0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s 0.13/0.34 % Computer : n021.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 05:04:50 EDT 2022 0.13/0.35 % CPUTime : 0.19/0.45 openjdk version "1.8.0_171" 0.19/0.45 OpenJDK Runtime Environment (build 1.8.0_171-b10) 0.19/0.45 OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode) 0.19/0.46 file=/export/starexec/sandbox2/benchmark/theBenchmark.p 0.70/0.73 start to proof: theBenchmark 14.25/14.39 % Version : CSE_E---1.4 14.25/14.39 % Problem : theBenchmark.p 14.25/14.39 % Proof found 14.25/14.39 % SZS status Theorem for theBenchmark.p 14.25/14.39 % SZS output start Proof 14.25/14.39 fof(op_implies_and, axiom, (![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))<=op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_and)). 14.25/14.39 fof(op_or, axiom, (![X1, X2]:not(and(not(X1),not(X2)))=or(X1,X2)<=op_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_or)). 14.25/14.39 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/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_ponens)). 14.25/14.39 fof(r3, axiom, (r3<=>![X4, X5]:is_a_theorem(implies(or(X4,X5),or(X5,X4)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r3)). 14.25/14.39 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_op_implies_and)). 14.25/14.39 fof(principia_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_modus_ponens)). 14.25/14.39 fof(principia_r3, axiom, r3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r3)). 14.25/14.39 fof(op_implies_or, axiom, (op_implies_or=>![X1, X2]:or(not(X1),X2)=implies(X1,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_or)). 14.25/14.39 fof(r1, axiom, (r1<=>![X4]:is_a_theorem(implies(or(X4,X4),X4))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r1)). 14.25/14.39 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_op_or)). 14.25/14.39 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_implies_or)). 14.25/14.39 fof(principia_r1, axiom, r1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r1)). 14.25/14.39 fof(r2, axiom, (![X4, X5]:is_a_theorem(implies(X5,or(X4,X5)))<=>r2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r2)). 14.25/14.39 fof(principia_r2, axiom, r2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r2)). 14.25/14.39 fof(r4, axiom, (r4<=>![X4, X5, X6]:is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r4)). 14.25/14.39 fof(r5, axiom, (![X4, X5, X6]:is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6))))<=>r5), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r5)). 14.25/14.39 fof(op_and, axiom, (op_and=>![X1, X2]:and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_and)). 14.25/14.39 fof(principia_r4, axiom, r4, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r4)). 14.25/14.39 fof(principia_r5, axiom, r5, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r5)). 14.25/14.39 fof(principia_op_and, axiom, op_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_and)). 14.25/14.39 fof(op_equiv, axiom, (![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))<=op_equiv), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_equiv)). 14.25/14.39 fof(principia_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_equiv)). 14.25/14.39 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(X2=X1<=is_a_theorem(equiv(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)). 14.25/14.39 fof(substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', substitution_of_equivalents)). 14.25/14.40 fof(implies_2, axiom, (![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))<=>implies_2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_2)). 14.25/14.40 fof(hilbert_implies_2, conjecture, implies_2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_implies_2)). 14.25/14.40 fof(c_0_26, plain, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), inference(fof_simplification,[status(thm)],[op_implies_and])). 14.25/14.40 fof(c_0_27, plain, (op_or=>![X1, X2]:not(and(not(X1),not(X2)))=or(X1,X2)), inference(fof_simplification,[status(thm)],[op_or])). 14.25/14.40 fof(c_0_28, 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_26])])])). 14.25/14.40 fof(c_0_29, 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])])])])])). 14.25/14.40 fof(c_0_30, plain, ![X152, X153]:((~r3|is_a_theorem(implies(or(X152,X153),or(X153,X152))))&(~is_a_theorem(implies(or(esk41_0,esk42_0),or(esk42_0,esk41_0)))|r3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])). 14.25/14.40 fof(c_0_31, 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_27])])])). 14.25/14.40 cnf(c_0_32, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_28])). 14.25/14.40 cnf(c_0_33, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])). 14.25/14.40 cnf(c_0_34, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_29])). 14.25/14.40 cnf(c_0_35, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[principia_modus_ponens])). 14.25/14.40 cnf(c_0_36, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3), inference(split_conjunct,[status(thm)],[c_0_30])). 14.25/14.40 cnf(c_0_37, plain, (r3), inference(split_conjunct,[status(thm)],[principia_r3])). 14.25/14.40 fof(c_0_38, plain, ![X184, X185]:(~op_implies_or|or(not(X184),X185)=implies(X184,X185)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])). 14.25/14.40 fof(c_0_39, plain, ![X150]:((~r1|is_a_theorem(implies(or(X150,X150),X150)))&(~is_a_theorem(implies(or(esk40_0,esk40_0),esk40_0))|r1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])). 14.25/14.40 cnf(c_0_40, plain, (not(and(not(X1),not(X2)))=or(X1,X2)|~op_or), inference(split_conjunct,[status(thm)],[c_0_31])). 14.25/14.40 cnf(c_0_41, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])). 14.25/14.40 cnf(c_0_42, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])). 14.25/14.40 cnf(c_0_43, 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_34, c_0_35])])). 14.25/14.40 cnf(c_0_44, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])). 14.25/14.40 cnf(c_0_45, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_38])). 14.25/14.40 cnf(c_0_46, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])). 14.25/14.40 cnf(c_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1), inference(split_conjunct,[status(thm)],[c_0_39])). 14.25/14.40 cnf(c_0_48, plain, (r1), inference(split_conjunct,[status(thm)],[principia_r1])). 14.25/14.40 fof(c_0_49, plain, ![X136, X137]:((~is_a_theorem(implies(esk33_0,or(esk32_0,esk33_0)))|r2)&(~r2|is_a_theorem(implies(X137,or(X136,X137))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])). 14.25/14.40 cnf(c_0_50, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41]), c_0_42])])). 14.25/14.40 cnf(c_0_51, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_43, c_0_44])). 14.25/14.40 cnf(c_0_52, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])). 14.25/14.40 cnf(c_0_53, plain, (is_a_theorem(implies(or(X1,X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])). 14.25/14.40 cnf(c_0_54, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~r2), inference(split_conjunct,[status(thm)],[c_0_49])). 14.25/14.40 cnf(c_0_55, plain, (r2), inference(split_conjunct,[status(thm)],[principia_r2])). 14.25/14.40 cnf(c_0_56, plain, (is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_43, c_0_50])). 14.25/14.40 cnf(c_0_57, plain, (is_a_theorem(or(X1,not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_51, c_0_52])). 14.25/14.40 cnf(c_0_58, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X1))), inference(spm,[status(thm)],[c_0_43, c_0_53])). 14.25/14.40 cnf(c_0_59, plain, (is_a_theorem(implies(X1,or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])). 14.25/14.40 cnf(c_0_60, plain, (is_a_theorem(not(X1))|~is_a_theorem(implies(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_56, c_0_57])). 14.25/14.40 cnf(c_0_61, plain, (is_a_theorem(not(X1))|~is_a_theorem(implies(X1,not(X1)))), inference(spm,[status(thm)],[c_0_58, c_0_52])). 14.25/14.40 cnf(c_0_62, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_43, c_0_59])). 14.25/14.40 cnf(c_0_63, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_60, c_0_50])). 14.25/14.40 cnf(c_0_64, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_61, c_0_50])). 14.25/14.40 cnf(c_0_65, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_51, c_0_62])). 14.25/14.40 fof(c_0_66, plain, ![X156, X157, X158]:((~r4|is_a_theorem(implies(or(X156,or(X157,X158)),or(X157,or(X156,X158)))))&(~is_a_theorem(implies(or(esk43_0,or(esk44_0,esk45_0)),or(esk44_0,or(esk43_0,esk45_0))))|r4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])). 14.25/14.40 cnf(c_0_67, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(not(not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_63, c_0_57])). 14.25/14.40 cnf(c_0_68, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_64, c_0_65])). 14.25/14.40 fof(c_0_69, plain, ![X131, X132, X133]:((~is_a_theorem(implies(implies(esk30_0,esk31_0),implies(or(esk29_0,esk30_0),or(esk29_0,esk31_0))))|r5)&(~r5|is_a_theorem(implies(implies(X132,X133),implies(or(X131,X132),or(X131,X133)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])). 14.25/14.40 fof(c_0_70, plain, ![X190, X191]:(~op_and|and(X190,X191)=not(or(not(X190),not(X191)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])). 14.25/14.40 cnf(c_0_71, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4), inference(split_conjunct,[status(thm)],[c_0_66])). 14.25/14.40 cnf(c_0_72, plain, (r4), inference(split_conjunct,[status(thm)],[principia_r4])). 14.25/14.40 cnf(c_0_73, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_67, c_0_68])). 14.25/14.40 cnf(c_0_74, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5), inference(split_conjunct,[status(thm)],[c_0_69])). 14.25/14.40 cnf(c_0_75, plain, (r5), inference(split_conjunct,[status(thm)],[principia_r5])). 14.25/14.40 cnf(c_0_76, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(spm,[status(thm)],[c_0_59, c_0_52])). 14.25/14.40 cnf(c_0_77, plain, (and(X1,X2)=not(or(not(X1),not(X2)))|~op_and), inference(split_conjunct,[status(thm)],[c_0_70])). 14.25/14.40 cnf(c_0_78, plain, (op_and), inference(split_conjunct,[status(thm)],[principia_op_and])). 14.25/14.40 fof(c_0_79, plain, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(fof_simplification,[status(thm)],[op_equiv])). 14.25/14.40 cnf(c_0_80, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])). 14.25/14.40 cnf(c_0_81, plain, (is_a_theorem(X1)|~is_a_theorem(not(not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_56, c_0_52])). 14.25/14.40 cnf(c_0_82, plain, (is_a_theorem(not(not(or(X1,X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_73, c_0_59])). 14.25/14.40 cnf(c_0_83, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])). 14.25/14.40 cnf(c_0_84, plain, (is_a_theorem(or(X1,implies(X2,not(X1))))), inference(spm,[status(thm)],[c_0_76, c_0_50])). 14.25/14.40 cnf(c_0_85, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77, c_0_52]), c_0_78])])). 14.25/14.40 cnf(c_0_86, plain, (is_a_theorem(not(or(X1,X1)))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_60, c_0_53])). 14.25/14.40 fof(c_0_87, 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_79])])])). 14.25/14.40 cnf(c_0_88, plain, (is_a_theorem(or(X1,or(X2,X3)))|~is_a_theorem(or(X2,or(X1,X3)))), inference(spm,[status(thm)],[c_0_43, c_0_80])). 14.25/14.40 cnf(c_0_89, plain, (is_a_theorem(or(X1,or(X2,not(X1))))), inference(spm,[status(thm)],[c_0_59, c_0_50])). 14.25/14.40 cnf(c_0_90, plain, (is_a_theorem(X1)|~is_a_theorem(implies(or(X2,X3),X1))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_81, c_0_82])). 14.25/14.40 cnf(c_0_91, plain, (is_a_theorem(implies(or(X1,X2),or(X1,X3)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_43, c_0_83])). 14.25/14.40 cnf(c_0_92, plain, (is_a_theorem(or(implies(X1,not(X2)),X2))), inference(spm,[status(thm)],[c_0_51, c_0_84])). 14.25/14.40 cnf(c_0_93, plain, (or(implies(X1,not(X2)),X3)=implies(and(X1,X2),X3)), inference(spm,[status(thm)],[c_0_50, c_0_85])). 14.25/14.40 cnf(c_0_94, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(not(not(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_52]), c_0_85])). 14.25/14.40 cnf(c_0_95, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_87])). 14.25/14.40 cnf(c_0_96, plain, (op_equiv), inference(split_conjunct,[status(thm)],[principia_op_equiv])). 14.25/14.40 cnf(c_0_97, plain, (is_a_theorem(or(X1,or(X2,not(X2))))), inference(spm,[status(thm)],[c_0_88, c_0_89])). 14.25/14.40 cnf(c_0_98, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_90, c_0_91])). 14.25/14.40 cnf(c_0_99, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(rw,[status(thm)],[c_0_92, c_0_93])). 14.25/14.40 cnf(c_0_100, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_94, c_0_68])). 14.25/14.40 cnf(c_0_101, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95, c_0_96])])). 14.25/14.40 cnf(c_0_102, plain, (is_a_theorem(or(X1,not(X1)))), inference(spm,[status(thm)],[c_0_58, c_0_97])). 14.25/14.40 cnf(c_0_103, plain, (or(and(X1,not(X2)),X3)=implies(implies(X1,X2),X3)), inference(spm,[status(thm)],[c_0_50, c_0_41])). 14.25/14.40 cnf(c_0_104, plain, (or(and(X1,X2),X3)=implies(implies(X1,not(X2)),X3)), inference(spm,[status(thm)],[c_0_52, c_0_85])). 14.25/14.40 cnf(c_0_105, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(and(X3,X2))), inference(spm,[status(thm)],[c_0_98, c_0_99])). 14.25/14.40 cnf(c_0_106, plain, (is_a_theorem(equiv(X1,X1))|~is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_100, c_0_101])). 14.25/14.40 cnf(c_0_107, plain, (is_a_theorem(implies(X1,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_102]), c_0_52])). 14.25/14.40 fof(c_0_108, plain, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X2=X1)), inference(fof_simplification,[status(thm)],[substitution_of_equivalents])). 14.25/14.40 cnf(c_0_109, plain, (implies(implies(X1,not(not(X2))),X3)=implies(implies(X1,X2),X3)), inference(rw,[status(thm)],[c_0_103, c_0_104])). 14.25/14.40 cnf(c_0_110, plain, (is_a_theorem(or(X1,implies(X2,X3)))|~is_a_theorem(equiv(X3,X2))), inference(spm,[status(thm)],[c_0_105, c_0_101])). 14.25/14.40 cnf(c_0_111, plain, (is_a_theorem(equiv(X1,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106, c_0_107])])). 14.25/14.40 fof(c_0_112, 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_108])])])])])). 14.25/14.40 cnf(c_0_113, plain, (and(implies(X1,not(X2)),or(X2,X1))=equiv(X1,not(X2))), inference(spm,[status(thm)],[c_0_101, c_0_50])). 14.25/14.40 cnf(c_0_114, plain, (and(implies(X1,not(not(X2))),X3)=and(implies(X1,X2),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_109]), c_0_85])). 14.25/14.40 cnf(c_0_115, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_57]), c_0_50])). 14.25/14.40 cnf(c_0_116, plain, (is_a_theorem(or(X1,implies(X2,X2)))), inference(spm,[status(thm)],[c_0_110, c_0_111])). 14.25/14.40 cnf(c_0_117, plain, (is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(implies(X2,not(X1)))), inference(spm,[status(thm)],[c_0_57, c_0_52])). 14.25/14.40 cnf(c_0_118, plain, (X2=X1|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_112])). 14.25/14.40 cnf(c_0_119, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[substitution_of_equivalents])). 14.25/14.40 cnf(c_0_120, plain, (equiv(X1,not(not(X2)))=equiv(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_52]), c_0_101])). 14.25/14.40 cnf(c_0_121, plain, (is_a_theorem(not(not(implies(X1,X1))))), inference(spm,[status(thm)],[c_0_115, c_0_116])). 14.25/14.40 cnf(c_0_122, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,X3))|~is_a_theorem(implies(X3,X2))), inference(spm,[status(thm)],[c_0_43, c_0_91])). 14.25/14.40 cnf(c_0_123, plain, (is_a_theorem(implies(X1,not(not(X2))))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_117, c_0_50])). 14.25/14.40 cnf(c_0_124, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_119])])). 14.25/14.40 cnf(c_0_125, plain, (is_a_theorem(equiv(not(not(X1)),X1))), inference(spm,[status(thm)],[c_0_111, c_0_120])). 14.25/14.40 cnf(c_0_126, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,X2),X1))), inference(spm,[status(thm)],[c_0_81, c_0_121])). 14.25/14.40 cnf(c_0_127, plain, (is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_52]), c_0_52])). 14.25/14.40 cnf(c_0_128, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X3,X2))|~is_a_theorem(implies(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_57]), c_0_50])). 14.25/14.40 cnf(c_0_129, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,not(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_43, c_0_123])). 14.25/14.40 cnf(c_0_130, plain, (not(not(X1))=X1), inference(spm,[status(thm)],[c_0_124, c_0_125])). 14.25/14.40 cnf(c_0_131, plain, (is_a_theorem(or(X1,implies(or(X1,X2),X2)))), inference(spm,[status(thm)],[c_0_126, c_0_127])). 14.25/14.40 cnf(c_0_132, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X2))|~is_a_theorem(or(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_52]), c_0_50])). 14.25/14.40 cnf(c_0_133, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,not(X2)))|~is_a_theorem(X2)), inference(rw,[status(thm)],[c_0_129, c_0_130])). 14.25/14.40 cnf(c_0_134, plain, (is_a_theorem(or(implies(or(X1,X2),X2),X1))), inference(spm,[status(thm)],[c_0_51, c_0_131])). 14.25/14.40 cnf(c_0_135, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(or(X2,X2),X1))), inference(spm,[status(thm)],[c_0_132, c_0_53])). 14.25/14.40 cnf(c_0_136, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,X3))|~is_a_theorem(implies(X3,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_52]), c_0_52])). 14.25/14.40 cnf(c_0_137, plain, (is_a_theorem(not(X1))|~is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_133, c_0_52])). 14.25/14.40 cnf(c_0_138, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_134]), c_0_52])). 14.25/14.40 cnf(c_0_139, plain, (is_a_theorem(implies(implies(X1,X2),or(X2,not(X1))))), inference(spm,[status(thm)],[c_0_44, c_0_52])). 14.25/14.40 cnf(c_0_140, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,or(X2,X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_57]), c_0_52])). 14.25/14.40 cnf(c_0_141, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(or(X3,X1),X2))), inference(spm,[status(thm)],[c_0_136, c_0_59])). 14.25/14.40 cnf(c_0_142, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_44, c_0_52])). 14.25/14.40 cnf(c_0_143, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_85])). 14.25/14.40 cnf(c_0_144, plain, (is_a_theorem(implies(implies(X1,X2),X3))|~is_a_theorem(implies(or(X2,not(X1)),X3))), inference(spm,[status(thm)],[c_0_136, c_0_139])). 14.25/14.40 cnf(c_0_145, plain, (is_a_theorem(implies(or(X1,X2),X1))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_140, c_0_91])). 14.25/14.40 cnf(c_0_146, plain, (is_a_theorem(or(X1,implies(X1,X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142]), c_0_50])). 14.25/14.40 cnf(c_0_147, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_143, c_0_101])). 14.25/14.40 cnf(c_0_148, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(or(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_50])). 14.25/14.40 cnf(c_0_149, plain, (is_a_theorem(or(implies(X1,X2),X1))), inference(spm,[status(thm)],[c_0_51, c_0_146])). 14.25/14.40 fof(c_0_150, plain, ![X148, X149]:((~is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0)))|implies_2)&(~implies_2|is_a_theorem(implies(implies(X148,implies(X148,X149)),implies(X148,X149))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])). 14.25/14.40 fof(c_0_151, negated_conjecture, ~implies_2, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_2])])). 14.25/14.40 cnf(c_0_152, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_124, c_0_147])). 14.25/14.40 cnf(c_0_153, plain, (is_a_theorem(implies(implies(implies(X1,X2),X1),X1))), inference(spm,[status(thm)],[c_0_148, c_0_149])). 14.25/14.40 cnf(c_0_154, plain, (implies_2|~is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0)))), inference(split_conjunct,[status(thm)],[c_0_150])). 14.25/14.40 cnf(c_0_155, negated_conjecture, (~implies_2), inference(split_conjunct,[status(thm)],[c_0_151])). 14.25/14.40 cnf(c_0_156, plain, (implies(implies(X1,X2),X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_153]), c_0_76])])). 14.25/14.40 cnf(c_0_157, plain, (~is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0)))), inference(sr,[status(thm)],[c_0_154, c_0_155])). 14.25/14.40 cnf(c_0_158, plain, (implies(X1,implies(X1,X2))=implies(X1,X2)), inference(spm,[status(thm)],[c_0_156, c_0_156])). 14.25/14.40 cnf(c_0_159, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157, c_0_158]), c_0_107])]), ['proof']). 14.25/14.40 % SZS output end Proof 14.25/14.40 % Total time : 13.576000 s 14.25/14.41 EOF