TSTP Solution File: KLE115+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE115+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n016.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 01:56:03 EDT 2022

% Result   : Theorem 0.43s 32.61s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  188 ( 188 unt;   0 def)
%            Number of atoms       :  188 ( 187 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   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    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  307 (  33 sgn  68   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(domain3,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).

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_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(domain1,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).

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(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(codomain1,axiom,
    ! [X4] : multiplication(X4,coantidomain(X4)) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).

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(codomain3,axiom,
    ! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).

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(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

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(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

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(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] : forward_diamond(X4,addition(domain(X5),domain(X6))) = addition(forward_diamond(X4,domain(X5)),forward_diamond(X4,domain(X6))),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(forward_diamond,axiom,
    ! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).

fof(c_0_20,plain,
    ! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
    inference(variable_rename,[status(thm)],[domain3]) ).

fof(c_0_21,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_22,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

fof(c_0_23,plain,
    ! [X5] : multiplication(antidomain(X5),X5) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_24,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_25,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_26,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_27,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_28,plain,
    ! [X5] : multiplication(X5,coantidomain(X5)) = zero,
    inference(variable_rename,[status(thm)],[codomain1]) ).

cnf(c_0_29,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_32,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_36,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_37,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_38,plain,
    multiplication(X1,coantidomain(X1)) = zero,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_39,plain,
    ! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
    inference(variable_rename,[status(thm)],[codomain3]) ).

fof(c_0_40,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_41,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_42,plain,
    antidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_43,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_33,c_0_30]) ).

cnf(c_0_44,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_45,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_46,plain,
    multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33]) ).

fof(c_0_47,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_48,plain,
    addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_49,plain,
    multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_33]) ).

cnf(c_0_50,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_40]) ).

cnf(c_0_51,plain,
    antidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_52,plain,
    addition(one,antidomain(X1)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_30]) ).

cnf(c_0_53,plain,
    multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_32]),c_0_33]) ).

cnf(c_0_54,plain,
    multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
    inference(spm,[status(thm)],[c_0_46,c_0_30]) ).

cnf(c_0_55,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_56,plain,
    addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_48,c_0_30]) ).

cnf(c_0_57,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(spm,[status(thm)],[c_0_49,c_0_30]) ).

cnf(c_0_58,plain,
    antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_51]),c_0_52]) ).

cnf(c_0_59,plain,
    multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
    inference(spm,[status(thm)],[c_0_53,c_0_30]) ).

cnf(c_0_60,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
    inference(spm,[status(thm)],[c_0_45,c_0_31]) ).

cnf(c_0_61,plain,
    multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_55]) ).

cnf(c_0_62,plain,
    addition(one,coantidomain(X1)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_56]),c_0_30]) ).

cnf(c_0_63,plain,
    multiplication(antidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_41]),c_0_55]) ).

cnf(c_0_64,plain,
    multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_55]) ).

cnf(c_0_65,plain,
    multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_43]) ).

cnf(c_0_66,plain,
    multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_55]) ).

cnf(c_0_67,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[c_0_37,c_0_55]) ).

cnf(c_0_68,plain,
    multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_31]) ).

fof(c_0_69,plain,
    ! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_70,plain,
    ! [X2] : multiplication(zero,X2) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_71,plain,
    addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_31]) ).

cnf(c_0_72,plain,
    antidomain(antidomain(antidomain(X1))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_31]),c_0_63]) ).

cnf(c_0_73,plain,
    multiplication(antidomain(antidomain(X1)),addition(one,X1)) = addition(X1,antidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_63]),c_0_30]) ).

cnf(c_0_74,plain,
    multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_64]),c_0_43]) ).

cnf(c_0_75,plain,
    multiplication(X1,coantidomain(coantidomain(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_56]),c_0_31]) ).

cnf(c_0_76,plain,
    multiplication(addition(antidomain(X1),X2),antidomain(X1)) = multiplication(addition(one,X2),antidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_66]),c_0_67]) ).

cnf(c_0_77,plain,
    addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_52]),c_0_55]),c_0_30]) ).

cnf(c_0_78,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_79,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_80,plain,
    addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_81,plain,
    addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_56]) ).

cnf(c_0_82,plain,
    addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_62]),c_0_31]) ).

cnf(c_0_83,plain,
    multiplication(X1,antidomain(coantidomain(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_41]),c_0_31]),c_0_72]) ).

cnf(c_0_84,plain,
    coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_56]),c_0_55]),c_0_75]) ).

cnf(c_0_85,plain,
    multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_62]),c_0_55]) ).

fof(c_0_86,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]) ).

cnf(c_0_87,plain,
    multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_32]),c_0_79]) ).

cnf(c_0_88,plain,
    coantidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_55,c_0_38]) ).

cnf(c_0_89,plain,
    multiplication(coantidomain(antidomain(antidomain(X1))),X1) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_80]),c_0_32]) ).

cnf(c_0_90,plain,
    addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_52]) ).

cnf(c_0_91,plain,
    coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).

cnf(c_0_92,plain,
    addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_34]) ).

cnf(c_0_93,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_86]) ).

cnf(c_0_94,plain,
    multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
    inference(spm,[status(thm)],[c_0_87,c_0_63]) ).

cnf(c_0_95,plain,
    coantidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_88]),c_0_43]) ).

cnf(c_0_96,plain,
    multiplication(addition(coantidomain(antidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_89]),c_0_43]) ).

cnf(c_0_97,plain,
    addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_72]) ).

cnf(c_0_98,plain,
    addition(X1,addition(X2,X1)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_92,c_0_44]) ).

cnf(c_0_99,plain,
    coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_62]) ).

cnf(c_0_100,plain,
    multiplication(antidomain(coantidomain(antidomain(antidomain(X1)))),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_55]) ).

cnf(c_0_101,plain,
    addition(X1,addition(X2,addition(X3,X1))) = addition(X1,addition(X2,X3)),
    inference(spm,[status(thm)],[c_0_98,c_0_34]) ).

cnf(c_0_102,plain,
    addition(one,addition(antidomain(X1),X2)) = addition(one,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_52]) ).

cnf(c_0_103,plain,
    multiplication(antidomain(addition(X1,X2)),X1) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_44]),c_0_32]) ).

cnf(c_0_104,plain,
    multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_99]),c_0_78]),c_0_31]) ).

cnf(c_0_105,plain,
    multiplication(antidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_100,c_0_72]) ).

cnf(c_0_106,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X2,addition(X3,X1))) = multiplication(antidomain(addition(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_53,c_0_92]) ).

cnf(c_0_107,plain,
    addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_41]),c_0_92]),c_0_92]),c_0_102]) ).

cnf(c_0_108,plain,
    multiplication(antidomain(addition(X1,X2)),addition(one,X1)) = antidomain(addition(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_103]),c_0_33]) ).

cnf(c_0_109,plain,
    multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
    inference(rw,[status(thm)],[c_0_104,c_0_72]) ).

cnf(c_0_110,plain,
    addition(antidomain(X1),antidomain(coantidomain(antidomain(X1)))) = antidomain(coantidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_105]),c_0_52]),c_0_31]),c_0_30]) ).

cnf(c_0_111,plain,
    addition(multiplication(X1,addition(one,X2)),X3) = addition(X1,addition(multiplication(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_34,c_0_60]) ).

cnf(c_0_112,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_106,c_0_107]),c_0_108]) ).

cnf(c_0_113,plain,
    multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
    inference(rw,[status(thm)],[c_0_109,c_0_91]) ).

cnf(c_0_114,plain,
    addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_84]),c_0_30]) ).

cnf(c_0_115,plain,
    addition(antidomain(X1),antidomain(coantidomain(antidomain(antidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_110]),c_0_52]) ).

cnf(c_0_116,plain,
    addition(X1,addition(multiplication(X1,antidomain(X2)),X3)) = addition(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_52]),c_0_31]) ).

cnf(c_0_117,plain,
    addition(antidomain(antidomain(X1)),antidomain(addition(X2,antidomain(X1)))) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_112]),c_0_52]),c_0_55]) ).

cnf(c_0_118,plain,
    multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_113]),c_0_43]) ).

cnf(c_0_119,plain,
    antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_91]),c_0_82]) ).

cnf(c_0_120,plain,
    addition(antidomain(antidomain(X1)),antidomain(coantidomain(antidomain(X1)))) = one,
    inference(spm,[status(thm)],[c_0_115,c_0_72]) ).

cnf(c_0_121,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_50,c_0_87]),c_0_51]),c_0_52]) ).

fof(c_0_122,plain,
    ! [X2] : multiplication(X2,zero) = zero,
    inference(variable_rename,[status(thm)],[right_annihilation]) ).

cnf(c_0_123,plain,
    multiplication(addition(multiplication(antidomain(X1),antidomain(X2)),X3),X1) = multiplication(X3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_116]),c_0_57]) ).

cnf(c_0_124,plain,
    addition(coantidomain(X1),addition(antidomain(coantidomain(X1)),X2)) = addition(one,X2),
    inference(rw,[status(thm)],[c_0_81,c_0_91]) ).

cnf(c_0_125,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X2,antidomain(X1))))) = antidomain(antidomain(addition(X2,antidomain(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_117]),c_0_72]),c_0_30]) ).

cnf(c_0_126,plain,
    multiplication(coantidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_115]),c_0_55]),c_0_119]),c_0_91]),c_0_119]) ).

cnf(c_0_127,plain,
    multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_120]),c_0_31]),c_0_119]),c_0_119]) ).

cnf(c_0_128,plain,
    addition(X1,multiplication(addition(X1,X2),antidomain(X3))) = addition(X1,multiplication(X2,antidomain(X3))),
    inference(spm,[status(thm)],[c_0_116,c_0_37]) ).

cnf(c_0_129,plain,
    multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_78,c_0_83]) ).

cnf(c_0_130,plain,
    multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_121]),c_0_55]) ).

cnf(c_0_131,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[c_0_122]) ).

cnf(c_0_132,plain,
    multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_123]),c_0_32]),c_0_78]) ).

cnf(c_0_133,plain,
    addition(coantidomain(X1),antidomain(antidomain(addition(X2,antidomain(coantidomain(X1)))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_52]) ).

cnf(c_0_134,plain,
    coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_72]),c_0_127]) ).

cnf(c_0_135,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_128,c_0_41]),c_0_55]) ).

cnf(c_0_136,plain,
    multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).

cnf(c_0_137,plain,
    multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_103]),c_0_43]) ).

cnf(c_0_138,plain,
    multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_132]),c_0_131]) ).

cnf(c_0_139,plain,
    multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_78,c_0_63]) ).

cnf(c_0_140,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(addition(X2,antidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_72]) ).

cnf(c_0_141,plain,
    addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_33]),c_0_134]),c_0_72]) ).

cnf(c_0_142,plain,
    multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_41]),c_0_55]) ).

cnf(c_0_143,plain,
    antidomain(multiplication(X1,antidomain(antidomain(multiplication(antidomain(X2),coantidomain(X1)))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_138]),c_0_51]),c_0_52]) ).

cnf(c_0_144,plain,
    multiplication(antidomain(antidomain(multiplication(X1,X2))),multiplication(X1,multiplication(X2,X3))) = multiplication(X1,multiplication(X2,X3)),
    inference(spm,[status(thm)],[c_0_139,c_0_78]) ).

cnf(c_0_145,plain,
    addition(antidomain(antidomain(X1)),antidomain(addition(antidomain(X1),X2))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_117,c_0_30]) ).

cnf(c_0_146,plain,
    addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_55]),c_0_55]) ).

cnf(c_0_147,plain,
    addition(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_72]),c_0_72]),c_0_30]) ).

cnf(c_0_148,plain,
    multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
    inference(spm,[status(thm)],[c_0_142,c_0_30]) ).

cnf(c_0_149,plain,
    multiplication(X1,antidomain(antidomain(multiplication(antidomain(X2),coantidomain(X1))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_143]),c_0_55]) ).

cnf(c_0_150,plain,
    addition(antidomain(antidomain(multiplication(X1,X2))),antidomain(antidomain(multiplication(X1,multiplication(X2,X3))))) = antidomain(antidomain(multiplication(X1,X2))),
    inference(spm,[status(thm)],[c_0_141,c_0_144]) ).

cnf(c_0_151,plain,
    addition(antidomain(antidomain(multiplication(X1,X2))),antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))) = antidomain(antidomain(multiplication(X1,X2))),
    inference(spm,[status(thm)],[c_0_145,c_0_50]) ).

cnf(c_0_152,plain,
    multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_146]),c_0_32]) ).

cnf(c_0_153,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X2,X1)))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_30]) ).

cnf(c_0_154,plain,
    addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),antidomain(X1))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_149]),c_0_33]),c_0_134]),c_0_72]) ).

cnf(c_0_155,plain,
    antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(antidomain(multiplication(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_63]),c_0_30]),c_0_151]) ).

fof(c_0_156,negated_conjecture,
    ~ ! [X4,X5,X6] : forward_diamond(X4,addition(domain(X5),domain(X6))) = addition(forward_diamond(X4,domain(X5)),forward_diamond(X4,domain(X6))),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_157,plain,
    ! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
    inference(variable_rename,[status(thm)],[forward_diamond]) ).

fof(c_0_158,plain,
    ! [X5] : domain(X5) = antidomain(antidomain(X5)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_159,plain,
    addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
    inference(spm,[status(thm)],[c_0_37,c_0_78]) ).

cnf(c_0_160,plain,
    multiplication(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_152]),c_0_43]) ).

cnf(c_0_161,plain,
    addition(antidomain(X1),antidomain(multiplication(antidomain(X2),antidomain(X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_72]),c_0_72]),c_0_30]) ).

cnf(c_0_162,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_155]),c_0_72]),c_0_52]),c_0_31]),c_0_72]),c_0_30]),c_0_50]) ).

fof(c_0_163,negated_conjecture,
    forward_diamond(esk1_0,addition(domain(esk2_0),domain(esk3_0))) != addition(forward_diamond(esk1_0,domain(esk2_0)),forward_diamond(esk1_0,domain(esk3_0))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])]) ).

cnf(c_0_164,plain,
    forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[c_0_157]) ).

cnf(c_0_165,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_158]) ).

cnf(c_0_166,plain,
    multiplication(addition(X1,multiplication(antidomain(multiplication(X2,X3)),X2)),X3) = multiplication(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_32]),c_0_33]) ).

cnf(c_0_167,plain,
    addition(antidomain(antidomain(X1)),multiplication(antidomain(X1),antidomain(X2))) = addition(antidomain(antidomain(X1)),antidomain(X2)),
    inference(spm,[status(thm)],[c_0_135,c_0_72]) ).

cnf(c_0_168,plain,
    multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_31]),c_0_162]) ).

cnf(c_0_169,plain,
    multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
    inference(spm,[status(thm)],[c_0_60,c_0_67]) ).

cnf(c_0_170,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(X1,X2)))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_141,c_0_139]) ).

cnf(c_0_171,negated_conjecture,
    forward_diamond(esk1_0,addition(domain(esk2_0),domain(esk3_0))) != addition(forward_diamond(esk1_0,domain(esk2_0)),forward_diamond(esk1_0,domain(esk3_0))),
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

cnf(c_0_172,plain,
    forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_165]) ).

cnf(c_0_173,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_166,c_0_167]),c_0_30]),c_0_141]) ).

cnf(c_0_174,plain,
    multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
    inference(spm,[status(thm)],[c_0_168,c_0_168]) ).

cnf(c_0_175,plain,
    addition(multiplication(X1,X2),multiplication(X2,addition(one,X2))) = multiplication(addition(X1,addition(one,X2)),X2),
    inference(spm,[status(thm)],[c_0_37,c_0_169]) ).

cnf(c_0_176,plain,
    multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_170]),c_0_72]),c_0_72]),c_0_72]) ).

cnf(c_0_177,plain,
    multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_147]),c_0_55]) ).

cnf(c_0_178,negated_conjecture,
    antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))))) != addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(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_171,c_0_165]),c_0_165]),c_0_165]),c_0_165]),c_0_172]),c_0_172]),c_0_172]) ).

cnf(c_0_179,plain,
    multiplication(antidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_162]),c_0_174]) ).

cnf(c_0_180,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(spm,[status(thm)],[c_0_175,c_0_176]),c_0_52]),c_0_31]),c_0_52]),c_0_30]),c_0_52]),c_0_55]) ).

cnf(c_0_181,plain,
    multiplication(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_177,c_0_142]) ).

cnf(c_0_182,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk3_0)))))) != antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_72]),c_0_72]) ).

cnf(c_0_183,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(X2))),
    inference(spm,[status(thm)],[c_0_167,c_0_179]) ).

cnf(c_0_184,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(addition(X1,X2)))) = antidomain(antidomain(addition(X1,X2))),
    inference(spm,[status(thm)],[c_0_180,c_0_181]) ).

cnf(c_0_185,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(antidomain(multiplication(esk1_0,esk3_0)))) != antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_155]),c_0_155]),c_0_155]) ).

cnf(c_0_186,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(X2))) = antidomain(antidomain(addition(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_59]),c_0_183]),c_0_184]) ).

cnf(c_0_187,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186]),c_0_45]),c_0_186]),c_0_162])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE115+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 14:13:49 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.37/23.40  eprover: CPU time limit exceeded, terminating
% 0.37/23.41  eprover: CPU time limit exceeded, terminating
% 0.37/23.41  eprover: CPU time limit exceeded, terminating
% 0.37/23.44  eprover: CPU time limit exceeded, terminating
% 0.43/32.61  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.43/32.61  
% 0.43/32.61  # Failure: Resource limit exceeded (time)
% 0.43/32.61  # OLD status Res
% 0.43/32.61  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.43/32.61  # Preprocessing time       : 0.015 s
% 0.43/32.61  # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.43/32.61  # Preprocessing time       : 0.020 s
% 0.43/32.61  
% 0.43/32.61  # Proof found!
% 0.43/32.61  # SZS status Theorem
% 0.43/32.61  # SZS output start CNFRefutation
% See solution above
% 0.43/32.61  # Proof object total steps             : 188
% 0.43/32.61  # Proof object clause steps            : 147
% 0.43/32.61  # Proof object formula steps           : 41
% 0.43/32.61  # Proof object conjectures             : 8
% 0.43/32.61  # Proof object clause conjectures      : 5
% 0.43/32.61  # Proof object formula conjectures     : 3
% 0.43/32.61  # Proof object initial clauses used    : 20
% 0.43/32.61  # Proof object initial formulas used   : 20
% 0.43/32.61  # Proof object generating inferences   : 115
% 0.43/32.61  # Proof object simplifying inferences  : 154
% 0.43/32.61  # Training examples: 0 positive, 0 negative
% 0.43/32.61  # Parsed axioms                        : 27
% 0.43/32.61  # Removed by relevancy pruning/SinE    : 0
% 0.43/32.61  # Initial clauses                      : 28
% 0.43/32.61  # Removed in clause preprocessing      : 8
% 0.43/32.61  # Initial clauses in saturation        : 20
% 0.43/32.61  # Processed clauses                    : 12377
% 0.43/32.61  # ...of these trivial                  : 8504
% 0.43/32.61  # ...subsumed                          : 2245
% 0.43/32.61  # ...remaining for further processing  : 1628
% 0.43/32.61  # Other redundant clauses eliminated   : 0
% 0.43/32.61  # Clauses deleted for lack of memory   : 216217
% 0.43/32.61  # Backward-subsumed                    : 0
% 0.43/32.61  # Backward-rewritten                   : 550
% 0.43/32.61  # Generated clauses                    : 889293
% 0.43/32.61  # ...of the previous two non-trivial   : 390370
% 0.43/32.61  # Contextual simplify-reflections      : 0
% 0.43/32.61  # Paramodulations                      : 889293
% 0.43/32.61  # Factorizations                       : 0
% 0.43/32.61  # Equation resolutions                 : 0
% 0.43/32.61  # Current number of processed clauses  : 1078
% 0.43/32.61  #    Positive orientable unit clauses  : 1059
% 0.43/32.61  #    Positive unorientable unit clauses: 17
% 0.43/32.61  #    Negative unit clauses             : 0
% 0.43/32.61  #    Non-unit-clauses                  : 2
% 0.43/32.61  # Current number of unprocessed clauses: 96542
% 0.43/32.61  # ...number of literals in the above   : 96542
% 0.43/32.61  # Current number of archived formulas  : 0
% 0.43/32.61  # Current number of archived clauses   : 558
% 0.43/32.61  # Clause-clause subsumption calls (NU) : 0
% 0.43/32.61  # Rec. Clause-clause subsumption calls : 0
% 0.43/32.61  # Non-unit clause-clause subsumptions  : 0
% 0.43/32.61  # Unit Clause-clause subsumption calls : 124
% 0.43/32.61  # Rewrite failures with RHS unbound    : 0
% 0.43/32.61  # BW rewrite match attempts            : 15997
% 0.43/32.61  # BW rewrite match successes           : 580
% 0.43/32.61  # Condensation attempts                : 0
% 0.43/32.61  # Condensation successes               : 0
% 0.43/32.61  # Termbank termtop insertions          : 13839470
% 0.43/32.61  
% 0.43/32.61  # -------------------------------------------------
% 0.43/32.61  # User time                : 8.272 s
% 0.43/32.61  # System time              : 0.120 s
% 0.43/32.61  # Total time               : 8.392 s
% 0.43/32.61  # Maximum resident set size: 156000 pages
% 0.43/46.43  eprover: CPU time limit exceeded, terminating
% 0.43/46.44  eprover: CPU time limit exceeded, terminating
% 0.43/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.45  eprover: No such file or directory
% 0.43/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.45  eprover: No such file or directory
% 0.43/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.46  eprover: No such file or directory
% 0.43/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.46  eprover: No such file or directory
% 0.43/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.46  eprover: No such file or directory
% 0.43/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.46  eprover: No such file or directory
% 0.43/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.47  eprover: No such file or directory
% 0.43/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.47  eprover: No such file or directory
% 0.43/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.47  eprover: No such file or directory
% 0.43/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.47  eprover: No such file or directory
% 0.43/46.47  eprover: CPU time limit exceeded, terminating
% 0.43/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.48  eprover: No such file or directory
% 0.43/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.48  eprover: No such file or directory
% 0.43/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.48  eprover: No such file or directory
% 0.43/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.48  eprover: No such file or directory
% 0.43/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49  eprover: No such file or directory
% 0.43/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49  eprover: No such file or directory
% 0.43/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.49  eprover: No such file or directory
% 0.43/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49  eprover: No such file or directory
% 0.43/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49  eprover: No such file or directory
% 0.43/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.50  eprover: No such file or directory
% 0.43/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.50  eprover: No such file or directory
% 0.43/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.50  eprover: No such file or directory
% 0.43/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.50  eprover: No such file or directory
% 0.43/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.51  eprover: No such file or directory
% 0.43/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.43/46.51  eprover: No such file or directory
% 0.43/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.51  eprover: No such file or directory
% 0.43/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.52  eprover: No such file or directory
% 0.43/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.52  eprover: No such file or directory
% 0.43/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.52  eprover: No such file or directory
% 0.43/46.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.43/46.53  eprover: No such file or directory
%------------------------------------------------------------------------------