0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -jar mcs_epr.jar %d %s 0.03/0.24 % Computer : n117.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 05:39:55 CDT 2018 0.03/0.24 % CPUTime : 0.06/0.32 openjdk version "1.8.0_144" 0.06/0.32 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.06/0.32 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.44 start to proof:theBenchmark.p 1.39/1.56 % Version : CSE_E---1.0 1.39/1.56 % Problem : theBenchmark.p 1.39/1.56 % Proof found! 1.39/1.56 % SZS status Theorem for theBenchmark.p 1.39/1.56 % SZS output start Proof 1.39/1.56 fof(additive_associativity, axiom, (![X3]:![X2]:![X1]:addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', additive_associativity)). 1.39/1.56 fof(idempotence, axiom, (![X1]:addition(X1,X1)=X1), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', idempotence)). 1.39/1.56 fof(order, axiom, (![X1]:![X2]:(leq(X1,X2)<=>X2=addition(X1,X2))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', order)). 1.39/1.56 fof(additive_commutativity, axiom, (![X1]:![X2]:addition(X2,X1)=addition(X1,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', additive_commutativity)). 1.39/1.56 fof(infty_unfold1, axiom, (![X1]:addition(multiplication(X1,strong_iteration(X1)),one)=strong_iteration(X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', infty_unfold1)). 1.39/1.56 fof(distributivity2, axiom, (![X1]:![X2]:![X3]:multiplication(addition(X1,X2),X3)=addition(multiplication(X1,X3),multiplication(X2,X3))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', distributivity2)). 1.39/1.56 fof(multiplicative_left_identity, axiom, (![X1]:X1=multiplication(one,X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', multiplicative_left_identity)). 1.39/1.56 fof(distributivity1, axiom, (![X1]:![X2]:![X3]:addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', distributivity1)). 1.39/1.56 fof(infty_coinduction, axiom, (![X1]:![X2]:![X3]:(leq(X3,multiplication(strong_iteration(X1),X2))<=leq(X3,addition(multiplication(X1,X3),X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', infty_coinduction)). 1.39/1.56 fof(multiplicative_associativity, axiom, (![X1]:![X2]:![X3]:multiplication(X1,multiplication(X2,X3))=multiplication(multiplication(X1,X2),X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', multiplicative_associativity)). 1.39/1.56 fof(multiplicative_right_identity, axiom, (![X1]:multiplication(X1,one)=X1), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax', multiplicative_right_identity)). 1.39/1.56 fof(goals, conjecture, (![X4]:(leq(multiplication(strong_iteration(X4),strong_iteration(X4)),strong_iteration(X4))&leq(strong_iteration(X4),multiplication(strong_iteration(X4),strong_iteration(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', goals)). 1.39/1.56 fof(c_0_12, plain, (![X4]:![X5]:![X6]:addition(X6,addition(X5,X4))=addition(addition(X6,X5),X4)), inference(variable_rename,[status(thm)],[additive_associativity])). 1.39/1.56 fof(c_0_13, plain, (![X2]:addition(X2,X2)=X2), inference(variable_rename,[status(thm)],[idempotence])). 1.39/1.56 fof(c_0_14, plain, (![X3]:![X4]:![X3]:![X4]:((~leq(X3,X4)|X4=addition(X3,X4))&(X4!=addition(X3,X4)|leq(X3,X4)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])])). 1.39/1.56 cnf(c_0_15,plain,(addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_12])). 1.39/1.56 cnf(c_0_16,plain,(addition(X1,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_13])). 1.39/1.56 cnf(c_0_17,plain,(leq(X1,X2)|X2!=addition(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_14])). 1.39/1.56 cnf(c_0_18,plain,(addition(X1,addition(X1,X2))=addition(X1,X2)), inference(spm,[status(thm)],[c_0_15, c_0_16])). 1.39/1.56 fof(c_0_19, plain, (![X3]:![X4]:addition(X4,X3)=addition(X3,X4)), inference(variable_rename,[status(thm)],[additive_commutativity])). 1.39/1.56 fof(c_0_20, plain, (![X2]:addition(multiplication(X2,strong_iteration(X2)),one)=strong_iteration(X2)), inference(variable_rename,[status(thm)],[infty_unfold1])). 1.39/1.56 cnf(c_0_21,plain,(leq(X1,addition(X1,X2))), inference(spm,[status(thm)],[c_0_17, c_0_18])). 1.39/1.56 cnf(c_0_22,plain,(addition(X1,X2)=addition(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_19])). 1.39/1.56 cnf(c_0_23,plain,(addition(multiplication(X1,strong_iteration(X1)),one)=strong_iteration(X1)), inference(split_conjunct,[status(thm)],[c_0_20])). 1.39/1.56 cnf(c_0_24,plain,(leq(X1,addition(X2,X1))), inference(spm,[status(thm)],[c_0_21, c_0_22])). 1.39/1.56 cnf(c_0_25,plain,(addition(one,multiplication(X1,strong_iteration(X1)))=strong_iteration(X1)), inference(rw,[status(thm)],[c_0_23, c_0_22])). 1.39/1.56 fof(c_0_26, plain, (![X4]:![X5]:![X6]:multiplication(addition(X4,X5),X6)=addition(multiplication(X4,X6),multiplication(X5,X6))), inference(variable_rename,[status(thm)],[distributivity2])). 1.39/1.56 fof(c_0_27, plain, (![X2]:X2=multiplication(one,X2)), inference(variable_rename,[status(thm)],[multiplicative_left_identity])). 1.39/1.56 cnf(c_0_28,plain,(X1=addition(X2,X1)|~leq(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_14])). 1.39/1.56 cnf(c_0_29,plain,(leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1))), inference(spm,[status(thm)],[c_0_24, c_0_25])). 1.39/1.56 cnf(c_0_30,plain,(multiplication(addition(X1,X2),X3)=addition(multiplication(X1,X3),multiplication(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_26])). 1.39/1.56 cnf(c_0_31,plain,(X1=multiplication(one,X1)), inference(split_conjunct,[status(thm)],[c_0_27])). 1.39/1.56 fof(c_0_32, plain, (![X4]:![X5]:![X6]:addition(multiplication(X4,X5),multiplication(X4,X6))=multiplication(X4,addition(X5,X6))), inference(variable_rename,[status(thm)],[distributivity1])). 1.39/1.56 fof(c_0_33, plain, (![X4]:![X5]:![X6]:(~leq(X6,addition(multiplication(X4,X6),X5))|leq(X6,multiplication(strong_iteration(X4),X5)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[infty_coinduction])])])). 1.39/1.56 fof(c_0_34, plain, (![X4]:![X5]:![X6]:multiplication(X4,multiplication(X5,X6))=multiplication(multiplication(X4,X5),X6)), inference(variable_rename,[status(thm)],[multiplicative_associativity])). 1.39/1.56 cnf(c_0_35,plain,(addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1)))=strong_iteration(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_22])). 1.39/1.56 cnf(c_0_36,plain,(addition(X1,multiplication(X2,X1))=multiplication(addition(X2,one),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_22])). 1.39/1.56 cnf(c_0_37,plain,(addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_32])). 1.39/1.56 fof(c_0_38, plain, (![X2]:multiplication(X2,one)=X2), inference(variable_rename,[status(thm)],[multiplicative_right_identity])). 1.39/1.56 cnf(c_0_39,plain,(leq(X1,multiplication(strong_iteration(X2),X3))|~leq(X1,addition(multiplication(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_33])). 1.39/1.56 cnf(c_0_40,plain,(multiplication(X1,multiplication(X2,X3))=multiplication(multiplication(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_34])). 1.39/1.56 cnf(c_0_41,plain,(multiplication(addition(X1,one),strong_iteration(X1))=strong_iteration(X1)), inference(rw,[status(thm)],[c_0_35, c_0_36])). 1.39/1.56 cnf(c_0_42,plain,(leq(multiplication(X1,X2),multiplication(X1,X3))|multiplication(X1,addition(X2,X3))!=multiplication(X1,X3)), inference(spm,[status(thm)],[c_0_17, c_0_37])). 1.39/1.56 cnf(c_0_43,plain,(addition(one,strong_iteration(X1))=strong_iteration(X1)), inference(spm,[status(thm)],[c_0_18, c_0_25])). 1.39/1.56 cnf(c_0_44,plain,(multiplication(X1,one)=X1), inference(split_conjunct,[status(thm)],[c_0_38])). 1.39/1.56 cnf(c_0_45,plain,(leq(X1,multiplication(strong_iteration(X2),X3))|~leq(X1,addition(X3,multiplication(X2,X1)))), inference(spm,[status(thm)],[c_0_39, c_0_22])). 1.39/1.56 cnf(c_0_46,plain,(addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))))=strong_iteration(multiplication(X1,X2))), inference(spm,[status(thm)],[c_0_25, c_0_40])). 1.39/1.56 cnf(c_0_47,plain,(multiplication(addition(one,X1),strong_iteration(X1))=strong_iteration(X1)), inference(spm,[status(thm)],[c_0_41, c_0_22])). 1.39/1.56 cnf(c_0_48,plain,(leq(X1,multiplication(X1,strong_iteration(X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])). 1.39/1.56 cnf(c_0_49,plain,(leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(X2))|~leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(multiplication(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_44])). 1.39/1.56 cnf(c_0_50,plain,(multiplication(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1))))=strong_iteration(multiplication(X1,strong_iteration(X1)))), inference(spm,[status(thm)],[c_0_47, c_0_25])). 1.39/1.56 cnf(c_0_51,plain,(leq(X1,X1)), inference(spm,[status(thm)],[c_0_17, c_0_16])). 1.39/1.56 cnf(c_0_52,plain,(leq(multiplication(X1,X2),multiplication(X1,multiplication(X2,strong_iteration(X3))))), inference(spm,[status(thm)],[c_0_48, c_0_40])). 1.39/1.56 cnf(c_0_53,plain,(leq(strong_iteration(multiplication(X1,strong_iteration(X1))),strong_iteration(X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51])])). 1.39/1.56 fof(c_0_54, negated_conjecture, (~(![X4]:(leq(multiplication(strong_iteration(X4),strong_iteration(X4)),strong_iteration(X4))&leq(strong_iteration(X4),multiplication(strong_iteration(X4),strong_iteration(X4)))))), inference(assume_negation,[status(cth)],[goals])). 1.39/1.56 cnf(c_0_55,plain,(leq(multiplication(X1,strong_iteration(X2)),multiplication(X1,strong_iteration(multiplication(X2,strong_iteration(X2)))))), inference(spm,[status(thm)],[c_0_52, c_0_50])). 1.39/1.56 cnf(c_0_56,plain,(addition(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1))))=strong_iteration(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_53]), c_0_22])). 1.39/1.56 fof(c_0_57, negated_conjecture, ((~leq(multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)),strong_iteration(esk1_0))|~leq(strong_iteration(esk2_0),multiplication(strong_iteration(esk2_0),strong_iteration(esk2_0))))), inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])])). 1.39/1.56 cnf(c_0_58,plain,(multiplication(X1,strong_iteration(multiplication(X2,strong_iteration(X2))))=multiplication(X1,strong_iteration(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_55]), c_0_37]), c_0_56])). 1.39/1.56 cnf(c_0_59,negated_conjecture,(~leq(strong_iteration(esk2_0),multiplication(strong_iteration(esk2_0),strong_iteration(esk2_0)))|~leq(multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)),strong_iteration(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_57])). 1.39/1.56 cnf(c_0_60,plain,(leq(X1,multiplication(strong_iteration(X2),X1))), inference(spm,[status(thm)],[c_0_45, c_0_21])). 1.39/1.56 cnf(c_0_61,plain,(strong_iteration(multiplication(X1,strong_iteration(X1)))=strong_iteration(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_58]), c_0_31])). 1.39/1.56 cnf(c_0_62,negated_conjecture,(~leq(multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)),strong_iteration(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])). 1.39/1.56 cnf(c_0_63,plain,(multiplication(strong_iteration(X1),strong_iteration(X1))=strong_iteration(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_61]), c_0_22]), c_0_25])). 1.39/1.56 cnf(c_0_64,negated_conjecture,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63]), c_0_51])]), ['proof']). 1.39/1.56 % SZS output end Proof 1.39/1.56 % User time : 0.996 s 1.39/1.56 % System time : 0.049 s 1.39/1.56 % Total time : 1.045 s 1.39/1.56 1.39/1.58 EOF