%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE073+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:55:43 EDT 2022
% Result : Theorem 0.51s 61.70s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 209 ( 209 unt; 0 def)
% Number of atoms : 209 ( 208 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 356 ( 50 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
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/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(goals,conjecture,
! [X4,X5,X6] : domain(multiplication(X4,addition(domain(X5),domain(X6)))) = addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_19,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_20,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_21,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_22,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_23,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_24,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_25,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_26,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_34,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]) ).
fof(c_0_35,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_36,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
addition(zero,X1) = X1,
inference(pm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_40,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_41,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,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_34]) ).
cnf(c_0_43,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_45,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_27]) ).
fof(c_0_46,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_47,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_48,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_49,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_51,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_52,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
addition(multiplication(antidomain(X1),X2),multiplication(antidomain(antidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_28]) ).
cnf(c_0_56,plain,
addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(coantidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_28]) ).
cnf(c_0_57,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_58,plain,
addition(multiplication(X1,antidomain(X2)),multiplication(X1,antidomain(antidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_53]) ).
cnf(c_0_59,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_43]),c_0_38]) ).
fof(c_0_60,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_61,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_27]) ).
cnf(c_0_62,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_30]) ).
cnf(c_0_63,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_43]),c_0_30]),c_0_59]) ).
cnf(c_0_64,plain,
addition(X1,multiplication(X1,coantidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_53]),c_0_53]) ).
cnf(c_0_65,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_29]),c_0_38]) ).
fof(c_0_66,plain,
! [X6,X7] : addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7))))) = antidomain(multiplication(X6,antidomain(antidomain(X7)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_67,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_69,plain,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_61]),c_0_53]),c_0_53]) ).
cnf(c_0_70,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
addition(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_27]) ).
cnf(c_0_72,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_29]),c_0_67]) ).
cnf(c_0_74,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_68]),c_0_38]) ).
cnf(c_0_75,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_76,plain,
addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2)) = zero,
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_77,plain,
antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_61]) ).
cnf(c_0_78,plain,
addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_36]),c_0_53]) ).
cnf(c_0_79,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,coantidomain(antidomain(X2))))) = antidomain(multiplication(X1,coantidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_75]),c_0_75]) ).
cnf(c_0_80,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_76]),c_0_30]) ).
cnf(c_0_81,plain,
antidomain(multiplication(X1,coantidomain(antidomain(multiplication(coantidomain(X1),X2))))) = one,
inference(rw,[status(thm)],[c_0_77,c_0_75]) ).
cnf(c_0_82,plain,
multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_29]),c_0_30]) ).
cnf(c_0_83,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_29]),c_0_38]) ).
cnf(c_0_84,plain,
antidomain(multiplication(antidomain(addition(X1,X2)),coantidomain(antidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_74]),c_0_61]) ).
cnf(c_0_85,plain,
antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_29]),c_0_74]),c_0_61]) ).
cnf(c_0_86,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_43]),c_0_67]) ).
cnf(c_0_87,plain,
multiplication(X1,coantidomain(antidomain(multiplication(coantidomain(X1),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_81]),c_0_28]) ).
cnf(c_0_88,plain,
coantidomain(coantidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_75]),c_0_83]),c_0_75]) ).
cnf(c_0_89,plain,
addition(multiplication(antidomain(X1),X2),multiplication(coantidomain(antidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[c_0_55,c_0_75]) ).
cnf(c_0_90,plain,
multiplication(antidomain(addition(X1,X2)),coantidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_84]),c_0_28]) ).
cnf(c_0_91,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_85]),c_0_28]) ).
cnf(c_0_92,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_72,c_0_86]),c_0_74]),c_0_61]) ).
cnf(c_0_93,plain,
addition(antidomain(multiplication(X1,multiplication(X2,X3))),antidomain(multiplication(X1,multiplication(X2,antidomain(antidomain(X3)))))) = antidomain(multiplication(X1,multiplication(X2,antidomain(antidomain(X3))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_52]),c_0_52]) ).
cnf(c_0_94,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_28]),c_0_28]) ).
cnf(c_0_95,plain,
multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_87]),c_0_88]),c_0_38]) ).
cnf(c_0_96,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_89]) ).
cnf(c_0_97,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_78,c_0_90]),c_0_88]),c_0_38]) ).
cnf(c_0_98,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_86,c_0_62]) ).
cnf(c_0_99,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_91]),c_0_30]) ).
cnf(c_0_100,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_83]),c_0_29]),c_0_30]) ).
cnf(c_0_101,plain,
addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_102,plain,
antidomain(multiplication(antidomain(X1),coantidomain(antidomain(multiplication(X1,X2))))) = one,
inference(rw,[status(thm)],[c_0_92,c_0_75]) ).
fof(c_0_103,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_104,plain,
addition(antidomain(multiplication(X1,multiplication(X2,X3))),antidomain(multiplication(X1,multiplication(X2,coantidomain(antidomain(X3)))))) = antidomain(multiplication(X1,multiplication(X2,coantidomain(antidomain(X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_75]),c_0_75]) ).
cnf(c_0_105,plain,
addition(antidomain(X1),antidomain(multiplication(coantidomain(antidomain(X1)),X2))) = antidomain(multiplication(coantidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_27]) ).
cnf(c_0_106,plain,
addition(multiplication(X1,antidomain(X2)),multiplication(X1,coantidomain(antidomain(X2)))) = X1,
inference(rw,[status(thm)],[c_0_58,c_0_75]) ).
cnf(c_0_107,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_80]),c_0_38]) ).
cnf(c_0_108,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_43]),c_0_30]) ).
cnf(c_0_109,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_75]) ).
cnf(c_0_110,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_98]),c_0_63]),c_0_30]),c_0_63]) ).
cnf(c_0_111,plain,
addition(X1,multiplication(coantidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_45]),c_0_28]),c_0_28]) ).
cnf(c_0_112,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_113,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_101]),c_0_30]) ).
cnf(c_0_114,plain,
multiplication(antidomain(X1),coantidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_102]),c_0_28]) ).
cnf(c_0_115,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_116,plain,
addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_117,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_118,plain,
antidomain(multiplication(coantidomain(antidomain(multiplication(X1,coantidomain(antidomain(X2))))),multiplication(X1,X2))) = antidomain(multiplication(X1,coantidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_62]),c_0_27]),c_0_105]) ).
cnf(c_0_119,plain,
multiplication(antidomain(addition(X1,antidomain(X2))),coantidomain(antidomain(X2))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_38]) ).
cnf(c_0_120,plain,
multiplication(antidomain(X1),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_52,c_0_108]) ).
cnf(c_0_121,plain,
multiplication(antidomain(X1),antidomain(addition(antidomain(X1),X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_75]),c_0_88]) ).
cnf(c_0_122,plain,
addition(antidomain(X1),antidomain(coantidomain(antidomain(X1)))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_94,c_0_110]) ).
cnf(c_0_123,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_43]),c_0_38]) ).
cnf(c_0_124,plain,
addition(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_27]) ).
cnf(c_0_125,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_106]),c_0_52]) ).
cnf(c_0_126,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_114]),c_0_88]),c_0_38]) ).
cnf(c_0_127,plain,
multiplication(coantidomain(X1),multiplication(X2,coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)))) = multiplication(X2,coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_115]),c_0_30]) ).
cnf(c_0_128,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_29]),c_0_117]),c_0_44]),c_0_45]) ).
cnf(c_0_129,plain,
antidomain(multiplication(antidomain(addition(X1,antidomain(X2))),X2)) = coantidomain(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_118,c_0_119]),c_0_75]),c_0_88]),c_0_120]),c_0_75]) ).
cnf(c_0_130,plain,
addition(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_94,c_0_97]) ).
cnf(c_0_131,plain,
multiplication(antidomain(X1),antidomain(addition(X2,antidomain(X1)))) = zero,
inference(pm,[status(thm)],[c_0_121,c_0_27]) ).
cnf(c_0_132,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_43]),c_0_117]),c_0_44]),c_0_45]) ).
cnf(c_0_133,plain,
multiplication(antidomain(antidomain(X1)),antidomain(coantidomain(antidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_122]),c_0_43]),c_0_38]) ).
cnf(c_0_134,plain,
addition(multiplication(X1,multiplication(X2,coantidomain(X3))),multiplication(X1,multiplication(X2,coantidomain(coantidomain(X3))))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_78]) ).
cnf(c_0_135,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_123]),c_0_124]) ).
cnf(c_0_136,plain,
multiplication(coantidomain(X1),multiplication(antidomain(X2),coantidomain(X1))) = multiplication(antidomain(X2),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_125]),c_0_100]),c_0_30]),c_0_100]) ).
cnf(c_0_137,plain,
multiplication(coantidomain(antidomain(multiplication(X1,X2))),antidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_126]),c_0_75]) ).
cnf(c_0_138,plain,
multiplication(coantidomain(multiplication(X1,X2)),coantidomain(X2)) = coantidomain(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_53]),c_0_53]) ).
cnf(c_0_139,plain,
antidomain(addition(X1,multiplication(coantidomain(antidomain(X1)),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_129,c_0_130]),c_0_75]),c_0_54]),c_0_62]),c_0_75]),c_0_88]) ).
cnf(c_0_140,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(addition(X2,antidomain(X1)))) = antidomain(addition(X2,antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_131]),c_0_38]) ).
cnf(c_0_141,plain,
addition(multiplication(X1,coantidomain(multiplication(X2,X3))),multiplication(X1,coantidomain(multiplication(coantidomain(coantidomain(X2)),X3)))) = multiplication(X1,coantidomain(multiplication(coantidomain(coantidomain(X2)),X3))),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_142,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_132]),c_0_52]),c_0_53]) ).
cnf(c_0_143,plain,
antidomain(coantidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_133]),c_0_63]),c_0_99]),c_0_38]) ).
cnf(c_0_144,plain,
multiplication(antidomain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),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(spm,[status(thm)],[c_0_134,c_0_96]),c_0_135]),c_0_100]),c_0_30]),c_0_135]),c_0_100]),c_0_136]) ).
cnf(c_0_145,plain,
multiplication(coantidomain(X1),coantidomain(coantidomain(multiplication(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_135]),c_0_100]),c_0_135]) ).
cnf(c_0_146,plain,
multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_113]),c_0_38]) ).
cnf(c_0_147,plain,
antidomain(addition(X1,antidomain(addition(X2,antidomain(X1))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_148,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_83]) ).
cnf(c_0_149,plain,
multiplication(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(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_141,c_0_62]),c_0_135]),c_0_100]),c_0_64]),c_0_135]),c_0_100]) ).
cnf(c_0_150,plain,
multiplication(antidomain(addition(coantidomain(antidomain(X1)),X2)),antidomain(X1)) = antidomain(addition(coantidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_80]),c_0_30]) ).
cnf(c_0_151,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_31,c_0_27]),c_0_31]) ).
fof(c_0_152,negated_conjecture,
~ ! [X4,X5,X6] : domain(multiplication(X4,addition(domain(X5),domain(X6)))) = addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6)))),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_153,plain,
multiplication(X1,multiplication(X2,coantidomain(coantidomain(multiplication(X1,X2))))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_83]) ).
cnf(c_0_154,plain,
multiplication(antidomain(X1),coantidomain(coantidomain(multiplication(X2,antidomain(X1))))) = coantidomain(coantidomain(multiplication(X2,antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_142]),c_0_143]),c_0_30]),c_0_143]),c_0_144]) ).
cnf(c_0_155,plain,
multiplication(coantidomain(addition(X1,X2)),coantidomain(coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_100]) ).
cnf(c_0_156,plain,
addition(multiplication(antidomain(multiplication(X1,X2)),X3),multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3)) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3),
inference(spm,[status(thm)],[c_0_49,c_0_72]) ).
cnf(c_0_157,plain,
multiplication(coantidomain(multiplication(X1,antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_142]),c_0_100]),c_0_38]) ).
cnf(c_0_158,plain,
antidomain(addition(X1,addition(X2,coantidomain(antidomain(X1))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_130]),c_0_75]),c_0_31]) ).
cnf(c_0_159,plain,
coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)) = coantidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_148]),c_0_149]) ).
cnf(c_0_160,plain,
multiplication(antidomain(addition(coantidomain(antidomain(X1)),X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_150]),c_0_88]) ).
cnf(c_0_161,plain,
addition(X1,addition(X2,multiplication(antidomain(X3),X1))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_151,c_0_94]) ).
fof(c_0_162,negated_conjecture,
domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0)))) != addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0)))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])]) ).
fof(c_0_163,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_164,plain,
multiplication(X1,coantidomain(coantidomain(multiplication(X1,antidomain(X2))))) = multiplication(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_165,plain,
multiplication(coantidomain(X1),coantidomain(coantidomain(multiplication(X1,antidomain(X2))))) = zero,
inference(spm,[status(thm)],[c_0_155,c_0_106]) ).
cnf(c_0_166,plain,
addition(multiplication(antidomain(multiplication(X1,X2)),X3),multiplication(antidomain(multiplication(X1,coantidomain(antidomain(X2)))),X3)) = multiplication(antidomain(multiplication(X1,coantidomain(antidomain(X2)))),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_75]),c_0_75]) ).
cnf(c_0_167,plain,
multiplication(coantidomain(antidomain(addition(coantidomain(antidomain(X1)),X2))),X1) = X1,
inference(spm,[status(thm)],[c_0_157,c_0_150]) ).
cnf(c_0_168,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(pm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_169,plain,
antidomain(addition(X1,addition(coantidomain(antidomain(X1)),X2))) = antidomain(addition(X1,X2)),
inference(pm,[status(thm)],[c_0_158,c_0_27]) ).
cnf(c_0_170,plain,
addition(X1,addition(X2,multiplication(X1,antidomain(X3)))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_151,c_0_69]) ).
cnf(c_0_171,plain,
multiplication(coantidomain(X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X2,coantidomain(multiplication(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_159]),c_0_159]) ).
cnf(c_0_172,plain,
multiplication(antidomain(addition(X1,coantidomain(antidomain(X2)))),X2) = zero,
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_173,plain,
addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
inference(pm,[status(thm)],[c_0_130,c_0_27]) ).
cnf(c_0_174,negated_conjecture,
domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0)))) != addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0)))),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_175,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_176,plain,
coantidomain(coantidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_164]),c_0_165]),c_0_30]) ).
cnf(c_0_177,plain,
addition(antidomain(multiplication(X1,X2)),multiplication(antidomain(multiplication(X1,coantidomain(antidomain(X2)))),antidomain(multiplication(X1,multiplication(X2,X3))))) = multiplication(antidomain(multiplication(X1,coantidomain(antidomain(X2)))),antidomain(multiplication(X1,multiplication(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_126]),c_0_52]),c_0_52]) ).
cnf(c_0_178,plain,
multiplication(antidomain(multiplication(X1,coantidomain(antidomain(X2)))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_83]),c_0_88]),c_0_94]),c_0_88]) ).
cnf(c_0_179,plain,
antidomain(addition(coantidomain(antidomain(X1)),X2)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_167]),c_0_31]),c_0_168]),c_0_169]) ).
cnf(c_0_180,plain,
addition(coantidomain(antidomain(X1)),multiplication(antidomain(X1),antidomain(X2))) = addition(coantidomain(antidomain(X1)),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_89]),c_0_27]) ).
cnf(c_0_181,plain,
multiplication(coantidomain(antidomain(addition(X1,coantidomain(antidomain(X2))))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_44]),c_0_53]),c_0_44]),c_0_53]) ).
cnf(c_0_182,plain,
antidomain(addition(X1,addition(X2,coantidomain(antidomain(X2))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_173]),c_0_75]),c_0_31]) ).
cnf(c_0_183,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))) != addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(esk1_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_174,c_0_175]),c_0_175]),c_0_175]),c_0_175]),c_0_175]),c_0_175]),c_0_175]) ).
cnf(c_0_184,plain,
antidomain(multiplication(antidomain(X1),antidomain(X2))) = coantidomain(multiplication(antidomain(X1),antidomain(X2))),
inference(spm,[status(thm)],[c_0_135,c_0_176]) ).
cnf(c_0_185,plain,
antidomain(multiplication(X1,coantidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
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_177,c_0_62]),c_0_143]),c_0_178]),c_0_27]),c_0_79]),c_0_143]),c_0_178]) ).
cnf(c_0_186,plain,
multiplication(antidomain(X1),coantidomain(antidomain(multiplication(antidomain(X2),X1)))) = zero,
inference(spm,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_187,plain,
antidomain(addition(X1,multiplication(antidomain(X1),antidomain(X2)))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_179]) ).
cnf(c_0_188,plain,
antidomain(addition(X1,coantidomain(antidomain(X2)))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_181]),c_0_31]),c_0_27]),c_0_182]) ).
cnf(c_0_189,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk3_0)))))) != antidomain(antidomain(addition(multiplication(esk1_0,antidomain(antidomain(esk2_0))),multiplication(esk1_0,antidomain(antidomain(esk3_0)))))),
inference(rw,[status(thm)],[c_0_183,c_0_54]) ).
cnf(c_0_190,plain,
multiplication(coantidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_80]),c_0_38]) ).
cnf(c_0_191,plain,
coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X2)))) = antidomain(multiplication(antidomain(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_75]),c_0_185]) ).
cnf(c_0_192,plain,
multiplication(coantidomain(antidomain(X1)),coantidomain(antidomain(multiplication(antidomain(X2),X1)))) = coantidomain(antidomain(multiplication(antidomain(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_186]),c_0_38]) ).
cnf(c_0_193,plain,
multiplication(antidomain(X1),coantidomain(antidomain(multiplication(antidomain(X1),X2)))) = coantidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_87]),c_0_88]),c_0_30]),c_0_88]) ).
cnf(c_0_194,plain,
antidomain(addition(X1,multiplication(antidomain(X1),coantidomain(antidomain(X2))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_75]),c_0_188]) ).
cnf(c_0_195,negated_conjecture,
addition(coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))),coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk3_0)))))) != coantidomain(antidomain(addition(multiplication(esk1_0,coantidomain(antidomain(esk2_0))),multiplication(esk1_0,coantidomain(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_189,c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_75]) ).
cnf(c_0_196,plain,
addition(coantidomain(antidomain(X1)),multiplication(antidomain(X1),coantidomain(antidomain(addition(X1,X2))))) = coantidomain(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_106,c_0_190]),c_0_179]),c_0_144]),c_0_27]),c_0_179]) ).
cnf(c_0_197,plain,
multiplication(antidomain(X1),coantidomain(antidomain(X2))) = coantidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_191]),c_0_52]),c_0_192]),c_0_193]) ).
cnf(c_0_198,plain,
antidomain(addition(X1,multiplication(antidomain(X1),coantidomain(X2)))) = antidomain(addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_135]),c_0_100]) ).
cnf(c_0_199,plain,
antidomain(addition(X1,multiplication(X2,coantidomain(antidomain(X3))))) = antidomain(addition(X1,multiplication(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_185]),c_0_188]) ).
cnf(c_0_200,negated_conjecture,
coantidomain(antidomain(addition(multiplication(esk1_0,coantidomain(antidomain(esk2_0))),multiplication(esk1_0,coantidomain(antidomain(esk3_0)))))) != addition(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),coantidomain(antidomain(multiplication(esk1_0,esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_185]),c_0_185]) ).
cnf(c_0_201,plain,
antidomain(addition(multiplication(X1,coantidomain(antidomain(X2))),X3)) = antidomain(addition(multiplication(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_185]),c_0_179]) ).
cnf(c_0_202,plain,
addition(coantidomain(antidomain(X1)),coantidomain(antidomain(multiplication(antidomain(X1),X2)))) = coantidomain(antidomain(addition(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_54]),c_0_43]),c_0_38]) ).
cnf(c_0_203,plain,
antidomain(addition(X1,multiplication(antidomain(X1),X2))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_188]) ).
cnf(c_0_204,negated_conjecture,
coantidomain(antidomain(addition(multiplication(esk1_0,esk2_0),multiplication(esk1_0,coantidomain(antidomain(esk3_0)))))) != addition(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),coantidomain(antidomain(multiplication(esk1_0,esk3_0)))),
inference(rw,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_205,plain,
addition(coantidomain(antidomain(X1)),antidomain(X2)) = coantidomain(antidomain(addition(X1,antidomain(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_202,c_0_164]),c_0_184]),c_0_176]),c_0_180]),c_0_176]),c_0_203]) ).
cnf(c_0_206,negated_conjecture,
addition(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),coantidomain(antidomain(multiplication(esk1_0,esk3_0)))) != coantidomain(antidomain(addition(multiplication(esk1_0,esk2_0),multiplication(esk1_0,esk3_0)))),
inference(rw,[status(thm)],[c_0_204,c_0_199]) ).
cnf(c_0_207,plain,
addition(coantidomain(antidomain(X1)),coantidomain(antidomain(X2))) = coantidomain(antidomain(addition(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_75]),c_0_188]) ).
cnf(c_0_208,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE073+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 10:06:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.33/23.39 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.44/46.41 eprover: CPU time limit exceeded, terminating
% 0.44/46.41 eprover: CPU time limit exceeded, terminating
% 0.44/46.42 eprover: CPU time limit exceeded, terminating
% 0.44/46.42 eprover: CPU time limit exceeded, terminating
% 0.51/61.70 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.51/61.70
% 0.51/61.70 # Failure: Resource limit exceeded (time)
% 0.51/61.70 # OLD status Res
% 0.51/61.70 # Preprocessing time : 0.015 s
% 0.51/61.70 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.51/61.70
% 0.51/61.70 # Failure: Resource limit exceeded (time)
% 0.51/61.70 # OLD status Res
% 0.51/61.70 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.51/61.70 # Preprocessing time : 0.014 s
% 0.51/61.70 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.51/61.70 # Preprocessing time : 0.014 s
% 0.51/61.70
% 0.51/61.70 # Proof found!
% 0.51/61.70 # SZS status Theorem
% 0.51/61.70 # SZS output start CNFRefutation
% See solution above
% 0.51/61.70 # Proof object total steps : 209
% 0.51/61.70 # Proof object clause steps : 170
% 0.51/61.70 # Proof object formula steps : 39
% 0.51/61.70 # Proof object conjectures : 11
% 0.51/61.70 # Proof object clause conjectures : 8
% 0.51/61.70 # Proof object formula conjectures : 3
% 0.51/61.70 # Proof object initial clauses used : 19
% 0.51/61.70 # Proof object initial formulas used : 19
% 0.51/61.70 # Proof object generating inferences : 131
% 0.51/61.70 # Proof object simplifying inferences : 222
% 0.51/61.70 # Training examples: 0 positive, 0 negative
% 0.51/61.70 # Parsed axioms : 21
% 0.51/61.70 # Removed by relevancy pruning/SinE : 0
% 0.51/61.70 # Initial clauses : 22
% 0.51/61.70 # Removed in clause preprocessing : 2
% 0.51/61.70 # Initial clauses in saturation : 20
% 0.51/61.70 # Processed clauses : 12595
% 0.51/61.70 # ...of these trivial : 5590
% 0.51/61.70 # ...subsumed : 4846
% 0.51/61.70 # ...remaining for further processing : 2159
% 0.51/61.70 # Other redundant clauses eliminated : 0
% 0.51/61.70 # Clauses deleted for lack of memory : 450708
% 0.51/61.70 # Backward-subsumed : 2
% 0.51/61.70 # Backward-rewritten : 709
% 0.51/61.70 # Generated clauses : 1088403
% 0.51/61.70 # ...of the previous two non-trivial : 678978
% 0.51/61.70 # Contextual simplify-reflections : 0
% 0.51/61.70 # Paramodulations : 1088402
% 0.51/61.70 # Factorizations : 0
% 0.51/61.70 # Equation resolutions : 1
% 0.51/61.70 # Current number of processed clauses : 1448
% 0.51/61.70 # Positive orientable unit clauses : 755
% 0.51/61.70 # Positive unorientable unit clauses: 10
% 0.51/61.70 # Negative unit clauses : 0
% 0.51/61.70 # Non-unit-clauses : 683
% 0.51/61.70 # Current number of unprocessed clauses: 59466
% 0.51/61.70 # ...number of literals in the above : 89247
% 0.51/61.70 # Current number of archived formulas : 0
% 0.51/61.70 # Current number of archived clauses : 713
% 0.51/61.70 # Clause-clause subsumption calls (NU) : 94453
% 0.51/61.70 # Rec. Clause-clause subsumption calls : 93988
% 0.51/61.70 # Non-unit clause-clause subsumptions : 1786
% 0.51/61.70 # Unit Clause-clause subsumption calls : 3150
% 0.51/61.70 # Rewrite failures with RHS unbound : 118
% 0.51/61.70 # BW rewrite match attempts : 11577
% 0.51/61.70 # BW rewrite match successes : 770
% 0.51/61.70 # Condensation attempts : 0
% 0.51/61.70 # Condensation successes : 0
% 0.51/61.70 # Termbank termtop insertions : 28841870
% 0.51/61.70
% 0.51/61.70 # -------------------------------------------------
% 0.51/61.70 # User time : 14.493 s
% 0.51/61.70 # System time : 0.151 s
% 0.51/61.70 # Total time : 14.644 s
% 0.51/61.70 # Maximum resident set size: 182148 pages
% 0.51/69.43 eprover: CPU time limit exceeded, terminating
% 0.51/69.43 eprover: CPU time limit exceeded, terminating
% 0.51/69.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.44 eprover: No such file or directory
% 0.51/69.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.45 eprover: No such file or directory
% 0.51/69.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.45 eprover: No such file or directory
% 0.51/69.45 eprover: CPU time limit exceeded, terminating
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.51 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.51 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51 eprover: No such file or directory
% 0.51/69.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.52 eprover: No such file or directory
% 0.51/69.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.52 eprover: No such file or directory
% 0.51/69.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.53 eprover: No such file or directory
% 0.51/69.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.53 eprover: No such file or directory
%------------------------------------------------------------------------------