(~op_implies_and|implies(X182,X183)=not(and(X182,not(X183)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])). 0.69/0.86 fof(c_0_21, plain, ![X188, X189]:(~op_or|not(and(not(X188),not(X189)))=or(X188,X189)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])). 0.69/0.86 cnf(c_0_22, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_20])). 0.69/0.86 cnf(c_0_23, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[rosser_op_implies_and])). 0.69/0.86 fof(c_0_24, plain, ![X168, X169]:((~modus_ponens|(~is_a_theorem(X168)|~is_a_theorem(implies(X168,X169))|is_a_theorem(X169)))&(((is_a_theorem(esk49_0)|modus_ponens)&(is_a_theorem(implies(esk49_0,esk50_0))|modus_ponens))&(~is_a_theorem(esk50_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])])])])])). 0.69/0.86 fof(c_0_25, plain, ![X102, X103, X104]:((~kn3|is_a_theorem(implies(implies(X102,X103),implies(not(and(X103,X104)),not(and(X104,X102))))))&(~is_a_theorem(implies(implies(esk16_0,esk17_0),implies(not(and(esk17_0,esk18_0)),not(and(esk18_0,esk16_0)))))|kn3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])). 0.69/0.86 cnf(c_0_26, plain, (not(and(not(X1),not(X2)))=or(X1,X2)|~op_or), inference(split_conjunct,[status(thm)],[c_0_21])). 0.69/0.86 cnf(c_0_27, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])). 0.69/0.86 cnf(c_0_28, plain, (op_or), inference(split_conjunct,[status(thm)],[rosser_op_or])). 0.69/0.86 cnf(c_0_29, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_24])). 0.69/0.86 cnf(c_0_30, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[rosser_modus_ponens])). 0.69/0.86 cnf(c_0_31, plain, (is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))|~kn3), inference(split_conjunct,[status(thm)],[c_0_25])). 0.69/0.86 cnf(c_0_32, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27]), c_0_28])])). 0.69/0.86 cnf(c_0_33, plain, (kn3), inference(split_conjunct,[status(thm)],[rosser_kn3])). 0.69/0.87 cnf(c_0_34, 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_29, c_0_30])])). 0.69/0.87 cnf(c_0_35, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32]), c_0_33])])). 0.69/0.87 cnf(c_0_36, plain, (is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_34, c_0_32])). 0.69/0.87 cnf(c_0_37, plain, (is_a_theorem(or(and(X1,X2),not(and(X2,X3))))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_34, c_0_35])). 0.69/0.87 fof(c_0_38, plain, ![X98, X99]:((~kn2|is_a_theorem(implies(and(X98,X99),X98)))&(~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))|kn2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])). 0.69/0.87 cnf(c_0_39, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(and(X3,X1)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_36, c_0_37])). 0.69/0.87 cnf(c_0_40, plain, (is_a_theorem(implies(and(X1,X2),X1))|~kn2), inference(split_conjunct,[status(thm)],[c_0_38])). 0.69/0.87 cnf(c_0_41, plain, (kn2), inference(split_conjunct,[status(thm)],[rosser_kn2])). 0.69/0.87 fof(c_0_42, plain, ![X163]:((~is_a_theorem(implies(esk46_0,and(esk46_0,esk46_0)))|kn1)&(~kn1|is_a_theorem(implies(X163,and(X163,X163))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])). 0.69/0.87 cnf(c_0_43, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(implies(X3,X1))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_39, c_0_27])). 0.69/0.87 cnf(c_0_44, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])). 0.69/0.87 cnf(c_0_45, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1), inference(split_conjunct,[status(thm)],[c_0_42])). 0.69/0.87 cnf(c_0_46, plain, (kn1), inference(split_conjunct,[status(thm)],[rosser_kn1])). 0.69/0.87 cnf(c_0_47, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(implies(X2,and(X1,X3)))), inference(spm,[status(thm)],[c_0_43, c_0_44])). 0.69/0.87 cnf(c_0_48, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])). 0.69/0.87 cnf(c_0_49, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,and(X1,X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_32]), c_0_27]), c_0_32])). 0.69/0.87 cnf(c_0_50, plain, (is_a_theorem(or(X1,and(not(X1),not(X1))))), inference(spm,[status(thm)],[c_0_48, c_0_32])). 0.69/0.87 cnf(c_0_51, plain, (is_a_theorem(or(not(X1),X1))), inference(spm,[status(thm)],[c_0_49, c_0_50])). 0.69/0.87 cnf(c_0_52, plain, (is_a_theorem(or(X1,not(and(X1,X2))))), inference(spm,[status(thm)],[c_0_49, c_0_51])). 0.69/0.87 cnf(c_0_53, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_36, c_0_52])). 0.69/0.87 cnf(c_0_54, plain, (is_a_theorem(not(and(not(X1),X1)))), inference(spm,[status(thm)],[c_0_47, c_0_48])). 0.69/0.87 cnf(c_0_55, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,X3))|~is_a_theorem(not(X3))), inference(spm,[status(thm)],[c_0_39, c_0_53])). 0.69/0.87 cnf(c_0_56, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X1)))), inference(spm,[status(thm)],[c_0_39, c_0_54])). 0.69/0.87 cnf(c_0_57, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(and(X2,X2)))), inference(spm,[status(thm)],[c_0_55, c_0_48])). 0.69/0.87 cnf(c_0_58, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_27]), c_0_32])). 0.69/0.87 cnf(c_0_59, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_57, c_0_53])). 0.69/0.87 cnf(c_0_60, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_58, c_0_51])). 0.69/0.87 cnf(c_0_61, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(not(X2)))), inference(spm,[status(thm)],[c_0_59, c_0_27])). 0.69/0.87 cnf(c_0_62, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_34, c_0_60])). 0.69/0.87 cnf(c_0_63, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_61, c_0_62])). 0.69/0.87 cnf(c_0_64, plain, (is_a_theorem(or(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_52, c_0_27])). 0.69/0.87 cnf(c_0_65, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(and(X1,X3))), inference(spm,[status(thm)],[c_0_47, c_0_63])). 0.69/0.87 cnf(c_0_66, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_34, c_0_48])). 0.69/0.87 fof(c_0_67, plain, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(fof_simplification,[status(thm)],[op_equiv])). 0.69/0.87 cnf(c_0_68, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_36, c_0_64])). 0.69/0.87 cnf(c_0_69, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_65, c_0_66])). 0.69/0.87 fof(c_0_70, plain, ![X186, X187]:(~op_equiv|equiv(X186,X187)=and(implies(X186,X187),implies(X187,X186))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])). 0.69/0.87 cnf(c_0_71, plain, (is_a_theorem(or(and(X1,X2),implies(X2,X3)))|~is_a_theorem(or(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_27]), c_0_32])). 0.69/0.87 cnf(c_0_72, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X2)))), inference(spm,[status(thm)],[c_0_57, c_0_56])). 0.69/0.87 cnf(c_0_73, plain, (is_a_theorem(implies(and(not(X1),X1),X2))), inference(spm,[status(thm)],[c_0_68, c_0_54])). 0.69/0.87 cnf(c_0_74, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X3)))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_39, c_0_69])). 0.69/0.87 cnf(c_0_75, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_70])). 0.69/0.87 cnf(c_0_76, plain, (op_equiv), inference(split_conjunct,[status(thm)],[rosser_op_equiv])). 0.69/0.87 cnf(c_0_77, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(and(X3,X1)))|~is_a_theorem(or(X2,X3))), inference(spm,[status(thm)],[c_0_36, c_0_71])). 0.69/0.87 cnf(c_0_78, plain, (is_a_theorem(not(and(X1,and(not(X2),X2))))), inference(spm,[status(thm)],[c_0_72, c_0_73])). 0.69/0.87 cnf(c_0_79, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X3)))|~is_a_theorem(X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_32]), c_0_27])). 0.69/0.87 cnf(c_0_80, plain, (not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_27, c_0_27])). 0.69/0.87 cnf(c_0_81, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76])])). 0.69/0.87 cnf(c_0_82, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X1))|~is_a_theorem(or(X2,X3))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_27]), c_0_32])). 0.69/0.87 cnf(c_0_83, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_39, c_0_78])). 0.69/0.87 cnf(c_0_84, plain, (is_a_theorem(implies(X1,not(not(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_79, c_0_51])). 0.69/0.87 cnf(c_0_85, plain, (implies(implies(X1,X2),and(X2,not(X1)))=not(equiv(X1,X2))), inference(spm,[status(thm)],[c_0_80, c_0_81])). 0.69/0.87 cnf(c_0_86, plain, (is_a_theorem(or(not(not(X1)),X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_82, c_0_60])). 0.69/0.87 cnf(c_0_87, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_83, c_0_84])). 0.69/0.87 cnf(c_0_88, plain, (is_a_theorem(or(equiv(X1,X2),or(and(and(X2,not(X1)),X3),implies(X3,and(X1,not(X2))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_85]), c_0_80]), c_0_32])). 0.69/0.87 cnf(c_0_89, plain, (is_a_theorem(X1)|~is_a_theorem(not(not(not(X2))))|~is_a_theorem(or(X1,X2))), inference(spm,[status(thm)],[c_0_36, c_0_86])). 0.69/0.87 cnf(c_0_90, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))), inference(spm,[status(thm)],[c_0_87, c_0_88])). 0.69/0.87 cnf(c_0_91, plain, (is_a_theorem(or(and(X1,X1),X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_82, c_0_48])). 0.69/0.87 cnf(c_0_92, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_89, c_0_62])). 0.69/0.87 cnf(c_0_93, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,and(not(X3),X3)))), inference(spm,[status(thm)],[c_0_39, c_0_90])). 0.69/0.87 cnf(c_0_94, plain, (is_a_theorem(X1)|~is_a_theorem(not(and(X2,X2)))|~is_a_theorem(or(X1,X2))), inference(spm,[status(thm)],[c_0_36, c_0_91])). 0.69/0.87 cnf(c_0_95, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_50]), c_0_27]), c_0_32])). 0.69/0.87 cnf(c_0_96, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,and(not(X3),X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_32]), c_0_27])). 0.69/0.87 cnf(c_0_97, plain, (is_a_theorem(or(implies(X1,X2),and(X1,not(X2))))), inference(spm,[status(thm)],[c_0_51, c_0_27])). 0.69/0.87 cnf(c_0_98, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,not(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_94, c_0_69])). 0.69/0.87 cnf(c_0_99, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(or(and(X1,X1),X1))), inference(spm,[status(thm)],[c_0_95, c_0_91])). 0.69/0.87 cnf(c_0_100, plain, (is_a_theorem(implies(X1,or(not(X2),X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_32])). 0.69/0.87 cnf(c_0_101, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(and(X2,X3))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_98, c_0_37])). 0.69/0.87 cnf(c_0_102, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(or(X1,X1))), inference(spm,[status(thm)],[c_0_99, c_0_91])). 0.69/0.87 cnf(c_0_103, plain, (is_a_theorem(or(or(not(X1),X1),X2))|~is_a_theorem(or(X2,X3))), inference(spm,[status(thm)],[c_0_82, c_0_100])). 0.69/0.87 cnf(c_0_104, plain, (is_a_theorem(or(X1,not(not(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_84, c_0_32])). 0.69/0.87 fof(c_0_105, plain, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X2=X1)), inference(fof_simplification,[status(thm)],[substitution_of_equivalents])). 0.69/0.87 cnf(c_0_106, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(or(X2,X2))), inference(spm,[status(thm)],[c_0_101, c_0_102])). 0.69/0.87 cnf(c_0_107, plain, (is_a_theorem(or(or(not(X1),X1),X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_103, c_0_104])). 0.69/0.87 fof(c_0_108, plain, ![X124, X125]:((~substitution_of_equivalents|(~is_a_theorem(equiv(X124,X125))|X125=X124))&((is_a_theorem(equiv(esk27_0,esk28_0))|substitution_of_equivalents)&(esk28_0!=esk27_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)],[c_0_105])])])])])). 0.69/0.87 cnf(c_0_109, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(or(X2,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_106, c_0_63])). 0.69/0.87 cnf(c_0_110, plain, (is_a_theorem(or(or(not(X1),X1),X2))), inference(spm,[status(thm)],[c_0_107, c_0_88])). 0.69/0.87 cnf(c_0_111, plain, (X2=X1|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_108])). 0.69/0.87 cnf(c_0_112, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[substitution_of_equivalents])). 0.69/0.87 cnf(c_0_113, plain, (is_a_theorem(and(X1,or(not(X2),X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_109, c_0_110])). 0.69/0.87 cnf(c_0_114, plain, (and(implies(X1,not(X2)),or(X2,X1))=equiv(X1,not(X2))), inference(spm,[status(thm)],[c_0_81, c_0_32])). 0.69/0.87 cnf(c_0_115, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111, c_0_112])])). 0.69/0.87 cnf(c_0_116, plain, (is_a_theorem(equiv(X1,not(not(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_60])])). 0.69/0.87 fof(c_0_117, plain, ![X108, X109]:((~or_1|is_a_theorem(implies(X108,or(X108,X109))))&(~is_a_theorem(implies(esk19_0,or(esk19_0,esk20_0)))|or_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])). 0.69/0.87 fof(c_0_118, negated_conjecture, ~or_1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_or_1])])). 0.69/0.87 cnf(c_0_119, plain, (not(not(X1))=X1), inference(spm,[status(thm)],[c_0_115, c_0_116])). 0.69/0.87 cnf(c_0_120, plain, (or_1|~is_a_theorem(implies(esk19_0,or(esk19_0,esk20_0)))), inference(split_conjunct,[status(thm)],[c_0_117])). 0.69/0.87 cnf(c_0_121, negated_conjecture, (~or_1), inference(split_conjunct,[status(thm)],[c_0_118])). 0.69/0.87 cnf(c_0_122, plain, (is_a_theorem(or(not(X1),or(X1,X2)))), inference(spm,[status(thm)],[c_0_64, c_0_32])). 0.69/0.87 cnf(c_0_123, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_32, c_0_119])). 0.69/0.87 cnf(c_0_124, plain, (~is_a_theorem(implies(esk19_0,or(esk19_0,esk20_0)))), inference(sr,[status(thm)],[c_0_120, c_0_121])). 0.69/0.87 cnf(c_0_125, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(rw,[status(thm)],[c_0_122, c_0_123])). 0.69/0.87 cnf(c_0_126, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124, c_0_125])]), ['proof']). 0.69/0.87 % SZS output end Proof 0.69/0.87 % Total time : 0.150000 s 0.69/0.88 EOF