%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE073+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:47 PM UTC 2026
% Result : Theorem 256.77s 33.69s
% Output : CNFRefutation 256.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 19
% Syntax : Number of formulae : 279 ( 279 unt; 0 def)
% Number of atoms : 279 ( 278 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 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 : 515 ( 78 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
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/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
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) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_19,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_20,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_21,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_22,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_23,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_26,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_27,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_28,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_33,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_34,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_35,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_38,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_39,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_40,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_41,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24]) ).
cnf(c_0_44,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_45,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_46,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_47,plain,
! [X30,X31] : addition(antidomain(multiplication(X30,X31)),antidomain(multiplication(X30,antidomain(antidomain(X31))))) = antidomain(multiplication(X30,antidomain(antidomain(X31)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_48,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_49,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
multiplication(antidomain(antidomain(X1)),addition(X1,one)) = addition(X1,antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_24]) ).
cnf(c_0_51,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_52,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,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_47]) ).
cnf(c_0_54,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_30]) ).
cnf(c_0_55,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_24]) ).
cnf(c_0_56,plain,
multiplication(antidomain(antidomain(X1)),addition(one,X1)) = addition(X1,antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_50,c_0_24]) ).
cnf(c_0_57,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_51]),c_0_24]) ).
cnf(c_0_58,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_52]),c_0_30]) ).
cnf(c_0_59,plain,
antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_41,c_0_51]) ).
cnf(c_0_61,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_36]) ).
cnf(c_0_62,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_52]),c_0_23]) ).
cnf(c_0_63,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_51]),c_0_36]) ).
fof(c_0_64,plain,
! [X35,X36] : addition(coantidomain(multiplication(X35,X36)),coantidomain(multiplication(coantidomain(coantidomain(X35)),X36))) = coantidomain(multiplication(coantidomain(coantidomain(X35)),X36)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_65,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_66,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_59]),c_0_39]) ).
cnf(c_0_67,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_23]) ).
cnf(c_0_68,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_55]) ).
cnf(c_0_69,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_51]),c_0_39]),c_0_63]) ).
cnf(c_0_70,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]) ).
cnf(c_0_71,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_65]),c_0_30]) ).
cnf(c_0_72,plain,
multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_66]),c_0_30]) ).
cnf(c_0_73,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_38]),c_0_36]),c_0_44]) ).
cnf(c_0_74,plain,
addition(antidomain(antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_24]) ).
fof(c_0_75,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_76,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23]) ).
cnf(c_0_77,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_39]) ).
fof(c_0_78,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_79,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_49]),c_0_29]) ).
cnf(c_0_80,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_29]),c_0_71]),c_0_57]) ).
cnf(c_0_81,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_38]),c_0_36]),c_0_73]) ).
cnf(c_0_82,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_74]),c_0_39]) ).
cnf(c_0_83,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_84,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_29]) ).
cnf(c_0_85,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_86,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_79]),c_0_30]) ).
cnf(c_0_87,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_80]),c_0_36]) ).
cnf(c_0_88,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_69]),c_0_82]) ).
cnf(c_0_89,plain,
multiplication(antidomain(X1),multiplication(antidomain(antidomain(X1)),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_90,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_38]),c_0_39]) ).
cnf(c_0_91,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_92,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,plain,
antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_79]),c_0_54]),c_0_55]) ).
cnf(c_0_94,plain,
multiplication(antidomain(X1),addition(one,multiplication(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_89]),c_0_23]),c_0_24]) ).
cnf(c_0_95,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_49]),c_0_52]) ).
cnf(c_0_97,plain,
multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_92]),c_0_30]) ).
cnf(c_0_98,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_88]),c_0_88]) ).
cnf(c_0_99,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_41]) ).
cnf(c_0_100,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_93]),c_0_39]) ).
cnf(c_0_101,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_102,plain,
multiplication(antidomain(addition(X1,X2)),addition(one,X2)) = antidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,plain,
multiplication(X1,addition(coantidomain(addition(X1,X2)),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_96]),c_0_30]) ).
cnf(c_0_104,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_38]),c_0_39]),c_0_98]) ).
cnf(c_0_105,plain,
addition(antidomain(multiplication(X1,X2)),addition(X3,antidomain(multiplication(X1,antidomain(antidomain(X2)))))) = addition(X3,antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(spm,[status(thm)],[c_0_99,c_0_53]) ).
cnf(c_0_106,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2))) = zero,
inference(spm,[status(thm)],[c_0_100,c_0_91]) ).
cnf(c_0_107,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)) = antidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_101]),c_0_102]) ).
cnf(c_0_108,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_91]),c_0_29]) ).
cnf(c_0_109,plain,
multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_51]),c_0_36]) ).
cnf(c_0_110,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_104,c_0_73]) ).
cnf(c_0_111,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_52]),c_0_30]) ).
cnf(c_0_112,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_79,c_0_28]) ).
cnf(c_0_113,plain,
addition(antidomain(antidomain(multiplication(X1,X2))),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_105]),c_0_55]) ).
cnf(c_0_114,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_73]),c_0_24]) ).
cnf(c_0_115,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_53]),c_0_29]) ).
cnf(c_0_116,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_108]),c_0_85]) ).
cnf(c_0_117,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_24]) ).
cnf(c_0_118,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_87,c_0_73]) ).
fof(c_0_119,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_120,plain,
multiplication(X1,antidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[c_0_109,c_0_88]) ).
cnf(c_0_121,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_43,c_0_110]),c_0_24]),c_0_55]),c_0_36]),c_0_24]) ).
cnf(c_0_122,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_38]),c_0_39]) ).
cnf(c_0_123,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_38]),c_0_39]) ).
cnf(c_0_124,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_52]),c_0_23]) ).
cnf(c_0_125,plain,
addition(antidomain(X1),antidomain(antidomain(multiplication(X1,addition(X2,antidomain(X2)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_54]),c_0_36]),c_0_24]) ).
cnf(c_0_126,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(X2,X3)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_54]),c_0_39]) ).
cnf(c_0_127,plain,
multiplication(antidomain(addition(X1,X2)),addition(antidomain(antidomain(X1)),X3)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_100]),c_0_30]) ).
cnf(c_0_128,plain,
antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_89]),c_0_54]),c_0_55]) ).
cnf(c_0_129,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_38]),c_0_39]) ).
cnf(c_0_130,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_83]),c_0_24]) ).
cnf(c_0_131,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[c_0_118,c_0_88]) ).
cnf(c_0_132,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_133,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_88]),c_0_98]),c_0_122]) ).
cnf(c_0_134,plain,
multiplication(X1,coantidomain(coantidomain(addition(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_109,c_0_91]) ).
cnf(c_0_135,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),multiplication(X1,X3))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_123]),c_0_85]),c_0_83]) ).
cnf(c_0_136,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(addition(X2,coantidomain(X1))))))) = antidomain(multiplication(X1,antidomain(antidomain(addition(X2,coantidomain(X1)))))),
inference(spm,[status(thm)],[c_0_53,c_0_124]) ).
cnf(c_0_137,plain,
multiplication(antidomain(antidomain(multiplication(X1,addition(X2,antidomain(X2))))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_125]),c_0_39]) ).
cnf(c_0_138,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_107]),c_0_73]),c_0_24]) ).
cnf(c_0_139,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_53,c_0_114]),c_0_54]),c_0_36]),c_0_54]),c_0_36]),c_0_24]) ).
cnf(c_0_140,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,addition(X3,X2))) = multiplication(antidomain(addition(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_67,c_0_99]) ).
cnf(c_0_141,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_35,c_0_79]),c_0_30]) ).
cnf(c_0_142,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_127,c_0_38]),c_0_36]),c_0_73]) ).
cnf(c_0_143,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_128]),c_0_39]) ).
cnf(c_0_144,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(X2,one),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_124]),c_0_41]) ).
cnf(c_0_145,plain,
addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_146,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_35,c_0_129]),c_0_24]),c_0_43]) ).
cnf(c_0_147,plain,
multiplication(addition(one,multiplication(X1,antidomain(X2))),antidomain(antidomain(X2))) = antidomain(antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]),c_0_23]),c_0_133]),c_0_73]) ).
cnf(c_0_148,plain,
multiplication(X1,antidomain(coantidomain(addition(X2,X1)))) = X1,
inference(rw,[status(thm)],[c_0_134,c_0_88]) ).
cnf(c_0_149,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(antidomain(X3),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_95]),c_0_73]) ).
cnf(c_0_150,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_151,plain,
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(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_136,c_0_137]),c_0_133]),c_0_73]),c_0_138]),c_0_54]),c_0_36]),c_0_73]),c_0_139]),c_0_133]),c_0_73]),c_0_138]),c_0_54]),c_0_36]),c_0_73]) ).
cnf(c_0_152,plain,
multiplication(antidomain(addition(X1,X2)),addition(X3,X2)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_153,plain,
addition(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_142]),c_0_24]),c_0_55]),c_0_39]) ).
cnf(c_0_154,plain,
multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X3)) = multiplication(antidomain(X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_143]),c_0_30]) ).
cnf(c_0_155,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X1,X2)))) = one,
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_144,c_0_142]),c_0_133]),c_0_24]),c_0_38]),c_0_24]),c_0_55]),c_0_24]),c_0_55]),c_0_133]),c_0_39]) ).
cnf(c_0_156,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_91]),c_0_41]),c_0_41]) ).
cnf(c_0_157,plain,
addition(X1,addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(one,X2),X1),X3),
inference(spm,[status(thm)],[c_0_145,c_0_39]) ).
cnf(c_0_158,plain,
addition(X1,multiplication(antidomain(X2),addition(X1,one))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_146]),c_0_41]),c_0_43]),c_0_41]),c_0_42]),c_0_24]),c_0_55]),c_0_39]) ).
cnf(c_0_159,plain,
multiplication(addition(one,X1),coantidomain(addition(X2,X1))) = coantidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_98]),c_0_98]) ).
cnf(c_0_160,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(antidomain(X3),X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_149]),c_0_54]),c_0_39]) ).
cnf(c_0_161,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_162,plain,
addition(multiplication(X1,X2),multiplication(addition(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X4)),multiplication(X3,X4)),
inference(spm,[status(thm)],[c_0_150,c_0_28]) ).
cnf(c_0_163,plain,
antidomain(multiplication(antidomain(addition(X1,antidomain(X2))),X2)) = antidomain(antidomain(addition(X1,antidomain(X2)))),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_164,plain,
addition(antidomain(X1),antidomain(multiplication(addition(X2,one),X1))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_153,c_0_117]) ).
cnf(c_0_165,plain,
multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_43,c_0_117]) ).
cnf(c_0_166,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_38]),c_0_36]),c_0_73]) ).
cnf(c_0_167,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_83,c_0_44]) ).
cnf(c_0_168,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X2,addition(X1,X3))))) = one,
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_169,plain,
addition(X1,addition(multiplication(antidomain(X2),X1),X3)) = addition(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_42]),c_0_36]),c_0_55]),c_0_39]) ).
cnf(c_0_170,plain,
multiplication(antidomain(X1),coantidomain(addition(antidomain(antidomain(X1)),X2))) = coantidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_101]),c_0_159]) ).
cnf(c_0_171,plain,
antidomain(addition(X1,antidomain(multiplication(antidomain(X2),X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_107]),c_0_73]),c_0_24]) ).
cnf(c_0_172,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,addition(X2,X3))) = multiplication(antidomain(addition(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_67,c_0_161]) ).
cnf(c_0_173,plain,
addition(X1,multiplication(addition(X1,X2),antidomain(X3))) = addition(X1,multiplication(X2,antidomain(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_55]),c_0_36]),c_0_36]) ).
cnf(c_0_174,plain,
antidomain(multiplication(antidomain(antidomain(X1)),multiplication(addition(X2,one),X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_73]) ).
cnf(c_0_175,plain,
addition(multiplication(X1,X2),multiplication(X2,addition(X2,one))) = multiplication(addition(X1,addition(X2,one)),X2),
inference(spm,[status(thm)],[c_0_28,c_0_165]) ).
cnf(c_0_176,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_177,plain,
addition(antidomain(multiplication(antidomain(X1),X2)),antidomain(antidomain(addition(X2,X3)))) = one,
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_178,plain,
addition(antidomain(X1),coantidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_170]),c_0_24]),c_0_57]),c_0_36]) ).
cnf(c_0_179,plain,
antidomain(multiplication(X1,addition(X2,antidomain(multiplication(antidomain(X3),X2))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_171]),c_0_23]) ).
cnf(c_0_180,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_30]) ).
cnf(c_0_181,plain,
multiplication(antidomain(addition(X1,X2)),addition(X2,addition(X3,X1))) = multiplication(antidomain(addition(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_67,c_0_161]) ).
cnf(c_0_182,plain,
multiplication(antidomain(addition(X1,X2)),addition(X2,X3)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_172,c_0_141]) ).
cnf(c_0_183,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_28,c_0_83]) ).
cnf(c_0_184,plain,
addition(antidomain(X1),multiplication(antidomain(antidomain(X1)),antidomain(X2))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_38]),c_0_39]) ).
cnf(c_0_185,plain,
antidomain(multiplication(antidomain(X1),multiplication(addition(X2,one),antidomain(X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_174,c_0_73]) ).
cnf(c_0_186,plain,
addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_107]),c_0_24]),c_0_55]),c_0_39]) ).
cnf(c_0_187,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_24]),c_0_55]),c_0_36]),c_0_24]),c_0_55]),c_0_24]),c_0_55]),c_0_39]) ).
cnf(c_0_188,plain,
addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_176]),c_0_133]),c_0_24]),c_0_38]),c_0_24]),c_0_55]),c_0_24]),c_0_55]),c_0_133]),c_0_24]),c_0_39]) ).
cnf(c_0_189,plain,
multiplication(antidomain(X1),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_83,c_0_129]) ).
cnf(c_0_190,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X2),antidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_73]),c_0_24]) ).
cnf(c_0_191,plain,
antidomain(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_192,plain,
multiplication(antidomain(addition(X1,X2)),addition(X3,X1)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_193,plain,
multiplication(addition(X1,multiplication(antidomain(multiplication(X2,X3)),X2)),X3) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_29]),c_0_23]) ).
cnf(c_0_194,plain,
addition(antidomain(antidomain(X1)),multiplication(antidomain(X1),antidomain(X2))) = addition(antidomain(antidomain(X1)),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_73]) ).
cnf(c_0_195,plain,
addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_196,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_73]) ).
cnf(c_0_197,plain,
multiplication(antidomain(multiplication(antidomain(X1),antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_190]),c_0_39]),c_0_133]),c_0_73]) ).
cnf(c_0_198,plain,
antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),antidomain(antidomain(X2)))) = antidomain(multiplication(antidomain(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_191]),c_0_73]) ).
cnf(c_0_199,plain,
antidomain(multiplication(antidomain(addition(antidomain(X1),X2)),X1)) = antidomain(antidomain(addition(antidomain(X1),X2))),
inference(spm,[status(thm)],[c_0_151,c_0_192]) ).
cnf(c_0_200,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(antidomain(X1)),X2))) = antidomain(multiplication(antidomain(antidomain(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_166]),c_0_24]),c_0_55]),c_0_36]),c_0_24]),c_0_55]),c_0_24]),c_0_55]),c_0_39]) ).
cnf(c_0_201,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))),antidomain(X2)) = antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_190]),c_0_36]) ).
cnf(c_0_202,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_193,c_0_194]),c_0_24]),c_0_195]) ).
cnf(c_0_203,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_196]),c_0_39]),c_0_133]),c_0_73]) ).
cnf(c_0_204,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),antidomain(X2)) = antidomain(X2),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_205,plain,
antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X1)) = antidomain(multiplication(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_73]) ).
cnf(c_0_206,plain,
antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_207,plain,
multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1)) = multiplication(antidomain(X2),X1),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_208,plain,
antidomain(multiplication(antidomain(antidomain(X1)),antidomain(X2))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_83]),c_0_207]) ).
cnf(c_0_209,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),antidomain(X1)) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_196]),c_0_36]) ).
cnf(c_0_210,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_29]),c_0_85]) ).
cnf(c_0_211,plain,
multiplication(antidomain(antidomain(X1)),antidomain(X2)) = antidomain(antidomain(multiplication(antidomain(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_208]),c_0_209]) ).
cnf(c_0_212,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_210,c_0_83]) ).
cnf(c_0_213,plain,
multiplication(antidomain(X1),addition(X1,one)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_23]) ).
cnf(c_0_214,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(antidomain(antidomain(X2)),X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_106]),c_0_85]) ).
cnf(c_0_215,plain,
addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1)))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[c_0_184,c_0_211]) ).
cnf(c_0_216,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,X2)) = zero,
inference(spm,[status(thm)],[c_0_212,c_0_44]) ).
cnf(c_0_217,plain,
multiplication(antidomain(X1),addition(one,X1)) = antidomain(X1),
inference(spm,[status(thm)],[c_0_213,c_0_24]) ).
cnf(c_0_218,plain,
multiplication(antidomain(addition(X1,X2)),addition(X2,antidomain(antidomain(X2)))) = zero,
inference(spm,[status(thm)],[c_0_214,c_0_56]) ).
cnf(c_0_219,plain,
antidomain(multiplication(X1,antidomain(antidomain(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_215,c_0_216]),c_0_54]),c_0_48]),c_0_23]),c_0_53]) ).
cnf(c_0_220,plain,
antidomain(addition(one,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_49]),c_0_29]) ).
cnf(c_0_221,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(addition(X2,antidomain(antidomain(X2)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_218]),c_0_54]),c_0_39]) ).
cnf(c_0_222,plain,
antidomain(addition(X1,one)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_91]),c_0_29]) ).
cnf(c_0_223,plain,
antidomain(multiplication(antidomain(antidomain(X1)),X2)) = antidomain(multiplication(antidomain(antidomain(X2)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_211]),c_0_73]) ).
cnf(c_0_224,plain,
multiplication(antidomain(addition(X1,antidomain(X2))),antidomain(antidomain(X2))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_38]),c_0_36]) ).
cnf(c_0_225,plain,
addition(antidomain(antidomain(X1)),antidomain(addition(antidomain(X1),X2))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_186,c_0_73]) ).
cnf(c_0_226,plain,
multiplication(antidomain(addition(X1,addition(X2,X3))),addition(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_108,c_0_99]) ).
cnf(c_0_227,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X1,antidomain(antidomain(X1)))))) = one,
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_113,c_0_56]),c_0_220]),c_0_54]),c_0_36]),c_0_73]),c_0_24]) ).
cnf(c_0_228,plain,
addition(antidomain(multiplication(antidomain(X1),X2)),antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1)))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1))))),
inference(spm,[status(thm)],[c_0_53,c_0_67]) ).
cnf(c_0_229,plain,
antidomain(addition(X1,antidomain(addition(X1,antidomain(antidomain(X1)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_107]),c_0_73]),c_0_24]) ).
cnf(c_0_230,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_53,c_0_50]),c_0_222]),c_0_54]),c_0_36]),c_0_73]),c_0_222]),c_0_54]),c_0_36]),c_0_73]),c_0_24]) ).
cnf(c_0_231,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X1) = multiplication(antidomain(antidomain(X2)),X1),
inference(spm,[status(thm)],[c_0_202,c_0_223]) ).
cnf(c_0_232,plain,
multiplication(antidomain(X1),antidomain(antidomain(addition(antidomain(X1),X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_73]),c_0_73]) ).
cnf(c_0_233,plain,
antidomain(addition(antidomain(X1),addition(X2,antidomain(antidomain(addition(X1,antidomain(antidomain(X1)))))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_36]) ).
cnf(c_0_234,plain,
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(spm,[status(thm)],[c_0_228,c_0_229]),c_0_90]),c_0_54]),c_0_36]),c_0_73]),c_0_230]),c_0_54]),c_0_36]),c_0_73]) ).
cnf(c_0_235,plain,
addition(antidomain(X1),addition(X2,antidomain(antidomain(X1)))) = addition(X2,one),
inference(spm,[status(thm)],[c_0_99,c_0_38]) ).
cnf(c_0_236,plain,
addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_153,c_0_91]) ).
cnf(c_0_237,plain,
multiplication(antidomain(antidomain(addition(antidomain(X1),X2))),X1) = multiplication(antidomain(antidomain(X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_58]),c_0_231]),c_0_133]),c_0_73]) ).
cnf(c_0_238,plain,
addition(antidomain(X1),antidomain(antidomain(addition(antidomain(X1),X2)))) = antidomain(antidomain(addition(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_232]),c_0_24]),c_0_55]),c_0_39]),c_0_24]) ).
cnf(c_0_239,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_151,c_0_233]),c_0_23]),c_0_234]),c_0_235]) ).
cnf(c_0_240,plain,
addition(antidomain(antidomain(X1)),antidomain(antidomain(addition(X2,X1)))) = antidomain(antidomain(addition(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_236]),c_0_24]) ).
cnf(c_0_241,plain,
addition(antidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(addition(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_237]),c_0_215]),c_0_238]) ).
cnf(c_0_242,plain,
antidomain(addition(antidomain(antidomain(X1)),multiplication(X1,addition(X2,one)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_239]),c_0_24]) ).
cnf(c_0_243,plain,
addition(X1,addition(multiplication(X1,X2),X3)) = addition(X3,multiplication(X1,addition(X2,one))),
inference(spm,[status(thm)],[c_0_161,c_0_43]) ).
fof(c_0_244,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_245,plain,
antidomain(antidomain(addition(X1,addition(antidomain(antidomain(X1)),X2)))) = antidomain(antidomain(addition(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241]),c_0_161]) ).
cnf(c_0_246,plain,
antidomain(addition(X1,addition(antidomain(antidomain(X1)),multiplication(X1,X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_24]) ).
cnf(c_0_247,plain,
multiplication(antidomain(antidomain(addition(antidomain(antidomain(X1)),X2))),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_155]),c_0_39]),c_0_133]) ).
cnf(c_0_248,plain,
addition(antidomain(antidomain(X1)),antidomain(X2)) = antidomain(antidomain(addition(antidomain(X2),X1))),
inference(spm,[status(thm)],[c_0_24,c_0_241]) ).
fof(c_0_249,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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])])])]) ).
fof(c_0_250,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_251,plain,
antidomain(addition(X1,addition(antidomain(antidomain(X1)),X2))) = antidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_245]),c_0_73]) ).
cnf(c_0_252,plain,
antidomain(addition(X1,antidomain(antidomain(addition(antidomain(antidomain(X1)),X2))))) = antidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_73]),c_0_49]),c_0_73]),c_0_24]) ).
cnf(c_0_253,plain,
addition(antidomain(antidomain(X1)),multiplication(antidomain(X1),antidomain(X2))) = antidomain(antidomain(addition(antidomain(X2),X1))),
inference(rw,[status(thm)],[c_0_194,c_0_248]) ).
cnf(c_0_254,plain,
multiplication(antidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_73]),c_0_206]) ).
cnf(c_0_255,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_249]) ).
cnf(c_0_256,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_257,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = antidomain(addition(antidomain(antidomain(X2)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_241]),c_0_252]) ).
cnf(c_0_258,plain,
antidomain(antidomain(addition(antidomain(X1),multiplication(antidomain(X2),X1)))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[c_0_215,c_0_241]) ).
cnf(c_0_259,plain,
addition(antidomain(antidomain(X1)),multiplication(antidomain(X2),antidomain(X1))) = antidomain(antidomain(addition(antidomain(X2),X1))),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_260,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_246,c_0_203]),c_0_73]),c_0_49]),c_0_24]) ).
cnf(c_0_261,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_255,c_0_256]),c_0_256]),c_0_256]),c_0_256]),c_0_256]),c_0_256]),c_0_256]) ).
cnf(c_0_262,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = antidomain(addition(X1,antidomain(antidomain(X2)))),
inference(spm,[status(thm)],[c_0_257,c_0_24]) ).
cnf(c_0_263,plain,
antidomain(addition(antidomain(X1),multiplication(antidomain(X2),X1))) = antidomain(addition(antidomain(X1),antidomain(X2))),
inference(spm,[status(thm)],[c_0_73,c_0_258]) ).
cnf(c_0_264,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X2) = multiplication(antidomain(antidomain(X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_259]),c_0_24]),c_0_260]),c_0_73]) ).
cnf(c_0_265,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_204]),c_0_24]),c_0_55]),c_0_36]),c_0_24]) ).
cnf(c_0_266,negated_conjecture,
antidomain(antidomain(addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),multiplication(esk1_0,antidomain(antidomain(esk3_0)))))) != antidomain(antidomain(multiplication(esk1_0,addition(esk3_0,antidomain(antidomain(esk2_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_261,c_0_241]),c_0_219]),c_0_241]),c_0_24]),c_0_219]) ).
cnf(c_0_267,plain,
antidomain(addition(X1,antidomain(antidomain(X2)))) = antidomain(addition(X2,antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_257,c_0_262]),c_0_262]) ).
cnf(c_0_268,plain,
antidomain(addition(antidomain(X1),X2)) = antidomain(antidomain(multiplication(antidomain(X2),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_263]),c_0_241]),c_0_73]),c_0_265]) ).
cnf(c_0_269,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_264,c_0_211]),c_0_73]),c_0_73]),c_0_254]) ).
cnf(c_0_270,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(X2)) = antidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_142,c_0_91]) ).
cnf(c_0_271,negated_conjecture,
antidomain(antidomain(addition(multiplication(esk1_0,esk2_0),antidomain(antidomain(multiplication(esk1_0,esk3_0)))))) != antidomain(antidomain(multiplication(esk1_0,addition(esk3_0,antidomain(antidomain(esk2_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_266,c_0_262]),c_0_219]) ).
cnf(c_0_272,plain,
antidomain(addition(X1,antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_73]),c_0_73]) ).
cnf(c_0_273,plain,
multiplication(antidomain(X1),antidomain(X2)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_67]),c_0_269]),c_0_270]) ).
cnf(c_0_274,negated_conjecture,
antidomain(multiplication(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,esk3_0)))) != antidomain(antidomain(multiplication(esk1_0,addition(esk3_0,antidomain(antidomain(esk2_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_272]),c_0_206]) ).
cnf(c_0_275,plain,
antidomain(addition(X1,multiplication(X2,antidomain(antidomain(X3))))) = antidomain(addition(X1,multiplication(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_219]),c_0_273]) ).
cnf(c_0_276,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,addition(esk3_0,antidomain(antidomain(esk2_0)))))) != antidomain(antidomain(multiplication(esk1_0,addition(esk2_0,esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_274,c_0_273]),c_0_35]) ).
cnf(c_0_277,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_275,c_0_35]),c_0_35]) ).
cnf(c_0_278,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_276,c_0_277]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE073+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:43:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 256.77/33.69 % Version: 3.5.1
% 256.77/33.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 256.77/33.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 256.77/33.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 256.77/33.69 % Starting new_bool_3 with 300s (1) cores
% 256.77/33.69 % Starting new_bool_1 with 300s (1) cores
% 256.77/33.69 % Starting sh5l with 300s (1) cores
% 256.77/33.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1388139 completed with status 0
% 256.77/33.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 256.77/33.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 256.77/33.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 256.77/33.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 256.77/33.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 256.77/33.69 % No SInE strategy applied
% 256.77/33.69 % Search class: FHUSM-FFSF21-DFFFFFNN
% 256.77/33.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 256.77/33.69 % Starting SubtermCWHack with 136s (1) cores
% 256.77/33.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 256.77/33.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 271s (1) cores
% 256.77/33.69 % Starting new_bool_3 with 271s (1) cores
% 256.77/33.69 % Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 256.77/33.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1388144 completed with status 0
% 256.77/33.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 256.77/33.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 256.77/33.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 256.77/33.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 256.77/33.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 256.77/33.69 % No SInE strategy applied
% 256.77/33.69 % Search class: FHUSM-FFSF21-DFFFFFNN
% 256.77/33.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 256.77/33.69 % Starting SubtermCWHack with 136s (1) cores
% 256.77/33.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 256.77/33.69 % Preprocessing time : 0.001 s
% 256.77/33.69 % Presaturation interreduction done
% 256.77/33.69
% 256.77/33.69 % Proof found!
% 256.77/33.69 % SZS status Theorem
% 256.77/33.69 % SZS output start CNFRefutation
% See solution above
% 256.77/33.69 % Parsed axioms : 21
% 256.77/33.69 % Removed by relevancy pruning/SinE : 0
% 256.77/33.69 % Initial clauses : 22
% 256.77/33.69 % Removed in clause preprocessing : 2
% 256.77/33.69 % Initial clauses in saturation : 20
% 256.77/33.69 % Processed clauses : 14797
% 256.77/33.69 % ...of these trivial : 9390
% 256.77/33.69 % ...subsumed : 3468
% 256.77/33.69 % ...remaining for further processing : 1939
% 256.77/33.69 % Other redundant clauses eliminated : 0
% 256.77/33.69 % Clauses deleted for lack of memory : 0
% 256.77/33.69 % Backward-subsumed : 0
% 256.77/33.69 % Backward-rewritten : 870
% 256.77/33.69 % Generated clauses : 1572982
% 256.77/33.69 % ...of the previous two non-redundant : 699533
% 256.77/33.69 % ...aggressively subsumed : 0
% 256.77/33.69 % Contextual simplify-reflections : 0
% 256.77/33.69 % Paramodulations : 1572982
% 256.77/33.69 % Factorizations : 0
% 256.77/33.69 % NegExts : 0
% 256.77/33.69 % Equation resolutions : 0
% 256.77/33.69 % Disequality decompositions : 0
% 256.77/33.69 % Total rewrite steps : 3756066
% 256.77/33.69 % ...of those cached : 3365497
% 256.77/33.69 % Propositional unsat checks : 0
% 256.77/33.69 % Propositional check models : 0
% 256.77/33.69 % Propositional check unsatisfiable : 0
% 256.77/33.69 % Propositional clauses : 0
% 256.77/33.69 % Propositional clauses after purity: 0
% 256.77/33.69 % Propositional unsat core size : 0
% 256.77/33.69 % Propositional preprocessing time : 0.000
% 256.77/33.69 % Propositional encoding time : 0.000
% 256.77/33.69 % Propositional solver time : 0.000
% 256.77/33.69 % Success case prop preproc time : 0.000
% 256.77/33.69 % Success case prop encoding time : 0.000
% 256.77/33.69 % Success case prop solver time : 0.000
% 256.77/33.69 % Current number of processed clauses : 1049
% 256.77/33.69 % Positive orientable unit clauses : 1026
% 256.77/33.69 % Positive unorientable unit clauses: 21
% 256.77/33.69 % Negative unit clauses : 0
% 256.77/33.69 % Non-unit-clauses : 2
% 256.77/33.69 % Current number of unprocessed clauses: 678135
% 256.77/33.69 % ...number of literals in the above : 678135
% 256.77/33.69 % Current number of archived formulas : 0
% 256.77/33.69 % Current number of archived clauses : 892
% 256.77/33.69 % Clause-clause subsumption calls (NU) : 0
% 256.77/33.69 % Rec. Clause-clause subsumption calls : 0
% 256.77/33.69 % Non-unit clause-clause subsumptions : 0
% 256.77/33.69 % Unit Clause-clause subsumption calls : 389
% 256.77/33.69 % Rewrite failures with RHS unbound : 0
% 256.77/33.69 % BW rewrite match attempts : 27548
% 256.77/33.69 % BW rewrite match successes : 1118
% 256.77/33.69 % Condensation attempts : 0
% 256.77/33.69 % Condensation successes : 0
% 256.77/33.69 % Termbank termtop insertions : 25021055
% 256.77/33.69 % Search garbage collected termcells : 47
% 256.77/33.69
% 256.77/33.69 % -------------------------------------------------
% 256.77/33.69 % User time : 29.422 s
% 256.77/33.69 % System time : 1.037 s
% 256.77/33.69 % Total time : 30.459 s
% 256.77/33.69 % Maximum resident set size: 3652 pages
% 256.77/33.69
% 256.77/33.69 % -------------------------------------------------
% 256.77/33.69 % User time : 156.565 s
% 256.77/33.69 % System time : 5.515 s
% 256.77/33.69 % Total time : 162.080 s
% 256.77/33.69 % Maximum resident set size: 4608 pages
% 256.77/33.69 % E exiting
%------------------------------------------------------------------------------