0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule --cpu-limit=%d %s 0.03/0.24 % Computer : n124.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:44:39 CDT 2018 0.03/0.24 % CPUTime : 0.03/0.24 # Version: 2.2pre001 0.03/0.24 # No SInE strategy applied 0.03/0.24 # Trying AutoSched0 for 151 seconds 73.13/73.35 # AutoSched0-Mode selected heuristic H_____011_C18_F1_PI_SE_SP_S2S 73.13/73.35 # and selection function SelectNewComplexAHP. 73.13/73.35 # 73.13/73.35 # Preprocessing time : 0.012 s 73.13/73.35 73.13/73.35 # Proof found! 73.13/73.35 # SZS status Theorem 73.13/73.35 # SZS output start CNFRefutation 73.13/73.35 fof(op_implies_and, axiom, (![X1, X2]:not(and(X1,not(X2)))=implies(X1,X2)<=op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_and)). 73.13/73.35 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)). 73.13/73.35 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)). 73.13/73.35 fof(op_or, axiom, (![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))<=op_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_or)). 73.13/73.35 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_implies_and)). 73.13/73.35 fof(op_possibly, axiom, (![X1]:not(necessarily(not(X1)))=possibly(X1)<=op_possibly), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_possibly)). 73.13/73.35 fof(and_3, axiom, (![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))<=>and_3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_3)). 73.13/73.35 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)). 73.13/73.35 fof(hilbert_or_1, axiom, or_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_or_1)). 73.13/73.35 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_or)). 73.13/73.35 fof(km5_op_possibly, axiom, op_possibly, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_op_possibly)). 73.13/73.35 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)). 73.13/73.35 fof(necessitation, axiom, (necessitation<=>![X1]:(is_a_theorem(necessarily(X1))<=is_a_theorem(X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', necessitation)). 73.13/73.35 fof(op_equiv, axiom, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_equiv)). 73.13/73.35 fof(implies_2, axiom, (implies_2<=>![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_2)). 73.13/73.35 fof(km5_necessitation, axiom, necessitation, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_necessitation)). 73.13/73.35 fof(hilbert_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_op_equiv)). 73.13/73.35 fof(and_2, axiom, (![X1, X2]:is_a_theorem(implies(and(X1,X2),X2))<=>and_2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_2)). 73.13/73.35 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)). 73.13/73.35 fof(modus_tollens, axiom, (modus_tollens<=>![X1, X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_tollens)). 73.13/73.35 fof(axiom_M, axiom, (axiom_M<=>![X1]:is_a_theorem(implies(necessarily(X1),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_M)). 73.13/73.35 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X2=X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)). 73.13/73.35 fof(hilbert_and_2, axiom, and_2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_2)). 73.13/73.35 fof(and_1, axiom, (and_1<=>![X1, X2]:is_a_theorem(implies(and(X1,X2),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_1)). 73.13/73.35 fof(hilbert_modus_tollens, axiom, modus_tollens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_tollens)). 73.13/73.35 fof(km5_axiom_M, axiom, axiom_M, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_axiom_M)). 73.13/73.35 fof(substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', substitution_of_equivalents)). 73.13/73.35 fof(implies_1, axiom, (![X1, X2]:is_a_theorem(implies(X1,implies(X2,X1)))<=>implies_1), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_1)). 73.13/73.35 fof(hilbert_and_1, axiom, and_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_1)). 73.13/73.35 fof(hilbert_implies_1, axiom, implies_1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_1)). 73.13/73.35 fof(axiom_5, axiom, (![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))<=>axiom_5), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_5)). 73.13/73.35 fof(implies_3, axiom, (implies_3<=>![X1, X2, X6]:is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X6),implies(X1,X6))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_3)). 73.13/73.35 fof(km5_axiom_5, axiom, axiom_5, file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_axiom_5)). 73.13/73.35 fof(hilbert_implies_3, axiom, implies_3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_3)). 73.13/73.35 fof(km4b_axiom_B, conjecture, axiom_B, file('/export/starexec/sandbox/benchmark/theBenchmark.p', km4b_axiom_B)). 73.13/73.35 fof(axiom_B, axiom, (axiom_B<=>![X1]:is_a_theorem(implies(X1,necessarily(possibly(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_B)). 73.13/73.35 fof(c_0_36, plain, ![X121, X122]:(~op_implies_and|not(and(X121,not(X122)))=implies(X121,X122)), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[op_implies_and])])])])])])). 73.13/73.35 fof(c_0_37, plain, ![X57, X58]:((~modus_ponens|(~is_a_theorem(X57)|~is_a_theorem(implies(X57,X58))|is_a_theorem(X58)))&(((is_a_theorem(esk26_0)|modus_ponens)&(is_a_theorem(implies(esk26_0,esk27_0))|modus_ponens))&(~is_a_theorem(esk27_0)|modus_ponens))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])])])). 73.13/73.35 fof(c_0_38, plain, ![X49, X50]:((~or_1|is_a_theorem(implies(X49,or(X49,X50))))&(~is_a_theorem(implies(esk22_0,or(esk22_0,esk23_0)))|or_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])])])). 73.13/73.35 fof(c_0_39, plain, ![X117, X118]:(~op_or|or(X117,X118)=not(and(not(X117),not(X118)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[op_or])])])])])])). 73.13/73.35 cnf(c_0_40, plain, (not(and(X1,not(X2)))=implies(X1,X2)|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_36])). 73.13/73.35 cnf(c_0_41, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])). 73.13/73.35 fof(c_0_42, plain, ![X210]:(~op_possibly|not(necessarily(not(X210)))=possibly(X210)), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[op_possibly])])])])])])). 73.13/73.35 fof(c_0_43, plain, ![X71, X72]:((~is_a_theorem(implies(esk32_0,implies(esk33_0,and(esk32_0,esk33_0))))|and_3)&(~and_3|is_a_theorem(implies(X71,implies(X72,and(X71,X72)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])])])). 73.13/73.35 cnf(c_0_44, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_37])). 73.13/73.35 cnf(c_0_45, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])). 73.13/73.35 cnf(c_0_46, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1), inference(split_conjunct,[status(thm)],[c_0_38])). 73.13/73.35 cnf(c_0_47, plain, (or_1), inference(split_conjunct,[status(thm)],[hilbert_or_1])). 73.13/73.35 cnf(c_0_48, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_39])). 73.13/73.35 cnf(c_0_49, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])). 73.13/73.35 cnf(c_0_50, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])). 73.13/73.35 cnf(c_0_51, plain, (not(necessarily(not(X1)))=possibly(X1)|~op_possibly), inference(split_conjunct,[status(thm)],[c_0_42])). 73.13/73.35 cnf(c_0_52, plain, (op_possibly), inference(split_conjunct,[status(thm)],[km5_op_possibly])). 73.13/73.35 cnf(c_0_53, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_43])). 73.13/73.35 cnf(c_0_54, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])). 73.13/73.35 cnf(c_0_55, 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_44, c_0_45])])). 73.13/73.35 cnf(c_0_56, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])). 73.13/73.35 cnf(c_0_57, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49]), c_0_50])])). 73.13/73.35 cnf(c_0_58, plain, (not(necessarily(not(X1)))=possibly(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])). 73.13/73.35 fof(c_0_59, plain, ![X185]:((~necessitation|(~is_a_theorem(X185)|is_a_theorem(necessarily(X185))))&((is_a_theorem(esk85_0)|necessitation)&(~is_a_theorem(necessarily(esk85_0))|necessitation))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[necessitation])])])])])])])])). 73.13/73.35 cnf(c_0_60, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])). 73.13/73.35 fof(c_0_61, plain, ![X125, X126]:(~op_equiv|equiv(X125,X126)=and(implies(X125,X126),implies(X126,X125))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])])])). 73.13/73.35 fof(c_0_62, plain, ![X113, X114]:((~implies_2|is_a_theorem(implies(implies(X113,implies(X113,X114)),implies(X113,X114))))&(~is_a_theorem(implies(implies(esk54_0,implies(esk54_0,esk55_0)),implies(esk54_0,esk55_0)))|implies_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])])])). 73.13/73.35 cnf(c_0_63, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_55, c_0_56])). 73.13/73.35 cnf(c_0_64, plain, (or(necessarily(not(X1)),X2)=implies(possibly(X1),X2)), inference(spm,[status(thm)],[c_0_57, c_0_58])). 73.13/73.35 cnf(c_0_65, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)), inference(split_conjunct,[status(thm)],[c_0_59])). 73.13/73.35 cnf(c_0_66, plain, (necessitation), inference(split_conjunct,[status(thm)],[km5_necessitation])). 73.13/73.35 cnf(c_0_67, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_55, c_0_60])). 73.13/73.35 cnf(c_0_68, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_61])). 73.13/73.35 cnf(c_0_69, plain, (op_equiv), inference(split_conjunct,[status(thm)],[hilbert_op_equiv])). 73.13/73.35 fof(c_0_70, plain, ![X9, X10]:((~is_a_theorem(implies(and(esk1_0,esk2_0),esk2_0))|and_2)&(~and_2|is_a_theorem(implies(and(X9,X10),X10)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])])])). 73.13/73.35 cnf(c_0_71, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_62])). 73.13/73.35 cnf(c_0_72, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])). 73.13/73.35 fof(c_0_73, plain, ![X101, X102]:((~modus_tollens|is_a_theorem(implies(implies(not(X102),not(X101)),implies(X101,X102))))&(~is_a_theorem(implies(implies(not(esk49_0),not(esk48_0)),implies(esk48_0,esk49_0)))|modus_tollens)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])])])). 73.13/73.35 cnf(c_0_74, plain, (is_a_theorem(implies(possibly(X1),X2))|~is_a_theorem(necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_63, c_0_64])). 73.13/73.35 cnf(c_0_75, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])). 73.13/73.35 fof(c_0_76, plain, ![X181]:((~axiom_M|is_a_theorem(implies(necessarily(X181),X181)))&(~is_a_theorem(implies(necessarily(esk83_0),esk83_0))|axiom_M)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])])])). 73.13/73.35 fof(c_0_77, plain, ![X15, X16]:((~substitution_of_equivalents|(~is_a_theorem(equiv(X15,X16))|X16=X15))&((is_a_theorem(equiv(esk5_0,esk6_0))|substitution_of_equivalents)&(esk6_0!=esk5_0|substitution_of_equivalents))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])])])). 73.13/73.35 cnf(c_0_78, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_55, c_0_67])). 73.13/73.35 cnf(c_0_79, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68, c_0_69])])). 73.13/73.35 cnf(c_0_80, plain, (is_a_theorem(implies(and(X1,X2),X2))|~and_2), inference(split_conjunct,[status(thm)],[c_0_70])). 73.13/73.35 cnf(c_0_81, plain, (and_2), inference(split_conjunct,[status(thm)],[hilbert_and_2])). 73.13/73.35 cnf(c_0_82, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])). 73.13/73.35 fof(c_0_83, plain, ![X77, X78]:((~and_1|is_a_theorem(implies(and(X77,X78),X77)))&(~is_a_theorem(implies(and(esk36_0,esk37_0),esk36_0))|and_1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])])])). 73.13/73.35 cnf(c_0_84, plain, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens), inference(split_conjunct,[status(thm)],[c_0_73])). 73.13/73.35 cnf(c_0_85, plain, (modus_tollens), inference(split_conjunct,[status(thm)],[hilbert_modus_tollens])). 73.13/73.35 cnf(c_0_86, plain, (is_a_theorem(implies(possibly(X1),X2))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_74, c_0_75])). 73.13/73.35 cnf(c_0_87, plain, (possibly(and(X1,not(X2)))=not(necessarily(implies(X1,X2)))), inference(spm,[status(thm)],[c_0_58, c_0_49])). 73.13/73.35 cnf(c_0_88, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M), inference(split_conjunct,[status(thm)],[c_0_76])). 73.13/73.35 cnf(c_0_89, plain, (axiom_M), inference(split_conjunct,[status(thm)],[km5_axiom_M])). 73.13/73.35 cnf(c_0_90, plain, (X2=X1|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_77])). 73.13/73.35 cnf(c_0_91, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[substitution_of_equivalents])). 73.13/73.35 cnf(c_0_92, 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_78, c_0_79])). 73.13/73.35 cnf(c_0_93, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])). 73.13/73.35 fof(c_0_94, plain, ![X99, X100]:((~is_a_theorem(implies(esk46_0,implies(esk47_0,esk46_0)))|implies_1)&(~implies_1|is_a_theorem(implies(X99,implies(X100,X99))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])])])). 73.13/73.35 cnf(c_0_95, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_55, c_0_82])). 73.13/73.35 cnf(c_0_96, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1), inference(split_conjunct,[status(thm)],[c_0_83])). 73.13/73.35 cnf(c_0_97, plain, (and_1), inference(split_conjunct,[status(thm)],[hilbert_and_1])). 73.13/73.35 cnf(c_0_98, 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_84, c_0_57]), c_0_85])])). 73.13/73.35 cnf(c_0_99, plain, (is_a_theorem(or(necessarily(implies(X1,X2)),X3))|~is_a_theorem(implies(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_49]), c_0_87]), c_0_57])). 73.13/73.35 cnf(c_0_100, plain, (is_a_theorem(implies(necessarily(X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88, c_0_89])])). 73.13/73.35 cnf(c_0_101, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])). 73.13/73.35 cnf(c_0_102, plain, (is_a_theorem(equiv(and(X1,X2),X2))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_67]), c_0_93])])). 73.13/73.35 cnf(c_0_103, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1), inference(split_conjunct,[status(thm)],[c_0_94])). 73.13/73.35 cnf(c_0_104, plain, (implies_1), inference(split_conjunct,[status(thm)],[hilbert_implies_1])). 73.13/73.35 cnf(c_0_105, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_95, c_0_60])). 73.13/73.35 cnf(c_0_106, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])). 73.13/73.35 cnf(c_0_107, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(spm,[status(thm)],[c_0_55, c_0_98])). 73.13/73.35 cnf(c_0_108, plain, (is_a_theorem(or(necessarily(implies(necessarily(X1),X1)),X2))), inference(spm,[status(thm)],[c_0_99, c_0_100])). 73.13/73.35 cnf(c_0_109, plain, (and(X1,X2)=X2|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_101, c_0_102])). 73.13/73.35 cnf(c_0_110, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_104])])). 73.13/73.35 cnf(c_0_111, plain, (is_a_theorem(equiv(and(X1,X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_105]), c_0_106])])). 73.13/73.35 cnf(c_0_112, plain, (is_a_theorem(implies(X1,necessarily(implies(necessarily(X2),X2))))), inference(spm,[status(thm)],[c_0_107, c_0_108])). 73.13/73.35 cnf(c_0_113, plain, (equiv(X1,X2)=implies(X2,X1)|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_79, c_0_109])). 73.13/73.35 cnf(c_0_114, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_55, c_0_110])). 73.13/73.35 cnf(c_0_115, plain, (and(X1,X1)=X1), inference(spm,[status(thm)],[c_0_101, c_0_111])). 73.13/73.35 cnf(c_0_116, plain, (is_a_theorem(necessarily(implies(necessarily(X1),X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_55, c_0_112])). 73.13/73.35 cnf(c_0_117, plain, (equiv(X1,X2)=implies(X2,X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_113, c_0_114])). 73.13/73.35 cnf(c_0_118, plain, (is_a_theorem(or(X1,or(not(X1),X2)))), inference(spm,[status(thm)],[c_0_56, c_0_57])). 73.13/73.35 cnf(c_0_119, plain, (not(not(X1))=or(X1,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_115]), c_0_57])). 73.13/73.35 cnf(c_0_120, plain, (is_a_theorem(implies(X1,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_93, c_0_109])). 73.13/73.35 cnf(c_0_121, plain, (is_a_theorem(necessarily(implies(necessarily(X1),X1)))), inference(spm,[status(thm)],[c_0_116, c_0_108])). 73.13/73.35 cnf(c_0_122, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_101, c_0_117])). 73.13/73.35 fof(c_0_123, plain, ![X174]:((~is_a_theorem(implies(possibly(esk79_0),necessarily(possibly(esk79_0))))|axiom_5)&(~axiom_5|is_a_theorem(implies(possibly(X174),necessarily(possibly(X174)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])])])). 73.13/73.35 fof(c_0_124, plain, ![X61, X62, X63]:((~implies_3|is_a_theorem(implies(implies(X61,X62),implies(implies(X62,X63),implies(X61,X63)))))&(~is_a_theorem(implies(implies(esk28_0,esk29_0),implies(implies(esk29_0,esk30_0),implies(esk28_0,esk30_0))))|implies_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])])])). 73.13/73.35 cnf(c_0_125, plain, (is_a_theorem(or(X1,not(not(not(X1)))))), inference(spm,[status(thm)],[c_0_118, c_0_119])). 73.13/73.35 cnf(c_0_126, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_120, c_0_121])). 73.13/73.35 cnf(c_0_127, plain, (necessarily(X1)=X1|~is_a_theorem(necessarily(X1))), inference(spm,[status(thm)],[c_0_122, c_0_100])). 73.13/73.35 cnf(c_0_128, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5), inference(split_conjunct,[status(thm)],[c_0_123])). 73.13/73.35 cnf(c_0_129, plain, (axiom_5), inference(split_conjunct,[status(thm)],[km5_axiom_5])). 73.13/73.35 cnf(c_0_130, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~implies_3), inference(split_conjunct,[status(thm)],[c_0_124])). 73.13/73.35 cnf(c_0_131, plain, (implies_3), inference(split_conjunct,[status(thm)],[hilbert_implies_3])). 73.13/73.35 cnf(c_0_132, plain, (is_a_theorem(equiv(X1,not(X2)))|~is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_92, c_0_57])). 73.13/73.35 cnf(c_0_133, plain, (is_a_theorem(or(not(X1),X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_125]), c_0_57])). 73.13/73.35 cnf(c_0_134, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_56, c_0_119])). 73.13/73.35 cnf(c_0_135, plain, (is_a_theorem(or(necessarily(implies(X1,X1)),X2))), inference(spm,[status(thm)],[c_0_99, c_0_126])). 73.13/73.35 cnf(c_0_136, plain, (necessarily(X1)=X1|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_127, c_0_75])). 73.13/73.35 cnf(c_0_137, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128, c_0_129])])). 73.13/73.35 cnf(c_0_138, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130, c_0_131])])). 73.13/73.35 cnf(c_0_139, plain, (is_a_theorem(equiv(X1,not(not(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134])])). 73.13/73.35 cnf(c_0_140, plain, (is_a_theorem(or(implies(X1,X1),X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136]), c_0_126])])). 73.13/73.35 cnf(c_0_141, plain, (is_a_theorem(equiv(necessarily(possibly(X1)),possibly(X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_137]), c_0_100])])). 73.13/73.35 fof(c_0_142, negated_conjecture, ~(axiom_B), inference(assume_negation,[status(cth)],[km4b_axiom_B])). 73.13/73.35 cnf(c_0_143, plain, (is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_55, c_0_138])). 73.13/73.35 cnf(c_0_144, plain, (not(not(X1))=X1), inference(spm,[status(thm)],[c_0_101, c_0_139])). 73.13/73.35 cnf(c_0_145, plain, (is_a_theorem(implies(X1,implies(X2,X2)))), inference(spm,[status(thm)],[c_0_107, c_0_140])). 73.13/73.35 cnf(c_0_146, plain, (not(not(X1))=implies(X2,X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_49, c_0_109])). 73.13/73.35 cnf(c_0_147, plain, (not(necessarily(possibly(X1)))=possibly(necessarily(not(X1)))), inference(spm,[status(thm)],[c_0_58, c_0_58])). 73.13/73.35 cnf(c_0_148, plain, (necessarily(possibly(X1))=possibly(X1)), inference(spm,[status(thm)],[c_0_101, c_0_141])). 73.13/73.35 fof(c_0_149, plain, ![X191]:((~axiom_B|is_a_theorem(implies(X191,necessarily(possibly(X191)))))&(~is_a_theorem(implies(esk88_0,necessarily(possibly(esk88_0))))|axiom_B)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_B])])])])])])). 73.13/73.35 fof(c_0_150, negated_conjecture, ~axiom_B, inference(fof_simplification,[status(thm)],[c_0_142])). 73.13/73.35 cnf(c_0_151, plain, (is_a_theorem(implies(implies(or(X1,X2),X3),implies(X1,X3)))), inference(spm,[status(thm)],[c_0_143, c_0_56])). 73.13/73.35 cnf(c_0_152, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_57, c_0_144])). 73.13/73.35 cnf(c_0_153, plain, (implies(X1,X1)=X2|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_122, c_0_145])). 73.13/73.35 cnf(c_0_154, plain, (is_a_theorem(implies(implies(X1,X2),implies(necessarily(X1),X2)))), inference(spm,[status(thm)],[c_0_143, c_0_100])). 73.13/73.35 cnf(c_0_155, plain, (implies(X1,X2)=X2|~is_a_theorem(X1)), inference(rw,[status(thm)],[c_0_146, c_0_144])). 73.13/73.35 cnf(c_0_156, plain, (implies(possibly(necessarily(not(X1))),X2)=or(necessarily(possibly(X1)),X2)), inference(spm,[status(thm)],[c_0_57, c_0_147])). 73.13/73.35 cnf(c_0_157, plain, (possibly(necessarily(not(X1)))=not(possibly(X1))), inference(rw,[status(thm)],[c_0_147, c_0_148])). 73.13/73.35 cnf(c_0_158, plain, (not(possibly(X1))=necessarily(not(X1))), inference(spm,[status(thm)],[c_0_144, c_0_58])). 73.13/73.35 cnf(c_0_159, plain, (axiom_B|~is_a_theorem(implies(esk88_0,necessarily(possibly(esk88_0))))), inference(split_conjunct,[status(thm)],[c_0_149])). 73.13/73.35 cnf(c_0_160, negated_conjecture, (~axiom_B), inference(split_conjunct,[status(thm)],[c_0_150])). 73.13/73.35 cnf(c_0_161, plain, (is_a_theorem(implies(implies(implies(X1,X2),X3),or(X1,X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_57]), c_0_152])). 73.13/73.35 cnf(c_0_162, plain, (implies(X1,X1)=implies(implies(X2,X3),implies(necessarily(X2),X3))), inference(spm,[status(thm)],[c_0_153, c_0_154])). 73.13/73.35 cnf(c_0_163, plain, (implies(implies(X1,X1),X2)=X2), inference(spm,[status(thm)],[c_0_155, c_0_126])). 73.13/73.35 cnf(c_0_164, plain, (or(X1,X1)=X1), inference(rw,[status(thm)],[c_0_119, c_0_144])). 73.13/73.35 cnf(c_0_165, plain, (or(possibly(X1),X2)=implies(necessarily(not(X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156, c_0_148]), c_0_157]), c_0_158])). 73.13/73.35 cnf(c_0_166, plain, (~is_a_theorem(implies(esk88_0,necessarily(possibly(esk88_0))))), inference(sr,[status(thm)],[c_0_159, c_0_160])). 73.13/73.35 cnf(c_0_167, plain, (is_a_theorem(or(X1,implies(necessarily(X1),X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162]), c_0_163])). 73.13/73.35 cnf(c_0_168, plain, (implies(necessarily(not(X1)),possibly(X1))=possibly(X1)), inference(spm,[status(thm)],[c_0_164, c_0_165])). 73.13/73.35 cnf(c_0_169, plain, (~is_a_theorem(implies(esk88_0,possibly(esk88_0)))), inference(rw,[status(thm)],[c_0_166, c_0_148])). 73.13/73.35 cnf(c_0_170, plain, (is_a_theorem(implies(X1,possibly(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_168]), c_0_152])). 73.13/73.35 cnf(c_0_171, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169, c_0_170])]), ['proof']). 73.13/73.35 # SZS output end CNFRefutation 73.13/73.35 # Proof object total steps : 172 73.13/73.35 # Proof object clause steps : 116 73.13/73.35 # Proof object formula steps : 56 73.13/73.35 # Proof object conjectures : 4 73.13/73.35 # Proof object clause conjectures : 1 73.13/73.35 # Proof object formula conjectures : 3 73.13/73.35 # Proof object initial clauses used : 36 73.13/73.35 # Proof object initial formulas used : 36 73.13/73.35 # Proof object generating inferences : 56 73.13/73.35 # Proof object simplifying inferences : 63 73.13/73.35 # Training examples: 0 positive, 0 negative 73.13/73.35 # Parsed axioms : 82 73.13/73.35 # Removed by relevancy pruning/SinE : 0 73.13/73.35 # Initial clauses : 140 73.13/73.35 # Removed in clause preprocessing : 0 73.13/73.35 # Initial clauses in saturation : 140 73.13/73.35 # Processed clauses : 150978 73.13/73.35 # ...of these trivial : 1368 73.13/73.35 # ...subsumed : 142457 73.13/73.35 # ...remaining for further processing : 7153 73.13/73.35 # Other redundant clauses eliminated : 0 73.13/73.35 # Clauses deleted for lack of memory : 1878473 73.13/73.35 # Backward-subsumed : 555 73.13/73.35 # Backward-rewritten : 739 73.13/73.35 # Generated clauses : 4737636 73.13/73.35 # ...of the previous two non-trivial : 3997821 73.13/73.35 # Contextual simplify-reflections : 0 73.13/73.35 # Paramodulations : 4737636 73.13/73.35 # Factorizations : 0 73.13/73.35 # Equation resolutions : 0 73.13/73.35 # Propositional unsat checks : 0 73.13/73.35 # Propositional check models : 0 73.13/73.35 # Propositional check unsatisfiable : 0 73.13/73.35 # Propositional clauses : 0 73.13/73.35 # Propositional clauses after purity: 0 73.13/73.35 # Propositional unsat core size : 0 73.13/73.35 # Current number of processed clauses : 5859 73.13/73.35 # Positive orientable unit clauses : 846 73.13/73.35 # Positive unorientable unit clauses: 82 73.13/73.35 # Negative unit clauses : 3 73.13/73.35 # Non-unit-clauses : 4928 73.13/73.35 # Current number of unprocessed clauses: 1701705 73.13/73.35 # ...number of literals in the above : 4666127 73.13/73.35 # Current number of archived formulas : 0 73.13/73.35 # Current number of archived clauses : 1294 73.13/73.35 # Clause-clause subsumption calls (NU) : 5226923 73.13/73.35 # Rec. Clause-clause subsumption calls : 4103011 73.13/73.35 # Non-unit clause-clause subsumptions : 139669 73.13/73.35 # Unit Clause-clause subsumption calls : 72399 73.13/73.35 # Rewrite failures with RHS unbound : 6564 73.13/73.35 # BW rewrite match attempts : 323812 73.13/73.35 # BW rewrite match successes : 1279 73.13/73.35 # Condensation attempts : 0 73.13/73.35 # Condensation successes : 0 73.13/73.35 # Termbank termtop insertions : 84130484 73.30/73.48 73.30/73.48 # ------------------------------------------------- 73.30/73.48 # User time : 71.655 s 73.30/73.48 # System time : 1.588 s 73.30/73.48 # Total time : 73.243 s 73.30/73.48 # Maximum resident set size: 1628 pages 73.30/73.48 EOF