0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -jar mcs_epr.jar %d %s 0.02/0.23 % Computer : n014.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:03:40 CDT 2018 0.02/0.23 % CPUTime : 0.06/0.30 openjdk version "1.8.0_144" 0.06/0.30 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.06/0.30 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.41 start to proof:theBenchmark.p 1.70/1.88 % Version : CSE_E---1.0 1.70/1.88 % Problem : theBenchmark.p 1.70/1.88 % Proof found! 1.70/1.88 % SZS status Theorem for theBenchmark.p 1.70/1.88 % SZS output start Proof 1.70/1.88 fof(right_distributivity, axiom, (![X1]:![X2]:![X3]:addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', right_distributivity)). 1.70/1.88 fof(domain1, axiom, (![X4]:zero=multiplication(antidomain(X4),X4)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', domain1)). 1.70/1.88 fof(additive_identity, axiom, (![X1]:addition(X1,zero)=X1), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', additive_identity)). 1.70/1.88 fof(additive_associativity, axiom, (![X3]:![X2]:![X1]:addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', additive_associativity)). 1.70/1.88 fof(additive_idempotence, axiom, (![X1]:X1=addition(X1,X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', additive_idempotence)). 1.70/1.88 fof(additive_commutativity, axiom, (![X1]:![X2]:addition(X2,X1)=addition(X1,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', additive_commutativity)). 1.70/1.88 fof(domain3, axiom, (![X4]:one=addition(antidomain(antidomain(X4)),antidomain(X4))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', domain3)). 1.70/1.88 fof(multiplicative_right_identity, axiom, (![X1]:X1=multiplication(X1,one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', multiplicative_right_identity)). 1.70/1.88 fof(left_distributivity, axiom, (![X1]:![X2]:![X3]:addition(multiplication(X1,X3),multiplication(X2,X3))=multiplication(addition(X1,X2),X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', left_distributivity)). 1.70/1.88 fof(multiplicative_associativity, axiom, (![X1]:![X2]:![X3]:multiplication(multiplication(X1,X2),X3)=multiplication(X1,multiplication(X2,X3))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', multiplicative_associativity)). 1.70/1.88 fof(left_annihilation, axiom, (![X1]:zero=multiplication(zero,X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', left_annihilation)). 1.70/1.88 fof(multiplicative_left_identity, axiom, (![X1]:X1=multiplication(one,X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax', multiplicative_left_identity)). 1.70/1.88 fof(domain2, axiom, (![X4]:![X5]:antidomain(multiplication(X4,antidomain(antidomain(X5))))=addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5)))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', domain2)). 1.70/1.88 fof(codomain3, axiom, (![X4]:one=addition(coantidomain(coantidomain(X4)),coantidomain(X4))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', codomain3)). 1.70/1.88 fof(codomain1, axiom, (![X4]:multiplication(X4,coantidomain(X4))=zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', codomain1)). 1.70/1.88 fof(codomain2, axiom, (![X4]:![X5]:addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)))=coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', codomain2)). 1.70/1.88 fof(goals, conjecture, (![X4]:![X5]:![X6]:addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6))))=domain(multiplication(X4,addition(domain(X5),domain(X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', goals)). 1.70/1.88 fof(domain4, axiom, (![X4]:domain(X4)=antidomain(antidomain(X4))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax', domain4)). 1.70/1.88 fof(c_0_18, plain, (![X4]:![X5]:![X6]:addition(multiplication(X4,X5),multiplication(X4,X6))=multiplication(X4,addition(X5,X6))), inference(variable_rename,[status(thm)],[right_distributivity])). 1.70/1.88 fof(c_0_19, plain, (![X5]:zero=multiplication(antidomain(X5),X5)), inference(variable_rename,[status(thm)],[domain1])). 1.70/1.88 fof(c_0_20, plain, (![X2]:addition(X2,zero)=X2), inference(variable_rename,[status(thm)],[additive_identity])). 1.70/1.88 fof(c_0_21, plain, (![X4]:![X5]:![X6]:addition(X6,addition(X5,X4))=addition(addition(X6,X5),X4)), inference(variable_rename,[status(thm)],[additive_associativity])). 1.70/1.88 fof(c_0_22, plain, (![X2]:X2=addition(X2,X2)), inference(variable_rename,[status(thm)],[additive_idempotence])). 1.70/1.88 cnf(c_0_23,plain,(addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_18])). 1.70/1.88 cnf(c_0_24,plain,(zero=multiplication(antidomain(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_19])). 1.70/1.88 cnf(c_0_25,plain,(addition(X1,zero)=X1), inference(split_conjunct,[status(thm)],[c_0_20])). 1.70/1.88 cnf(c_0_26,plain,(addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_21])). 1.70/1.88 cnf(c_0_27,plain,(X1=addition(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_22])). 1.70/1.88 fof(c_0_28, plain, (![X3]:![X4]:addition(X4,X3)=addition(X3,X4)), inference(variable_rename,[status(thm)],[additive_commutativity])). 1.70/1.88 fof(c_0_29, plain, (![X5]:one=addition(antidomain(antidomain(X5)),antidomain(X5))), inference(variable_rename,[status(thm)],[domain3])). 1.70/1.88 fof(c_0_30, plain, (![X2]:X2=multiplication(X2,one)), inference(variable_rename,[status(thm)],[multiplicative_right_identity])). 1.70/1.88 fof(c_0_31, plain, (![X4]:![X5]:![X6]:addition(multiplication(X4,X6),multiplication(X5,X6))=multiplication(addition(X4,X5),X6)), inference(variable_rename,[status(thm)],[left_distributivity])). 1.70/1.88 cnf(c_0_32,plain,(multiplication(antidomain(X1),addition(X2,X1))=multiplication(antidomain(X1),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25])). 1.70/1.88 cnf(c_0_33,plain,(addition(X1,addition(X1,X2))=addition(X1,X2)), inference(spm,[status(thm)],[c_0_26, c_0_27])). 1.70/1.88 cnf(c_0_34,plain,(addition(X1,X2)=addition(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_28])). 1.70/1.88 fof(c_0_35, plain, (![X4]:![X5]:![X6]:multiplication(multiplication(X4,X5),X6)=multiplication(X4,multiplication(X5,X6))), inference(variable_rename,[status(thm)],[multiplicative_associativity])). 1.70/1.88 fof(c_0_36, plain, (![X2]:zero=multiplication(zero,X2)), inference(variable_rename,[status(thm)],[left_annihilation])). 1.70/1.88 cnf(c_0_37,plain,(one=addition(antidomain(antidomain(X1)),antidomain(X1))), inference(split_conjunct,[status(thm)],[c_0_29])). 1.70/1.88 cnf(c_0_38,plain,(X1=multiplication(X1,one)), inference(split_conjunct,[status(thm)],[c_0_30])). 1.70/1.88 cnf(c_0_39,plain,(addition(multiplication(X1,X2),multiplication(X3,X2))=multiplication(addition(X1,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_31])). 1.70/1.88 cnf(c_0_40,plain,(multiplication(antidomain(addition(X1,X2)),X1)=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_24])). 1.70/1.88 cnf(c_0_41,plain,(addition(zero,X1)=X1), inference(spm,[status(thm)],[c_0_34, c_0_25])). 1.70/1.88 fof(c_0_42, plain, (![X2]:X2=multiplication(one,X2)), inference(variable_rename,[status(thm)],[multiplicative_left_identity])). 1.70/1.88 fof(c_0_43, plain, (![X6]:![X7]:antidomain(multiplication(X6,antidomain(antidomain(X7))))=addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7)))))), inference(variable_rename,[status(thm)],[domain2])). 1.70/1.88 cnf(c_0_44,plain,(multiplication(multiplication(X1,X2),X3)=multiplication(X1,multiplication(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_35])). 1.70/1.88 cnf(c_0_45,plain,(zero=multiplication(zero,X1)), inference(split_conjunct,[status(thm)],[c_0_36])). 1.70/1.88 cnf(c_0_46,plain,(addition(antidomain(X1),antidomain(antidomain(X1)))=one), inference(rw,[status(thm)],[c_0_37, c_0_34])). 1.70/1.88 cnf(c_0_47,plain,(antidomain(one)=zero), inference(spm,[status(thm)],[c_0_38, c_0_24])). 1.70/1.88 cnf(c_0_48,plain,(multiplication(addition(antidomain(addition(X1,X2)),X3),X1)=multiplication(X3,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41])). 1.70/1.88 cnf(c_0_49,plain,(X1=multiplication(one,X1)), inference(split_conjunct,[status(thm)],[c_0_42])). 1.70/1.88 fof(c_0_50, plain, (![X5]:one=addition(coantidomain(coantidomain(X5)),coantidomain(X5))), inference(variable_rename,[status(thm)],[codomain3])). 1.70/1.88 fof(c_0_51, plain, (![X5]:multiplication(X5,coantidomain(X5))=zero), inference(variable_rename,[status(thm)],[codomain1])). 1.70/1.88 cnf(c_0_52,plain,(antidomain(multiplication(X1,antidomain(antidomain(X2))))=addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2)))))), inference(split_conjunct,[status(thm)],[c_0_43])). 1.70/1.88 cnf(c_0_53,plain,(multiplication(antidomain(X1),multiplication(X1,X2))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_24]), c_0_45])). 1.70/1.88 cnf(c_0_54,plain,(antidomain(zero)=one), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_41])). 1.70/1.88 cnf(c_0_55,plain,(addition(one,antidomain(X1))=one), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_46]), c_0_34])). 1.70/1.88 cnf(c_0_56,plain,(addition(X1,addition(X2,X3))=addition(X3,addition(X1,X2))), inference(spm,[status(thm)],[c_0_34, c_0_26])). 1.70/1.88 cnf(c_0_57,plain,(multiplication(antidomain(antidomain(addition(X1,X2))),X1)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_46]), c_0_49])). 1.70/1.88 cnf(c_0_58,plain,(one=addition(coantidomain(coantidomain(X1)),coantidomain(X1))), inference(split_conjunct,[status(thm)],[c_0_50])). 1.70/1.88 cnf(c_0_59,plain,(multiplication(X1,coantidomain(X1))=zero), inference(split_conjunct,[status(thm)],[c_0_51])). 1.70/1.88 cnf(c_0_60,plain,(antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))))=one), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54]), c_0_55])). 1.70/1.88 cnf(c_0_61,plain,(addition(X1,addition(X2,X1))=addition(X2,X1)), inference(spm,[status(thm)],[c_0_56, c_0_27])). 1.70/1.88 cnf(c_0_62,plain,(multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1))=antidomain(antidomain(antidomain(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_46]), c_0_38])). 1.70/1.88 cnf(c_0_63,plain,(multiplication(antidomain(antidomain(X1)),X1)=X1), inference(spm,[status(thm)],[c_0_57, c_0_25])). 1.70/1.88 fof(c_0_64, plain, (![X6]:![X7]:addition(coantidomain(multiplication(X6,X7)),coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)))=coantidomain(multiplication(coantidomain(coantidomain(X6)),X7))), inference(variable_rename,[status(thm)],[codomain2])). 1.70/1.88 cnf(c_0_65,plain,(addition(coantidomain(X1),coantidomain(coantidomain(X1)))=one), inference(rw,[status(thm)],[c_0_58, c_0_34])). 1.70/1.88 cnf(c_0_66,plain,(coantidomain(one)=zero), inference(spm,[status(thm)],[c_0_49, c_0_59])). 1.70/1.88 cnf(c_0_67,plain,(multiplication(X1,multiplication(coantidomain(X1),X2))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_59]), c_0_45])). 1.70/1.88 cnf(c_0_68,plain,(addition(X1,multiplication(antidomain(X2),antidomain(antidomain(multiplication(X2,X3)))))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_60]), c_0_49]), c_0_49])). 1.70/1.88 cnf(c_0_69,plain,(multiplication(antidomain(antidomain(addition(X1,X2))),X2)=X2), inference(spm,[status(thm)],[c_0_57, c_0_61])). 1.70/1.88 cnf(c_0_70,plain,(antidomain(antidomain(antidomain(X1)))=antidomain(X1)), inference(rw,[status(thm)],[c_0_62, c_0_63])). 1.70/1.88 cnf(c_0_71,plain,(addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)))=coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_64])). 1.70/1.88 cnf(c_0_72,plain,(coantidomain(zero)=one), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_41])). 1.70/1.88 cnf(c_0_73,plain,(addition(one,coantidomain(X1))=one), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_65]), c_0_34])). 1.70/1.88 cnf(c_0_74,plain,(multiplication(addition(antidomain(X1),X2),X1)=multiplication(X2,X1)), inference(spm,[status(thm)],[c_0_48, c_0_25])). 1.70/1.88 cnf(c_0_75,plain,(addition(X1,addition(X2,X3))=addition(X3,addition(X2,X1))), inference(spm,[status(thm)],[c_0_56, c_0_34])). 1.70/1.88 cnf(c_0_76,plain,(multiplication(X1,addition(multiplication(coantidomain(X1),X2),X3))=multiplication(X1,X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_67]), c_0_41])). 1.70/1.88 cnf(c_0_77,plain,(addition(X1,multiplication(antidomain(addition(X2,X3)),antidomain(antidomain(X3))))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70])). 1.70/1.88 cnf(c_0_78,plain,(multiplication(antidomain(addition(X1,X2)),addition(X1,X3))=multiplication(antidomain(addition(X1,X2)),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_40]), c_0_41])). 1.70/1.88 cnf(c_0_79,plain,(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_60]), c_0_49])). 1.70/1.88 cnf(c_0_80,plain,(addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4))=addition(multiplication(X1,addition(X2,X3)),X4)), inference(spm,[status(thm)],[c_0_26, c_0_23])). 1.70/1.88 cnf(c_0_81,plain,(coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1))=one), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_24]), c_0_72]), c_0_73])). 1.70/1.88 cnf(c_0_82,plain,(multiplication(addition(X1,addition(X2,antidomain(X3))),X3)=multiplication(addition(X2,X1),X3)), inference(spm,[status(thm)],[c_0_74, c_0_75])). 1.70/1.88 cnf(c_0_83,plain,(multiplication(addition(X1,X2),coantidomain(X1))=multiplication(X2,coantidomain(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_59]), c_0_41])). 1.70/1.88 cnf(c_0_84,plain,(multiplication(addition(X1,antidomain(X2)),X2)=multiplication(X1,X2)), inference(spm,[status(thm)],[c_0_74, c_0_34])). 1.70/1.88 cnf(c_0_85,plain,(multiplication(X1,addition(coantidomain(X1),X2))=multiplication(X1,X2)), inference(spm,[status(thm)],[c_0_76, c_0_38])). 1.70/1.88 cnf(c_0_86,plain,(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2)))=zero), inference(spm,[status(thm)],[c_0_41, c_0_77])). 1.70/1.88 cnf(c_0_87,plain,(multiplication(antidomain(addition(antidomain(X1),X2)),antidomain(antidomain(X1)))=antidomain(addition(antidomain(X1),X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_46]), c_0_38])). 1.70/1.88 cnf(c_0_88,plain,(multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(X1,X2))),X3))=multiplication(antidomain(X1),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_79]), c_0_41])). 1.70/1.88 cnf(c_0_89,plain,(antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))=one), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_59]), c_0_54]), c_0_55])). 1.70/1.88 cnf(c_0_90,plain,(addition(X1,addition(multiplication(X1,X2),X3))=addition(multiplication(X1,addition(one,X2)),X3)), inference(spm,[status(thm)],[c_0_80, c_0_38])). 1.70/1.88 cnf(c_0_91,plain,(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)=zero), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_81]), c_0_44]), c_0_38])). 1.70/1.88 cnf(c_0_92,plain,(multiplication(addition(X1,X2),coantidomain(X2))=multiplication(X1,coantidomain(X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84])). 1.70/1.88 cnf(c_0_93,plain,(multiplication(X1,coantidomain(coantidomain(X1)))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_65]), c_0_38])). 1.70/1.88 cnf(c_0_94,plain,(multiplication(antidomain(X1),addition(X1,X2))=multiplication(antidomain(X1),X2)), inference(spm,[status(thm)],[c_0_32, c_0_34])). 1.70/1.88 cnf(c_0_95,plain,(antidomain(addition(X1,antidomain(X1)))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_34])). 1.70/1.88 cnf(c_0_96,plain,(addition(X1,multiplication(X2,X1))=multiplication(addition(X2,one),X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_49]), c_0_34])). 1.70/1.88 cnf(c_0_97,plain,(multiplication(antidomain(X1),antidomain(multiplication(X1,X2)))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_46]), c_0_38]), c_0_70])). 1.70/1.88 cnf(c_0_98,plain,(addition(X1,multiplication(X2,antidomain(antidomain(coantidomain(X2)))))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_89]), c_0_49]), c_0_49])). 1.70/1.88 cnf(c_0_99,plain,(addition(X1,addition(multiplication(X1,antidomain(X2)),X3))=addition(X1,X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_55]), c_0_38])). 1.70/1.88 cnf(c_0_100,plain,(multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1)=multiplication(X2,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_91]), c_0_41])). 1.70/1.88 cnf(c_0_101,plain,(coantidomain(coantidomain(coantidomain(X1)))=coantidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_65]), c_0_49]), c_0_93])). 1.70/1.88 cnf(c_0_102,plain,(multiplication(antidomain(antidomain(X1)),antidomain(antidomain(X1)))=antidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_46]), c_0_38])). 1.70/1.88 cnf(c_0_103,plain,(addition(antidomain(X1),antidomain(multiplication(X1,addition(X2,antidomain(X2)))))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_95]), c_0_54]), c_0_38]), c_0_54]), c_0_38]), c_0_34])). 1.70/1.88 cnf(c_0_104,plain,(addition(antidomain(X1),antidomain(multiplication(X1,X2)))=antidomain(multiplication(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_34]), c_0_55]), c_0_49]), c_0_34])). 1.70/1.88 cnf(c_0_105,plain,(multiplication(X1,addition(X2,antidomain(antidomain(coantidomain(X1)))))=multiplication(X1,X2)), inference(spm,[status(thm)],[c_0_23, c_0_98])). 1.70/1.88 cnf(c_0_106,plain,(multiplication(addition(multiplication(antidomain(X1),antidomain(X2)),X3),X1)=multiplication(X3,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_99]), c_0_74])). 1.70/1.88 cnf(c_0_107,plain,(multiplication(X1,coantidomain(addition(X1,X2)))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_33]), c_0_59])). 1.70/1.88 cnf(c_0_108,plain,(multiplication(coantidomain(antidomain(X1)),X1)=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_65]), c_0_49]), c_0_101])). 1.70/1.88 cnf(c_0_109,plain,(multiplication(antidomain(antidomain(addition(X1,X2))),multiplication(X1,X3))=multiplication(X1,X3)), inference(spm,[status(thm)],[c_0_44, c_0_57])). 1.70/1.88 cnf(c_0_110,plain,(multiplication(antidomain(X1),antidomain(X1))=antidomain(X1)), inference(spm,[status(thm)],[c_0_102, c_0_70])). 1.70/1.88 cnf(c_0_111,plain,(addition(X1,multiplication(X1,X2))=multiplication(X1,addition(X2,one))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_38]), c_0_34])). 1.70/1.88 cnf(c_0_112,plain,(antidomain(multiplication(X1,addition(X2,antidomain(X2))))=antidomain(X1)), inference(rw,[status(thm)],[c_0_103, c_0_104])). 1.70/1.88 cnf(c_0_113,plain,(multiplication(X1,antidomain(coantidomain(X1)))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_46]), c_0_38])). 1.70/1.88 cnf(c_0_114,plain,(multiplication(antidomain(X1),multiplication(antidomain(X2),X1))=zero), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_106]), c_0_24]), c_0_44])). 1.70/1.88 cnf(c_0_115,plain,(multiplication(X1,addition(coantidomain(addition(X1,X2)),X3))=multiplication(X1,X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_107]), c_0_41])). 1.70/1.88 cnf(c_0_116,plain,(multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1)))=antidomain(antidomain(X1))), inference(spm,[status(thm)],[c_0_108, c_0_70])). 1.70/1.88 cnf(c_0_117,plain,(multiplication(antidomain(antidomain(addition(antidomain(antidomain(X1)),X2))),X1)=X1), inference(spm,[status(thm)],[c_0_109, c_0_63])). 1.70/1.88 cnf(c_0_118,plain,(addition(X1,multiplication(antidomain(antidomain(X1)),X2))=multiplication(antidomain(antidomain(X1)),addition(X1,X2))), inference(spm,[status(thm)],[c_0_23, c_0_63])). 1.70/1.88 cnf(c_0_119,plain,(multiplication(antidomain(X1),addition(X2,antidomain(X1)))=multiplication(antidomain(X1),addition(X2,one))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_110]), c_0_34]), c_0_111])). 1.70/1.88 cnf(c_0_120,plain,(addition(one,addition(antidomain(X1),X2))=addition(X2,one)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_55]), c_0_56])). 1.70/1.88 cnf(c_0_121,plain,(antidomain(multiplication(X1,addition(X2,addition(X3,antidomain(addition(X2,X3))))))=antidomain(X1)), inference(spm,[status(thm)],[c_0_112, c_0_26])). 1.70/1.88 cnf(c_0_122,plain,(multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2))=multiplication(X1,X2)), inference(spm,[status(thm)],[c_0_44, c_0_113])). 1.70/1.88 cnf(c_0_123,plain,(multiplication(antidomain(X1),addition(multiplication(antidomain(X2),X1),X3))=multiplication(antidomain(X1),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_114]), c_0_41])). 1.70/1.88 cnf(c_0_124,plain,(multiplication(X1,coantidomain(coantidomain(addition(X1,X2))))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_65]), c_0_38])). 1.70/1.88 cnf(c_0_125,plain,(addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1)))=coantidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_116]), c_0_34]), c_0_55]), c_0_38]), c_0_34])). 1.70/1.88 cnf(c_0_126,plain,(multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1)))=coantidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_46]), c_0_49])). 1.70/1.88 cnf(c_0_127,plain,(multiplication(antidomain(multiplication(antidomain(X1),X2)),X1)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_104]), c_0_70])). 1.70/1.88 cnf(c_0_128,plain,(multiplication(antidomain(antidomain(X1)),addition(X1,one))=addition(X1,antidomain(antidomain(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_110]), c_0_119])). 1.70/1.88 cnf(c_0_129,plain,(antidomain(addition(X1,one))=zero), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_120]), c_0_38])). 1.70/1.88 cnf(c_0_130,plain,(antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X1,X2)))))=antidomain(antidomain(X1))), inference(spm,[status(thm)],[c_0_121, c_0_94])). 1.70/1.88 cnf(c_0_131,plain,(multiplication(X1,addition(multiplication(antidomain(X2),coantidomain(X1)),X3))=multiplication(X1,X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_122])). 1.70/1.88 cnf(c_0_132,plain,(coantidomain(antidomain(X1))=antidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_125]), c_0_101]), c_0_126])). 1.70/1.88 cnf(c_0_133,plain,(multiplication(antidomain(X1),antidomain(addition(X1,X2)))=antidomain(addition(X1,X2))), inference(spm,[status(thm)],[c_0_127, c_0_57])). 1.70/1.88 cnf(c_0_134,plain,(addition(antidomain(X1),antidomain(addition(X1,antidomain(antidomain(X1)))))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_128]), c_0_129]), c_0_54]), c_0_38]), c_0_70]), c_0_129]), c_0_54]), c_0_38]), c_0_70]), c_0_34])). 1.70/1.88 cnf(c_0_135,plain,(antidomain(antidomain(addition(X1,multiplication(antidomain(X2),antidomain(antidomain(X1))))))=antidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131]), c_0_132]), c_0_133])). 1.70/1.88 cnf(c_0_136,plain,(antidomain(multiplication(X1,multiplication(X2,addition(X3,antidomain(X3)))))=antidomain(multiplication(X1,X2))), inference(spm,[status(thm)],[c_0_112, c_0_44])). 1.70/1.88 cnf(c_0_137,plain,(addition(X1,addition(X2,X3))=addition(X2,addition(X1,X3))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_34]), c_0_26])). 1.70/1.88 cnf(c_0_138,plain,(antidomain(addition(X1,antidomain(antidomain(X1))))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_128]), c_0_70]), c_0_134])). 1.70/1.88 cnf(c_0_139,plain,(multiplication(antidomain(X1),antidomain(addition(X2,X1)))=antidomain(addition(X2,X1))), inference(spm,[status(thm)],[c_0_127, c_0_69])). 1.70/1.88 cnf(c_0_140,plain,(antidomain(addition(X1,multiplication(antidomain(X2),antidomain(antidomain(X1)))))=antidomain(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_135]), c_0_70])). 1.70/1.88 cnf(c_0_141,plain,(antidomain(multiplication(X1,antidomain(antidomain(X2))))=antidomain(multiplication(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_32]), c_0_63])). 1.70/1.88 cnf(c_0_142,plain,(multiplication(antidomain(addition(X1,X2)),antidomain(X2))=antidomain(addition(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_69]), c_0_70]), c_0_70])). 1.70/1.88 cnf(c_0_143,plain,(addition(X1,addition(multiplication(X1,X2),X3))=addition(multiplication(X1,addition(X2,one)),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_38]), c_0_137])). 1.70/1.88 cnf(c_0_144,plain,(antidomain(multiplication(X1,addition(X2,one)))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_138]), c_0_26]), c_0_34]), c_0_46])). 1.70/1.88 cnf(c_0_145,plain,(addition(X1,multiplication(antidomain(addition(X2,X3)),antidomain(antidomain(X2))))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_57]), c_0_70])). 1.70/1.88 cnf(c_0_146,plain,(multiplication(antidomain(multiplication(antidomain(X1),X2)),multiplication(X1,X3))=multiplication(X1,X3)), inference(spm,[status(thm)],[c_0_44, c_0_127])). 1.70/1.88 cnf(c_0_147,plain,(multiplication(antidomain(multiplication(antidomain(X1),X2)),antidomain(X2))=antidomain(X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140]), c_0_141])). 1.70/1.88 cnf(c_0_148,plain,(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))=antidomain(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_140]), c_0_141])). 1.70/1.88 cnf(c_0_149,plain,(antidomain(addition(X1,addition(antidomain(antidomain(X1)),multiplication(X1,X2))))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_143]), c_0_144]), c_0_144]), c_0_34])). 1.70/1.88 cnf(c_0_150,plain,(multiplication(antidomain(antidomain(addition(antidomain(antidomain(addition(X1,X2))),X3))),X1)=X1), inference(spm,[status(thm)],[c_0_109, c_0_57])). 1.70/1.88 cnf(c_0_151,plain,(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))=zero), inference(spm,[status(thm)],[c_0_41, c_0_145])). 1.70/1.88 cnf(c_0_152,plain,(multiplication(antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),X3)),X1)=X1), inference(spm,[status(thm)],[c_0_146, c_0_127])). 1.70/1.88 cnf(c_0_153,plain,(multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1))=multiplication(antidomain(X2),X1)), inference(spm,[status(thm)],[c_0_127, c_0_147])). 1.70/1.88 cnf(c_0_154,plain,(multiplication(X1,antidomain(multiplication(antidomain(X2),coantidomain(X1))))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_148]), c_0_113])). 1.70/1.88 cnf(c_0_155,plain,(multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1))=antidomain(coantidomain(coantidomain(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_65]), c_0_38])). 1.70/1.88 cnf(c_0_156,plain,(multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X3,X1),X2))=multiplication(antidomain(multiplication(X1,X2)),multiplication(X3,X2))), inference(spm,[status(thm)],[c_0_32, c_0_39])). 1.70/1.88 cnf(c_0_157,plain,(antidomain(addition(X1,antidomain(multiplication(antidomain(X1),X2))))=antidomain(antidomain(multiplication(antidomain(X1),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_127]), c_0_70]), c_0_33]), c_0_34])). 1.70/1.88 cnf(c_0_158,plain,(multiplication(antidomain(multiplication(antidomain(addition(X1,X2)),X3)),X1)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_104]), c_0_70])). 1.70/1.88 cnf(c_0_159,plain,(antidomain(addition(X1,addition(antidomain(X1),X2)))=zero), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_95]), c_0_26]), c_0_54]), c_0_38])). 1.70/1.88 cnf(c_0_160,plain,(multiplication(antidomain(multiplication(antidomain(X1),multiplication(antidomain(X2),X3))),X2)=X2), inference(spm,[status(thm)],[c_0_152, c_0_153])). 1.70/1.88 cnf(c_0_161,plain,(multiplication(X1,antidomain(antidomain(coantidomain(coantidomain(X1)))))=X1), inference(spm,[status(thm)],[c_0_154, c_0_155])). 1.70/1.88 cnf(c_0_162,plain,(multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X2)),X2)=multiplication(antidomain(X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_46]), c_0_49]), c_0_146])). 1.70/1.88 cnf(c_0_163,plain,(antidomain(addition(antidomain(X1),multiplication(antidomain(addition(X1,X2)),X3)))=antidomain(antidomain(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_34])). 1.70/1.88 cnf(c_0_164,plain,(antidomain(addition(X1,antidomain(multiplication(X1,X2))))=zero), inference(spm,[status(thm)],[c_0_159, c_0_104])). 1.70/1.88 cnf(c_0_165,plain,(addition(antidomain(X1),antidomain(addition(X2,X1)))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_69]), c_0_70]), c_0_34])). 1.70/1.88 cnf(c_0_166,plain,(multiplication(antidomain(multiplication(antidomain(X1),antidomain(X2))),X2)=X2), inference(spm,[status(thm)],[c_0_160, c_0_161])). 1.70/1.88 cnf(c_0_167,plain,(multiplication(antidomain(multiplication(antidomain(X1),X2)),X2)=multiplication(antidomain(antidomain(X1)),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163]), c_0_70])). 1.70/1.88 cnf(c_0_168,plain,(antidomain(multiplication(X1,addition(X2,antidomain(multiplication(X2,X3)))))=antidomain(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_164]), c_0_26]), c_0_25])). 1.70/1.88 cnf(c_0_169,plain,(multiplication(antidomain(antidomain(X1)),antidomain(antidomain(addition(X2,X1))))=antidomain(antidomain(X1))), inference(spm,[status(thm)],[c_0_142, c_0_165])). 1.70/1.88 cnf(c_0_170,plain,(addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),antidomain(X1)))))=antidomain(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_166]), c_0_34])). 1.70/1.88 cnf(c_0_171,plain,(multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),X2)=multiplication(antidomain(X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_167]), c_0_167]), c_0_70])). 1.70/1.88 cnf(c_0_172,plain,(multiplication(antidomain(addition(X1,X2)),antidomain(X1))=antidomain(addition(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_57]), c_0_70]), c_0_70])). 1.70/1.88 cnf(c_0_173,plain,(antidomain(multiplication(antidomain(antidomain(multiplication(X1,X2))),X1))=antidomain(multiplication(X1,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_32]), c_0_70])). 1.70/1.88 cnf(c_0_174,plain,(antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2))))=multiplication(antidomain(X1),antidomain(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169, c_0_170]), c_0_70]), c_0_70]), c_0_171]), c_0_70])). 1.70/1.88 cnf(c_0_175,plain,(multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1)))=multiplication(antidomain(X2),antidomain(X1))), inference(spm,[status(thm)],[c_0_153, c_0_70])). 1.70/1.88 cnf(c_0_176,plain,(antidomain(addition(X1,antidomain(addition(antidomain(X1),X2))))=antidomain(X1)), inference(spm,[status(thm)],[c_0_140, c_0_172])). 1.70/1.88 cnf(c_0_177,plain,(addition(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))=antidomain(multiplication(antidomain(X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165, c_0_140]), c_0_141]), c_0_141]), c_0_34])). 1.70/1.88 cnf(c_0_178,plain,(multiplication(antidomain(X1),addition(X2,addition(X1,X3)))=multiplication(antidomain(X1),addition(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_32]), c_0_23]), c_0_26])). 1.70/1.88 cnf(c_0_179,plain,(antidomain(multiplication(antidomain(X1),antidomain(X2)))=antidomain(multiplication(antidomain(X2),antidomain(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173, c_0_174]), c_0_44]), c_0_175])). 1.70/1.88 cnf(c_0_180,plain,(antidomain(addition(X1,antidomain(antidomain(multiplication(antidomain(X2),X1)))))=antidomain(X1)), inference(spm,[status(thm)],[c_0_176, c_0_177])). 1.70/1.88 cnf(c_0_181,plain,(antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X2,X1)))))=antidomain(antidomain(X1))), inference(spm,[status(thm)],[c_0_121, c_0_178])). 1.70/1.88 cnf(c_0_182,plain,(multiplication(antidomain(X1),antidomain(antidomain(X2)))=antidomain(antidomain(multiplication(antidomain(X1),X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174, c_0_163]), c_0_141])). 1.70/1.88 cnf(c_0_183,plain,(multiplication(antidomain(X1),antidomain(X2))=multiplication(antidomain(X2),antidomain(X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174, c_0_179]), c_0_174])). 1.70/1.88 cnf(c_0_184,plain,(antidomain(addition(X1,antidomain(addition(X1,X2))))=antidomain(addition(X1,antidomain(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_70]), c_0_26]), c_0_34]), c_0_165])). 1.70/1.88 cnf(c_0_185,plain,(antidomain(addition(X1,antidomain(antidomain(addition(X1,X2)))))=antidomain(addition(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_57]), c_0_70]), c_0_33]), c_0_70]), c_0_34])). 1.70/1.88 cnf(c_0_186,plain,(multiplication(antidomain(antidomain(X1)),antidomain(X2))=antidomain(antidomain(multiplication(antidomain(X2),X1)))), inference(spm,[status(thm)],[c_0_182, c_0_183])). 1.70/1.88 cnf(c_0_187,plain,(addition(multiplication(X1,antidomain(antidomain(coantidomain(X1)))),X2)=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_89]), c_0_49]), c_0_49])). 1.70/1.88 cnf(c_0_188,plain,(antidomain(addition(X1,antidomain(antidomain(X2))))=antidomain(addition(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184, c_0_184]), c_0_184]), c_0_185])). 1.70/1.88 cnf(c_0_189,plain,(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X1),X2)))=multiplication(antidomain(X2),antidomain(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_186]), c_0_70]), c_0_70]), c_0_183])). 1.70/1.88 cnf(c_0_190,plain,(multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2))=multiplication(X1,X2)), inference(spm,[status(thm)],[c_0_23, c_0_187])). 1.70/1.88 cnf(c_0_191,plain,(antidomain(addition(antidomain(antidomain(X1)),X2))=antidomain(addition(X2,X1))), inference(spm,[status(thm)],[c_0_188, c_0_34])). 1.70/1.88 cnf(c_0_192,plain,(multiplication(antidomain(X1),antidomain(X2))=antidomain(addition(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189, c_0_190]), c_0_189]), c_0_132]), c_0_70]), c_0_191]), c_0_142])). 1.70/1.88 cnf(c_0_193,plain,(multiplication(antidomain(addition(X1,X2)),X3)=multiplication(antidomain(X1),multiplication(antidomain(X2),X3))), inference(spm,[status(thm)],[c_0_44, c_0_192])). 1.70/1.88 cnf(c_0_194,plain,(addition(X1,multiplication(antidomain(X2),multiplication(antidomain(X3),X1)))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_193]), c_0_34]), c_0_55]), c_0_49])). 1.70/1.88 cnf(c_0_195,plain,(multiplication(antidomain(antidomain(addition(X1,X2))),addition(X2,X1))=addition(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_57]), c_0_26]), c_0_61]), c_0_26]), c_0_61])). 1.70/1.88 cnf(c_0_196,plain,(addition(X1,addition(X2,multiplication(antidomain(X3),addition(X1,X2))))=addition(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194, c_0_195]), c_0_26])). 1.70/1.88 fof(c_0_197, negated_conjecture, (~(![X4]:![X5]:![X6]:addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6))))=domain(multiplication(X4,addition(domain(X5),domain(X6)))))), inference(assume_negation,[status(cth)],[goals])). 1.70/1.88 cnf(c_0_198,plain,(addition(multiplication(X1,X2),addition(X3,multiplication(X1,X4)))=addition(X3,multiplication(X1,addition(X4,X2)))), inference(spm,[status(thm)],[c_0_56, c_0_23])). 1.70/1.88 cnf(c_0_199,plain,(addition(X1,addition(X2,multiplication(antidomain(X3),addition(X2,X1))))=addition(X2,X1)), inference(spm,[status(thm)],[c_0_137, c_0_196])). 1.70/1.88 fof(c_0_200, negated_conjecture, (addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0))))!=domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])])). 1.70/1.88 fof(c_0_201, plain, (![X5]:domain(X5)=antidomain(antidomain(X5))), inference(variable_rename,[status(thm)],[domain4])). 1.70/1.88 cnf(c_0_202,plain,(addition(X1,multiplication(antidomain(X2),addition(X1,X3)))=addition(X1,multiplication(antidomain(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198, c_0_199]), c_0_26]), c_0_34]), c_0_96]), c_0_34]), c_0_55]), c_0_49])). 1.70/1.88 cnf(c_0_203,plain,(multiplication(antidomain(antidomain(addition(X1,X2))),multiplication(X2,X3))=multiplication(X2,X3)), inference(spm,[status(thm)],[c_0_44, c_0_69])). 1.70/1.88 cnf(c_0_204,negated_conjecture,(addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0))))!=domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_200])). 1.70/1.88 cnf(c_0_205,plain,(domain(X1)=antidomain(antidomain(X1))), inference(split_conjunct,[status(thm)],[c_0_201])). 1.70/1.88 cnf(c_0_206,plain,(addition(X1,multiplication(antidomain(X2),addition(X3,X1)))=addition(X1,multiplication(antidomain(X2),X3))), inference(spm,[status(thm)],[c_0_202, c_0_34])). 1.70/1.88 cnf(c_0_207,plain,(multiplication(antidomain(multiplication(X1,X2)),antidomain(addition(X3,X1)))=antidomain(addition(X3,X1))), inference(spm,[status(thm)],[c_0_127, c_0_203])). 1.70/1.88 cnf(c_0_208,negated_conjecture,(addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk3_0))))))!=antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_204, c_0_205]), c_0_205]), c_0_205]), c_0_205]), c_0_205]), c_0_205]), c_0_205])). 1.70/1.88 cnf(c_0_209,plain,(addition(antidomain(antidomain(X1)),antidomain(addition(X2,X1)))=addition(antidomain(antidomain(X1)),antidomain(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_46]), c_0_38]), c_0_192])). 1.70/1.88 cnf(c_0_210,plain,(antidomain(addition(X1,addition(multiplication(X1,X2),X3)))=antidomain(addition(X3,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_207, c_0_192]), c_0_56])). 1.70/1.88 cnf(c_0_211,negated_conjecture,(addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(antidomain(multiplication(esk1_0,esk3_0))))!=antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208, c_0_141]), c_0_141])). 1.70/1.88 cnf(c_0_212,plain,(antidomain(multiplication(X1,addition(X2,antidomain(antidomain(X3)))))=antidomain(multiplication(X1,addition(X2,X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_188]), c_0_141])). 1.70/1.88 cnf(c_0_213,plain,(addition(antidomain(antidomain(X1)),antidomain(addition(X1,X2)))=addition(antidomain(antidomain(X1)),antidomain(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209, c_0_143]), c_0_210]), c_0_144])). 1.70/1.88 cnf(c_0_214,plain,(antidomain(addition(X1,multiplication(antidomain(X1),X2)))=antidomain(addition(X2,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189, c_0_192]), c_0_192])). 1.70/1.88 cnf(c_0_215,negated_conjecture,(addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(antidomain(multiplication(esk1_0,esk3_0))))!=antidomain(antidomain(multiplication(esk1_0,addition(esk2_0,esk3_0))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211, c_0_212]), c_0_34]), c_0_212]), c_0_34])). 1.70/1.88 cnf(c_0_216,plain,(addition(antidomain(antidomain(X1)),antidomain(X2))=antidomain(multiplication(antidomain(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213, c_0_214]), c_0_209]), c_0_104])). 1.70/1.88 cnf(c_0_217,negated_conjecture,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_215, c_0_216]), c_0_192]), c_0_23])]), ['proof']). 1.70/1.88 % SZS output end Proof 1.70/1.88 % User time : 1.324 s 1.70/1.88 % System time : 0.052 s 1.70/1.88 % Total time : 1.376 s 1.70/1.88 1.82/1.91 EOF