## TSTP Solution File: KLE089+1 by Metis---2.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KLE089+1 : TPTP v7.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n143.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Aug 29 14:32:45 EDT 2018

% Result   : Theorem 0.90s
% Output   : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   56
% Syntax   : Number of formulae    :  254 ( 151 unt;   0 def)
%            Number of atoms       :  400 ( 399 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  292 ( 146   ~; 141   |;   2   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  365 (  13 sgn  60   !;   2   ?)

%------------------------------------------------------------------------------

! [A] : addition(A,zero) = A ).

! [A] : addition(A,A) = A ).

fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).

fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).

fof(left_distributivity,axiom,

fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).

fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero ).

fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).

fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).

fof(goals,conjecture,
! [X0,X1] :
=> multiplication(domain(X0),X1) = zero ) ).

fof(subgoal_0,plain,
! [X0,X1] :
=> multiplication(domain(X0),X1) = zero ),
inference(strip,[],[goals]) ).

fof(negate_0_0,plain,
~ ! [X0,X1] :
=> multiplication(domain(X0),X1) = zero ),
inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).

fof(normalize_0_1,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[domain1]) ).

fof(normalize_0_3,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).

fof(normalize_0_5,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
inference(canonicalize,[],[left_distributivity]) ).

fof(normalize_0_7,plain,
inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
! [A] : addition(A,zero) = A,

fof(normalize_0_9,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,

fof(normalize_0_11,plain,
inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,

fof(normalize_0_13,plain,
inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
? [X0,X1] :
( multiplication(domain(X0),X1) != zero
inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_15,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero
inference(skolemize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).

fof(normalize_0_18,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).

fof(normalize_0_20,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
! [A] : addition(A,A) = A,

fof(normalize_0_22,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).

fof(normalize_0_24,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_23]) ).

fof(normalize_0_25,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(conjunct,[],[normalize_0_15]) ).

cnf(refute_0_0,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(multiplication(antidomain(X_73),X_73),X_74),
inference(subst,[],[refute_0_0:[bind(A,\$fot(antidomain(X_73))),bind(B,\$fot(X_73)),bind(C,\$fot(X_74))]]) ).

cnf(refute_0_2,plain,
multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
multiplication(antidomain(X_73),X_73) = zero,
inference(subst,[],[refute_0_2:[bind(X0,\$fot(X_73))]]) ).

cnf(refute_0_4,plain,
( multiplication(antidomain(X_73),X_73) != zero
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(multiplication(antidomain(X_73),X_73),X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74) ),
introduced(tautology,[equality,[\$cnf( \$equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(multiplication(antidomain(X_73),X_73),X_74)) ),[1,0],\$fot(zero)]]) ).

cnf(refute_0_5,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(multiplication(antidomain(X_73),X_73),X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74) ),
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(X_73),X_73),zero) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74),
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(multiplication(antidomain(X_73),X_73),X_74)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_8,plain,
multiplication(zero,X_74) = zero,
inference(subst,[],[refute_0_7:[bind(A,\$fot(X_74))]]) ).

cnf(refute_0_9,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(zero,X_74)
| multiplication(zero,X_74) != zero
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero ),
introduced(tautology,[equality,[\$cnf( ~ \$equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),zero) ),[0],\$fot(multiplication(zero,X_74))]]) ).

cnf(refute_0_10,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(zero,X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero ),
inference(resolve,[\$cnf( \$equal(multiplication(zero,X_74),zero) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero,
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(zero,X_74)) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) = zero,
inference(subst,[],[refute_0_11:[bind(X_73,\$fot(antidomain(skolemFOFtoCNF_X0))),bind(X_74,\$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_13,plain,
inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_14,plain,
inference(subst,[],[refute_0_13:[bind(A,\$fot(X_38)),bind(B,\$fot(antidomain(X_40))),bind(C,\$fot(X_40))]]) ).

cnf(refute_0_15,plain,
multiplication(antidomain(X_40),X_40) = zero,
inference(subst,[],[refute_0_2:[bind(X0,\$fot(X_40))]]) ).

cnf(refute_0_16,plain,
| multiplication(antidomain(X_40),X_40) != zero

cnf(refute_0_17,plain,
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(X_40),X_40),zero) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,

cnf(refute_0_19,plain,
inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_20,plain,
inference(subst,[],[refute_0_19:[bind(A,\$fot(multiplication(X_38,X_40)))]]) ).

cnf(refute_0_21,plain,

cnf(refute_0_22,plain,

cnf(refute_0_23,plain,

cnf(refute_0_24,plain,
inference(subst,[],[refute_0_23:[bind(X_38,\$fot(antidomain(skolemFOFtoCNF_X0))),bind(X_40,\$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_25,plain,
inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_26,plain,

cnf(refute_0_27,plain,
inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_28,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(X_21)),bind(B,\$fot(X_22)),bind(C,\$fot(A))]]) ).

cnf(refute_0_29,plain,
X = X,
introduced(tautology,[refl,[\$fot(X)]]) ).

cnf(refute_0_30,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[\$cnf( \$equal(X,X) ),[0],\$fot(Y)]]) ).

cnf(refute_0_31,plain,
( X != Y
| Y = X ),
inference(resolve,[\$cnf( \$equal(X,X) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,

cnf(refute_0_33,plain,

cnf(refute_0_34,plain,

cnf(refute_0_35,plain,

cnf(refute_0_36,plain,

cnf(refute_0_37,plain,
inference(subst,[],[refute_0_36:[bind(A,\$fot(domain(skolemFOFtoCNF_X0))),bind(X_21,\$fot(X_97)),bind(X_22,\$fot(antidomain(skolemFOFtoCNF_X1)))]]) ).

cnf(refute_0_38,plain,
inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_39,plain,

cnf(refute_0_40,plain,

cnf(refute_0_41,plain,
inference(subst,[],[refute_0_40:[bind(A,\$fot(antidomain(skolemFOFtoCNF_X1))),bind(B,\$fot(domain(skolemFOFtoCNF_X0)))]]) ).

cnf(refute_0_42,plain,

cnf(refute_0_43,plain,

cnf(refute_0_44,plain,

cnf(refute_0_45,plain,

cnf(refute_0_46,plain,

cnf(refute_0_47,plain,

cnf(refute_0_48,plain,
inference(subst,[],[refute_0_36:[bind(A,\$fot(X_96)),bind(X_21,\$fot(X_97)),bind(X_22,\$fot(X_98))]]) ).

cnf(refute_0_49,plain,
inference(subst,[],[refute_0_25:[bind(A,\$fot(X_98)),bind(B,\$fot(X_97))]]) ).

cnf(refute_0_50,plain,

cnf(refute_0_51,plain,

cnf(refute_0_52,plain,

cnf(refute_0_53,plain,

cnf(refute_0_54,plain,

cnf(refute_0_55,plain,

cnf(refute_0_56,plain,

cnf(refute_0_57,plain,
inference(subst,[],[refute_0_56:[bind(X_96,\$fot(antidomain(skolemFOFtoCNF_X1))),bind(X_97,\$fot(domain(skolemFOFtoCNF_X0))),bind(X_98,\$fot(X_97))]]) ).

cnf(refute_0_58,plain,

cnf(refute_0_59,plain,

cnf(refute_0_60,plain,

cnf(refute_0_61,plain,
inference(subst,[],[refute_0_60:[bind(X_97,\$fot(antidomain(skolemFOFtoCNF_X0)))]]) ).

cnf(refute_0_62,plain,
inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_63,plain,
inference(subst,[],[refute_0_40:[bind(A,\$fot(antidomain(X0))),bind(B,\$fot(antidomain(antidomain(X0))))]]) ).

cnf(refute_0_64,plain,

cnf(refute_0_65,plain,

cnf(refute_0_66,plain,

cnf(refute_0_67,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_68,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_31:[bind(X,\$fot(domain(X0))),bind(Y,\$fot(antidomain(antidomain(X0))))]]) ).

cnf(refute_0_69,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[\$cnf( \$equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,

cnf(refute_0_71,plain,
| antidomain(antidomain(X0)) != domain(X0)

cnf(refute_0_72,plain,
( antidomain(antidomain(X0)) != domain(X0)

cnf(refute_0_73,plain,
inference(resolve,[\$cnf( \$equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_69,refute_0_72]) ).

cnf(refute_0_74,plain,

cnf(refute_0_75,plain,

cnf(refute_0_76,plain,

cnf(refute_0_77,plain,
inference(subst,[],[refute_0_76:[bind(X0,\$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_78,plain,

cnf(refute_0_79,plain,

cnf(refute_0_80,plain,

cnf(refute_0_81,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(X_22)),bind(B,\$fot(X_22)),bind(C,\$fot(X_23))]]) ).

cnf(refute_0_82,plain,
inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_83,plain,
inference(subst,[],[refute_0_82:[bind(A,\$fot(X_22))]]) ).

cnf(refute_0_84,plain,

cnf(refute_0_85,plain,

cnf(refute_0_86,plain,

cnf(refute_0_87,plain,
inference(subst,[],[refute_0_86:[bind(X_22,\$fot(antidomain(X0))),bind(X_23,\$fot(domain(X0)))]]) ).

cnf(refute_0_88,plain,

cnf(refute_0_89,plain,

cnf(refute_0_90,plain,

cnf(refute_0_91,plain,
inference(subst,[],[refute_0_40:[bind(A,\$fot(one)),bind(B,\$fot(antidomain(X0)))]]) ).

cnf(refute_0_92,plain,

cnf(refute_0_93,plain,

cnf(refute_0_94,plain,

cnf(refute_0_95,plain,

cnf(refute_0_96,plain,

cnf(refute_0_97,plain,

cnf(refute_0_98,plain,
inference(subst,[],[refute_0_97:[bind(X0,\$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_99,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(antidomain(X0))),bind(B,\$fot(domain(X0))),bind(C,\$fot(X_23))]]) ).

cnf(refute_0_100,plain,

cnf(refute_0_101,plain,

cnf(refute_0_102,plain,

cnf(refute_0_103,plain,

cnf(refute_0_104,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(domain(X0))),bind(B,\$fot(antidomain(domain(X0)))),bind(C,\$fot(X_23))]]) ).

cnf(refute_0_105,plain,
inference(subst,[],[refute_0_76:[bind(X0,\$fot(antidomain(X0)))]]) ).

cnf(refute_0_106,plain,
| antidomain(antidomain(X0)) != domain(X0)

cnf(refute_0_107,plain,
inference(resolve,[\$cnf( \$equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_69,refute_0_106]) ).

cnf(refute_0_108,plain,

cnf(refute_0_109,plain,
domain(antidomain(X_6)) = antidomain(antidomain(antidomain(X_6))),
inference(subst,[],[refute_0_67:[bind(X0,\$fot(antidomain(X_6)))]]) ).

cnf(refute_0_110,plain,
domain(X_6) = antidomain(antidomain(X_6)),
inference(subst,[],[refute_0_67:[bind(X0,\$fot(X_6))]]) ).

cnf(refute_0_111,plain,
( domain(X_6) != antidomain(antidomain(X_6))
| antidomain(antidomain(X_6)) = domain(X_6) ),
inference(subst,[],[refute_0_31:[bind(X,\$fot(domain(X_6))),bind(Y,\$fot(antidomain(antidomain(X_6))))]]) ).

cnf(refute_0_112,plain,
antidomain(antidomain(X_6)) = domain(X_6),
inference(resolve,[\$cnf( \$equal(domain(X_6),antidomain(antidomain(X_6))) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
( antidomain(antidomain(X_6)) != domain(X_6)
| domain(antidomain(X_6)) != antidomain(antidomain(antidomain(X_6)))
| domain(antidomain(X_6)) = antidomain(domain(X_6)) ),
introduced(tautology,[equality,[\$cnf( \$equal(domain(antidomain(X_6)),antidomain(antidomain(antidomain(X_6)))) ),[1,0],\$fot(domain(X_6))]]) ).

cnf(refute_0_114,plain,
( domain(antidomain(X_6)) != antidomain(antidomain(antidomain(X_6)))
| domain(antidomain(X_6)) = antidomain(domain(X_6)) ),
inference(resolve,[\$cnf( \$equal(antidomain(antidomain(X_6)),domain(X_6)) )],[refute_0_112,refute_0_113]) ).

cnf(refute_0_115,plain,
domain(antidomain(X_6)) = antidomain(domain(X_6)),
inference(resolve,[\$cnf( \$equal(domain(antidomain(X_6)),antidomain(antidomain(antidomain(X_6)))) )],[refute_0_109,refute_0_114]) ).

cnf(refute_0_116,plain,
domain(antidomain(X0)) = antidomain(domain(X0)),
inference(subst,[],[refute_0_115:[bind(X_6,\$fot(X0))]]) ).

cnf(refute_0_117,plain,

cnf(refute_0_118,plain,
| domain(antidomain(X0)) != antidomain(domain(X0))

cnf(refute_0_119,plain,
( domain(antidomain(X0)) != antidomain(domain(X0))

cnf(refute_0_120,plain,
inference(resolve,[\$cnf( \$equal(domain(antidomain(X0)),antidomain(domain(X0))) )],[refute_0_116,refute_0_119]) ).

cnf(refute_0_121,plain,

cnf(refute_0_122,plain,

cnf(refute_0_123,plain,

cnf(refute_0_124,plain,

cnf(refute_0_125,plain,

cnf(refute_0_126,plain,

cnf(refute_0_127,plain,
inference(subst,[],[refute_0_126:[bind(X0,\$fot(X_36)),bind(X_23,\$fot(X_37))]]) ).

cnf(refute_0_128,plain,
inference(subst,[],[refute_0_25:[bind(A,\$fot(X_37)),bind(B,\$fot(antidomain(domain(X_36))))]]) ).

cnf(refute_0_129,plain,

cnf(refute_0_130,plain,

cnf(refute_0_131,plain,

cnf(refute_0_132,plain,

cnf(refute_0_133,plain,

cnf(refute_0_134,plain,
inference(subst,[],[refute_0_133:[bind(X_36,\$fot(X0)),bind(X_37,\$fot(X_64))]]) ).

cnf(refute_0_135,plain,

cnf(refute_0_136,plain,

cnf(refute_0_137,plain,

cnf(refute_0_138,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(one)),bind(B,\$fot(antidomain(X_26)))]]) ).

cnf(refute_0_139,plain,
inference(subst,[],[refute_0_97:[bind(X0,\$fot(X_26))]]) ).

cnf(refute_0_140,plain,

cnf(refute_0_141,plain,

cnf(refute_0_142,plain,

cnf(refute_0_143,plain,
inference(subst,[],[refute_0_142:[bind(C,\$fot(X_64)),bind(X_26,\$fot(X0))]]) ).

cnf(refute_0_144,plain,
inference(subst,[],[refute_0_27:[bind(A,\$fot(X_21)),bind(B,\$fot(X_22)),bind(C,\$fot(X_23))]]) ).

cnf(refute_0_145,plain,
inference(subst,[],[refute_0_25:[bind(A,\$fot(X_22)),bind(B,\$fot(X_21))]]) ).

cnf(refute_0_146,plain,

cnf(refute_0_147,plain,

cnf(refute_0_148,plain,

cnf(refute_0_149,plain,

cnf(refute_0_150,plain,

cnf(refute_0_151,plain,

cnf(refute_0_152,plain,

cnf(refute_0_153,plain,
inference(subst,[],[refute_0_152:[bind(A,\$fot(X_22)),bind(B,\$fot(X_21)),bind(C,\$fot(X_23))]]) ).

cnf(refute_0_154,plain,

cnf(refute_0_155,plain,

cnf(refute_0_156,plain,

cnf(refute_0_157,plain,

cnf(refute_0_158,plain,

cnf(refute_0_159,plain,
inference(subst,[],[refute_0_158:[bind(X_21,\$fot(one)),bind(X_22,\$fot(antidomain(X0))),bind(X_23,\$fot(X_64))]]) ).

cnf(refute_0_160,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[\$cnf( \$equal(Y,Z) ),[0],\$fot(X)]]) ).

cnf(refute_0_161,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[\$cnf( \$equal(Y,X) )],[refute_0_31,refute_0_160]) ).

cnf(refute_0_162,plain,

cnf(refute_0_163,plain,

cnf(refute_0_164,plain,

cnf(refute_0_165,plain,

cnf(refute_0_166,plain,

cnf(refute_0_167,plain,

cnf(refute_0_168,plain,
inference(subst,[],[refute_0_36:[bind(A,\$fot(antidomain(X0))),bind(X_21,\$fot(X_97)),bind(X_22,\$fot(one))]]) ).

cnf(refute_0_169,plain,

cnf(refute_0_170,plain,

cnf(refute_0_171,plain,

cnf(refute_0_172,plain,
inference(subst,[],[refute_0_56:[bind(X_96,\$fot(one)),bind(X_97,\$fot(antidomain(X0))),bind(X_98,\$fot(X_97))]]) ).

cnf(refute_0_173,plain,

cnf(refute_0_174,plain,

cnf(refute_0_175,plain,

cnf(refute_0_176,plain,
inference(subst,[],[refute_0_175:[bind(X0,\$fot(domain(X0))),bind(X_97,\$fot(X_64))]]) ).

cnf(refute_0_177,plain,

cnf(refute_0_178,plain,

cnf(refute_0_179,plain,

cnf(refute_0_180,plain,

cnf(refute_0_181,plain,

cnf(refute_0_182,plain,
inference(subst,[],[refute_0_181:[bind(X_64,\$fot(antidomain(skolemFOFtoCNF_X1)))]]) ).

cnf(refute_0_183,plain,

cnf(refute_0_184,plain,

cnf(refute_0_185,plain,

cnf(refute_0_186,plain,

cnf(refute_0_187,plain,

cnf(refute_0_188,plain,

cnf(refute_0_189,plain,

cnf(refute_0_190,plain,

cnf(refute_0_191,plain,
| multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),

cnf(refute_0_192,plain,
| multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),

cnf(refute_0_193,plain,
multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),

cnf(refute_0_194,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_24]) ).

cnf(refute_0_195,plain,
multiplication(one,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(subst,[],[refute_0_194:[bind(A,\$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_196,plain,
( multiplication(one,skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(one,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[\$cnf( \$equal(multiplication(one,skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[0],\$fot(skolemFOFtoCNF_X1)]]) ).

cnf(refute_0_197,plain,
( multiplication(one,skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[\$cnf( \$equal(multiplication(one,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_195,refute_0_196]) ).

cnf(refute_0_198,plain,
skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[\$cnf( \$equal(multiplication(one,skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_193,refute_0_197]) ).

cnf(refute_0_199,plain,
( skolemFOFtoCNF_X1 != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_31:[bind(X,\$fot(skolemFOFtoCNF_X1)),bind(Y,\$fot(multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)))]]) ).

cnf(refute_0_200,plain,
multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(resolve,[\$cnf( \$equal(skolemFOFtoCNF_X1,multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) != zero
| multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)),zero) ),[0,1],\$fot(skolemFOFtoCNF_X1)]]) ).

cnf(refute_0_202,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) != zero
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero ),
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_200,refute_0_201]) ).

cnf(refute_0_203,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero,
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)),zero) )],[refute_0_12,refute_0_202]) ).

cnf(refute_0_204,plain,
antidomain(antidomain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_69:[bind(X0,\$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_205,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),
introduced(tautology,[refl,[\$fot(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_206,plain,
( antidomain(antidomain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)) ),[1,0],\$fot(domain(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_207,plain,
( antidomain(antidomain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[\$cnf( \$equal(antidomain(antidomain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_204,refute_0_207]) ).

cnf(refute_0_209,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),zero) ),[0],\$fot(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_210,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero,
inference(resolve,[\$cnf( \$equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),zero) )],[refute_0_203,refute_0_210]) ).

cnf(refute_0_212,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_213,plain,
\$false,
inference(resolve,[\$cnf( \$equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),zero) )],[refute_0_211,refute_0_212]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v7.1.0. Released v4.0.0.
% 0.00/0.04  % Command  : metis --show proof --show saturation %s
% 0.03/0.23  % Computer : n143.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.625MB
% 0.03/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Tue Aug 28 15:05:41 CDT 2018
% 0.03/0.23  % CPUTime  :
% 0.03/0.23  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.90/1.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.90/1.14
% 0.90/1.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.99/1.18  % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.99/1.18
%------------------------------------------------------------------------------
```