TSTP Solution File: KLE064+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 02:15:00 EDT 2022
% Result : Theorem 8.36s 8.57s
% Output : CNFRefutation 8.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 111 ( 67 unt; 0 def)
% Number of atoms : 172 ( 171 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 124 ( 63 ~; 56 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 149 ( 7 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_1,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_3,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_5,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_7,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_9,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_11,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) != multiplication(domain(X1),X0)
& addition(domain(X0),domain(X1)) = domain(X1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_13,plain,
( addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)
& addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(addition(domain(C),B),C) = addition(multiplication(domain(C),C),multiplication(B,C)),
inference(subst,[],[refute_0_0:[bind(A,$fot(domain(C)))]]) ).
cnf(refute_0_2,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
multiplication(addition(one,X_41),X_42) = addition(multiplication(one,X_42),multiplication(X_41,X_42)),
inference(subst,[],[refute_0_0:[bind(A,$fot(one)),bind(B,$fot(X_41)),bind(C,$fot(X_42))]]) ).
cnf(refute_0_4,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
multiplication(one,X_42) = X_42,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_42))]]) ).
cnf(refute_0_6,plain,
( multiplication(addition(one,X_41),X_42) != addition(multiplication(one,X_42),multiplication(X_41,X_42))
| multiplication(one,X_42) != X_42
| multiplication(addition(one,X_41),X_42) = addition(X_42,multiplication(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_41),X_42),addition(multiplication(one,X_42),multiplication(X_41,X_42))) ),[1,0],$fot(X_42)]]) ).
cnf(refute_0_7,plain,
( multiplication(addition(one,X_41),X_42) != addition(multiplication(one,X_42),multiplication(X_41,X_42))
| multiplication(addition(one,X_41),X_42) = addition(X_42,multiplication(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_42),X_42) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiplication(addition(one,X_41),X_42) = addition(X_42,multiplication(X_41,X_42)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_41),X_42),addition(multiplication(one,X_42),multiplication(X_41,X_42))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
multiplication(addition(one,domain(X0)),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(subst,[],[refute_0_8:[bind(X_41,$fot(domain(X0))),bind(X_42,$fot(X0))]]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiplication(addition(one,domain(X0)),X0) != addition(X0,multiplication(domain(X0),X0))
| addition(X0,multiplication(domain(X0),X0)) = multiplication(addition(one,domain(X0)),X0) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(addition(one,domain(X0)),X0))),bind(Y,$fot(addition(X0,multiplication(domain(X0),X0))))]]) ).
cnf(refute_0_14,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(addition(one,domain(X0)),X0),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),addition(X0,multiplication(domain(X0),X0))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( addition(X0,multiplication(domain(X0),X0)) != multiplication(addition(one,domain(X0)),X0)
| addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) ),[0],$fot(multiplication(addition(one,domain(X0)),X0))]]) ).
cnf(refute_0_16,plain,
( addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0) ),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(addition(one,domain(X0)),X0)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
multiplication(one,X0) = X0,
inference(subst,[],[refute_0_4:[bind(A,$fot(X0))]]) ).
cnf(refute_0_19,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_20,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_21,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_22,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_22:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_24,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_25,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
multiplication(addition(one,domain(X0)),X0) = multiplication(addition(one,domain(X0)),X0),
introduced(tautology,[refl,[$fot(multiplication(addition(one,domain(X0)),X0))]]) ).
cnf(refute_0_28,plain,
( addition(one,domain(X0)) != one
| multiplication(addition(one,domain(X0)),X0) != multiplication(addition(one,domain(X0)),X0)
| multiplication(addition(one,domain(X0)),X0) = multiplication(one,X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(addition(one,domain(X0)),X0)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_29,plain,
( addition(one,domain(X0)) != one
| multiplication(addition(one,domain(X0)),X0) = multiplication(one,X0) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(addition(one,domain(X0)),X0)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplication(addition(one,domain(X0)),X0) = multiplication(one,X0),
inference(resolve,[$cnf( $equal(addition(one,domain(X0)),one) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiplication(addition(one,domain(X0)),X0) != multiplication(one,X0)
| multiplication(one,X0) != X0
| multiplication(addition(one,domain(X0)),X0) = X0 ),
inference(subst,[],[refute_0_32:[bind(X,$fot(multiplication(addition(one,domain(X0)),X0))),bind(Y,$fot(multiplication(one,X0))),bind(Z,$fot(X0))]]) ).
cnf(refute_0_34,plain,
( multiplication(one,X0) != X0
| multiplication(addition(one,domain(X0)),X0) = X0 ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(one,X0)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
multiplication(addition(one,domain(X0)),X0) = X0,
inference(resolve,[$cnf( $equal(multiplication(one,X0),X0) )],[refute_0_18,refute_0_34]) ).
cnf(refute_0_36,plain,
( multiplication(addition(one,domain(X0)),X0) != X0
| multiplication(addition(one,domain(X0)),X0) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(domain(X0),X0)) ),[0],$fot(X0)]]) ).
cnf(refute_0_37,plain,
( multiplication(addition(one,domain(X0)),X0) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),X0) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
X0 = multiplication(domain(X0),X0),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(domain(X0),X0)) )],[refute_0_17,refute_0_37]) ).
cnf(refute_0_39,plain,
C = multiplication(domain(C),C),
inference(subst,[],[refute_0_38:[bind(X0,$fot(C))]]) ).
cnf(refute_0_40,plain,
( C != multiplication(domain(C),C)
| multiplication(domain(C),C) = C ),
inference(subst,[],[refute_0_12:[bind(X,$fot(C)),bind(Y,$fot(multiplication(domain(C),C)))]]) ).
cnf(refute_0_41,plain,
multiplication(domain(C),C) = C,
inference(resolve,[$cnf( $equal(C,multiplication(domain(C),C)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiplication(addition(domain(C),B),C) != addition(multiplication(domain(C),C),multiplication(B,C))
| multiplication(domain(C),C) != C
| multiplication(addition(domain(C),B),C) = addition(C,multiplication(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(domain(C),B),C),addition(multiplication(domain(C),C),multiplication(B,C))) ),[1,0],$fot(C)]]) ).
cnf(refute_0_43,plain,
( multiplication(addition(domain(C),B),C) != addition(multiplication(domain(C),C),multiplication(B,C))
| multiplication(addition(domain(C),B),C) = addition(C,multiplication(B,C)) ),
inference(resolve,[$cnf( $equal(multiplication(domain(C),C),C) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiplication(addition(domain(C),B),C) = addition(C,multiplication(B,C)),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(C),B),C),addition(multiplication(domain(C),C),multiplication(B,C))) )],[refute_0_1,refute_0_43]) ).
cnf(refute_0_45,plain,
multiplication(addition(domain(X_117),domain(X1)),X_117) = addition(X_117,multiplication(domain(X1),X_117)),
inference(subst,[],[refute_0_44:[bind(B,$fot(domain(X1))),bind(C,$fot(X_117))]]) ).
cnf(refute_0_46,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_47,plain,
domain(addition(X_117,X1)) = addition(domain(X_117),domain(X1)),
inference(subst,[],[refute_0_46:[bind(X0,$fot(X_117))]]) ).
cnf(refute_0_48,plain,
( domain(addition(X_117,X1)) != addition(domain(X_117),domain(X1))
| addition(domain(X_117),domain(X1)) = domain(addition(X_117,X1)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(domain(addition(X_117,X1)))),bind(Y,$fot(addition(domain(X_117),domain(X1))))]]) ).
cnf(refute_0_49,plain,
addition(domain(X_117),domain(X1)) = domain(addition(X_117,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X_117,X1)),addition(domain(X_117),domain(X1))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( addition(domain(X_117),domain(X1)) != domain(addition(X_117,X1))
| multiplication(addition(domain(X_117),domain(X1)),X_117) != addition(X_117,multiplication(domain(X1),X_117))
| multiplication(domain(addition(X_117,X1)),X_117) = addition(X_117,multiplication(domain(X1),X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(domain(X_117),domain(X1)),X_117),addition(X_117,multiplication(domain(X1),X_117))) ),[0,0],$fot(domain(addition(X_117,X1)))]]) ).
cnf(refute_0_51,plain,
( multiplication(addition(domain(X_117),domain(X1)),X_117) != addition(X_117,multiplication(domain(X1),X_117))
| multiplication(domain(addition(X_117,X1)),X_117) = addition(X_117,multiplication(domain(X1),X_117)) ),
inference(resolve,[$cnf( $equal(addition(domain(X_117),domain(X1)),domain(addition(X_117,X1))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiplication(domain(addition(X_117,X1)),X_117) = addition(X_117,multiplication(domain(X1),X_117)),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(X_117),domain(X1)),X_117),addition(X_117,multiplication(domain(X1),X_117))) )],[refute_0_45,refute_0_51]) ).
cnf(refute_0_53,plain,
multiplication(addition(one,domain(X0)),X_44) = addition(X_44,multiplication(domain(X0),X_44)),
inference(subst,[],[refute_0_8:[bind(X_41,$fot(domain(X0))),bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_54,plain,
( addition(one,domain(X0)) != one
| multiplication(addition(one,domain(X0)),X_44) != addition(X_44,multiplication(domain(X0),X_44))
| multiplication(one,X_44) = addition(X_44,multiplication(domain(X0),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,domain(X0)),X_44),addition(X_44,multiplication(domain(X0),X_44))) ),[0,0],$fot(one)]]) ).
cnf(refute_0_55,plain,
( multiplication(addition(one,domain(X0)),X_44) != addition(X_44,multiplication(domain(X0),X_44))
| multiplication(one,X_44) = addition(X_44,multiplication(domain(X0),X_44)) ),
inference(resolve,[$cnf( $equal(addition(one,domain(X0)),one) )],[refute_0_26,refute_0_54]) ).
cnf(refute_0_56,plain,
multiplication(one,X_44) = addition(X_44,multiplication(domain(X0),X_44)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X_44),addition(X_44,multiplication(domain(X0),X_44))) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
multiplication(one,X_44) = X_44,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_44))]]) ).
cnf(refute_0_58,plain,
( multiplication(one,X_44) != X_44
| multiplication(one,X_44) != addition(X_44,multiplication(domain(X0),X_44))
| X_44 = addition(X_44,multiplication(domain(X0),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,X_44),addition(X_44,multiplication(domain(X0),X_44))) ),[0],$fot(X_44)]]) ).
cnf(refute_0_59,plain,
( multiplication(one,X_44) != addition(X_44,multiplication(domain(X0),X_44))
| X_44 = addition(X_44,multiplication(domain(X0),X_44)) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_44),X_44) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
X_44 = addition(X_44,multiplication(domain(X0),X_44)),
inference(resolve,[$cnf( $equal(multiplication(one,X_44),addition(X_44,multiplication(domain(X0),X_44))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( X_44 != addition(X_44,multiplication(domain(X0),X_44))
| addition(X_44,multiplication(domain(X0),X_44)) = X_44 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_44)),bind(Y,$fot(addition(X_44,multiplication(domain(X0),X_44))))]]) ).
cnf(refute_0_62,plain,
addition(X_44,multiplication(domain(X0),X_44)) = X_44,
inference(resolve,[$cnf( $equal(X_44,addition(X_44,multiplication(domain(X0),X_44))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
addition(X_117,multiplication(domain(X1),X_117)) = X_117,
inference(subst,[],[refute_0_62:[bind(X0,$fot(X1)),bind(X_44,$fot(X_117))]]) ).
cnf(refute_0_64,plain,
( addition(X_117,multiplication(domain(X1),X_117)) != X_117
| multiplication(domain(addition(X_117,X1)),X_117) != addition(X_117,multiplication(domain(X1),X_117))
| multiplication(domain(addition(X_117,X1)),X_117) = X_117 ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(addition(X_117,X1)),X_117),addition(X_117,multiplication(domain(X1),X_117))) ),[1],$fot(X_117)]]) ).
cnf(refute_0_65,plain,
( multiplication(domain(addition(X_117,X1)),X_117) != addition(X_117,multiplication(domain(X1),X_117))
| multiplication(domain(addition(X_117,X1)),X_117) = X_117 ),
inference(resolve,[$cnf( $equal(addition(X_117,multiplication(domain(X1),X_117)),X_117) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiplication(domain(addition(X_117,X1)),X_117) = X_117,
inference(resolve,[$cnf( $equal(multiplication(domain(addition(X_117,X1)),X_117),addition(X_117,multiplication(domain(X1),X_117))) )],[refute_0_52,refute_0_65]) ).
cnf(refute_0_67,plain,
multiplication(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_66:[bind(X1,$fot(skolemFOFtoCNF_X1)),bind(X_117,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_68,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_69,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_70,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_46,refute_0_69]) ).
cnf(refute_0_71,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_70:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_72,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) ),[0],$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_73,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| multiplication(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),[0,0],$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_76,plain,
( multiplication(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(multiplication(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_67,refute_0_76]) ).
cnf(refute_0_78,plain,
addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_79,plain,
addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_62:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(X_44,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_80,plain,
( addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)
| addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_81,plain,
( skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)
| addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),skolemFOFtoCNF_X0) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) )],[refute_0_81,refute_0_78]) ).
cnf(refute_0_83,plain,
( multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))),bind(Y,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_84,plain,
multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) )],[refute_0_83,refute_0_82]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X1),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_77,refute_0_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 09:38:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.36/8.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/8.57
% 8.36/8.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.36/8.57
%------------------------------------------------------------------------------