TSTP Solution File: KLE055+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 02:14:57 EDT 2022
% Result : Theorem 0.64s 0.83s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 26
% Syntax : Number of formulae : 124 ( 76 unt; 0 def)
% Number of atoms : 191 ( 190 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 135 ( 68 ~; 62 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 171 ( 2 sgn 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
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(goals,conjecture,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ) ).
fof(subgoal_0,plain,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_1,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_3,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X0] :
( addition(X0,domain(X0)) != domain(X0)
& addition(X0,one) = one ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
& addition(skolemFOFtoCNF_X0,one) = one ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
addition(skolemFOFtoCNF_X0,one) = one,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_10,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_12,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_14,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_16,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(X_47,addition(one,X_49)) = addition(multiplication(X_47,one),multiplication(X_47,X_49)),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_47)),bind(B,$fot(one)),bind(C,$fot(X_49))]]) ).
cnf(refute_0_2,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
multiplication(X_47,one) = X_47,
inference(subst,[],[refute_0_2:[bind(A,$fot(X_47))]]) ).
cnf(refute_0_4,plain,
( multiplication(X_47,addition(one,X_49)) != addition(multiplication(X_47,one),multiplication(X_47,X_49))
| multiplication(X_47,one) != X_47
| multiplication(X_47,addition(one,X_49)) = addition(X_47,multiplication(X_47,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_47,addition(one,X_49)),addition(multiplication(X_47,one),multiplication(X_47,X_49))) ),[1,0],$fot(X_47)]]) ).
cnf(refute_0_5,plain,
( multiplication(X_47,addition(one,X_49)) != addition(multiplication(X_47,one),multiplication(X_47,X_49))
| multiplication(X_47,addition(one,X_49)) = addition(X_47,multiplication(X_47,X_49)) ),
inference(resolve,[$cnf( $equal(multiplication(X_47,one),X_47) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
multiplication(X_47,addition(one,X_49)) = addition(X_47,multiplication(X_47,X_49)),
inference(resolve,[$cnf( $equal(multiplication(X_47,addition(one,X_49)),addition(multiplication(X_47,one),multiplication(X_47,X_49))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
multiplication(X_51,addition(one,skolemFOFtoCNF_X0)) = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_6:[bind(X_47,$fot(X_51)),bind(X_49,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_8,plain,
addition(skolemFOFtoCNF_X0,one) = one,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_14,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
addition(skolemFOFtoCNF_X0,one) = addition(one,skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_14:[bind(A,$fot(one)),bind(B,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_16,plain,
( addition(skolemFOFtoCNF_X0,one) != addition(one,skolemFOFtoCNF_X0)
| addition(skolemFOFtoCNF_X0,one) != one
| addition(one,skolemFOFtoCNF_X0) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0,one),one) ),[0],$fot(addition(one,skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_17,plain,
( addition(skolemFOFtoCNF_X0,one) != one
| addition(one,skolemFOFtoCNF_X0) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,one),addition(one,skolemFOFtoCNF_X0)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
addition(one,skolemFOFtoCNF_X0) = one,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,one),one) )],[refute_0_8,refute_0_17]) ).
cnf(refute_0_19,plain,
( addition(one,skolemFOFtoCNF_X0) != one
| multiplication(X_51,addition(one,skolemFOFtoCNF_X0)) != addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))
| multiplication(X_51,one) = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_51,addition(one,skolemFOFtoCNF_X0)),addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_20,plain,
( multiplication(X_51,addition(one,skolemFOFtoCNF_X0)) != addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))
| multiplication(X_51,one) = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(addition(one,skolemFOFtoCNF_X0),one) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiplication(X_51,one) = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(multiplication(X_51,addition(one,skolemFOFtoCNF_X0)),addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
multiplication(X_51,one) = X_51,
inference(subst,[],[refute_0_2:[bind(A,$fot(X_51))]]) ).
cnf(refute_0_23,plain,
( multiplication(X_51,one) != X_51
| multiplication(X_51,one) != addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))
| X_51 = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_51,one),addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))) ),[0],$fot(X_51)]]) ).
cnf(refute_0_24,plain,
( multiplication(X_51,one) != addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))
| X_51 = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(multiplication(X_51,one),X_51) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
X_51 = addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(multiplication(X_51,one),addition(X_51,multiplication(X_51,skolemFOFtoCNF_X0))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
domain(skolemFOFtoCNF_X0) = addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_25:[bind(X_51,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_27,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_28,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_29,plain,
multiplication(addition(X_66,one),X_68) = addition(multiplication(X_66,X_68),multiplication(one,X_68)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_66)),bind(B,$fot(one)),bind(C,$fot(X_68))]]) ).
cnf(refute_0_30,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_31,plain,
multiplication(one,X_68) = X_68,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_68))]]) ).
cnf(refute_0_32,plain,
( multiplication(addition(X_66,one),X_68) != addition(multiplication(X_66,X_68),multiplication(one,X_68))
| multiplication(one,X_68) != X_68
| multiplication(addition(X_66,one),X_68) = addition(multiplication(X_66,X_68),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_66,one),X_68),addition(multiplication(X_66,X_68),multiplication(one,X_68))) ),[1,1],$fot(X_68)]]) ).
cnf(refute_0_33,plain,
( multiplication(addition(X_66,one),X_68) != addition(multiplication(X_66,X_68),multiplication(one,X_68))
| multiplication(addition(X_66,one),X_68) = addition(multiplication(X_66,X_68),X_68) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_68),X_68) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiplication(addition(X_66,one),X_68) = addition(multiplication(X_66,X_68),X_68),
inference(resolve,[$cnf( $equal(multiplication(addition(X_66,one),X_68),addition(multiplication(X_66,X_68),multiplication(one,X_68))) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
addition(multiplication(X_66,X_68),X_68) = addition(X_68,multiplication(X_66,X_68)),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_68)),bind(B,$fot(multiplication(X_66,X_68)))]]) ).
cnf(refute_0_36,plain,
( addition(multiplication(X_66,X_68),X_68) != addition(X_68,multiplication(X_66,X_68))
| multiplication(addition(X_66,one),X_68) != addition(multiplication(X_66,X_68),X_68)
| multiplication(addition(X_66,one),X_68) = addition(X_68,multiplication(X_66,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_66,one),X_68),addition(multiplication(X_66,X_68),X_68)) ),[1],$fot(addition(X_68,multiplication(X_66,X_68)))]]) ).
cnf(refute_0_37,plain,
( multiplication(addition(X_66,one),X_68) != addition(multiplication(X_66,X_68),X_68)
| multiplication(addition(X_66,one),X_68) = addition(X_68,multiplication(X_66,X_68)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_66,X_68),X_68),addition(X_68,multiplication(X_66,X_68))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiplication(addition(X_66,one),X_68) = addition(X_68,multiplication(X_66,X_68)),
inference(resolve,[$cnf( $equal(multiplication(addition(X_66,one),X_68),addition(multiplication(X_66,X_68),X_68)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiplication(addition(domain(X0),one),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(subst,[],[refute_0_38:[bind(X_66,$fot(domain(X0))),bind(X_68,$fot(X0))]]) ).
cnf(refute_0_40,plain,
( multiplication(addition(domain(X0),one),X0) != addition(X0,multiplication(domain(X0),X0))
| addition(X0,multiplication(domain(X0),X0)) = multiplication(addition(domain(X0),one),X0) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(addition(domain(X0),one),X0))),bind(Y,$fot(addition(X0,multiplication(domain(X0),X0))))]]) ).
cnf(refute_0_41,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(addition(domain(X0),one),X0),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(X0),one),X0),addition(X0,multiplication(domain(X0),X0))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( addition(X0,multiplication(domain(X0),X0)) != multiplication(addition(domain(X0),one),X0)
| addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| multiplication(addition(domain(X0),one),X0) = multiplication(domain(X0),X0) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) ),[0],$fot(multiplication(addition(domain(X0),one),X0))]]) ).
cnf(refute_0_43,plain,
( addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| multiplication(addition(domain(X0),one),X0) = multiplication(domain(X0),X0) ),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(addition(domain(X0),one),X0)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiplication(addition(domain(X0),one),X0) = multiplication(domain(X0),X0),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) )],[refute_0_27,refute_0_43]) ).
cnf(refute_0_45,plain,
multiplication(one,X0) = X0,
inference(subst,[],[refute_0_30:[bind(A,$fot(X0))]]) ).
cnf(refute_0_46,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_47,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_14:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_48,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_49,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplication(addition(one,domain(X0)),X0) = multiplication(addition(one,domain(X0)),X0),
introduced(tautology,[refl,[$fot(multiplication(addition(one,domain(X0)),X0))]]) ).
cnf(refute_0_52,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_53,plain,
( addition(one,domain(X0)) != one
| multiplication(addition(one,domain(X0)),X0) = multiplication(one,X0) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(addition(one,domain(X0)),X0)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiplication(addition(one,domain(X0)),X0) = multiplication(one,X0),
inference(resolve,[$cnf( $equal(addition(one,domain(X0)),one) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_56,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiplication(addition(one,domain(X0)),X0) != multiplication(one,X0)
| multiplication(one,X0) != X0
| multiplication(addition(one,domain(X0)),X0) = X0 ),
inference(subst,[],[refute_0_56:[bind(X,$fot(multiplication(addition(one,domain(X0)),X0))),bind(Y,$fot(multiplication(one,X0))),bind(Z,$fot(X0))]]) ).
cnf(refute_0_58,plain,
( multiplication(one,X0) != X0
| multiplication(addition(one,domain(X0)),X0) = X0 ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),multiplication(one,X0)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
multiplication(addition(one,domain(X0)),X0) = X0,
inference(resolve,[$cnf( $equal(multiplication(one,X0),X0) )],[refute_0_45,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) = addition(multiplication(X_66,X_68),multiplication(X_67,X_68)),
inference(subst,[],[refute_0_9:[bind(A,$fot(multiplication(X_67,X_68))),bind(B,$fot(multiplication(X_66,X_68)))]]) ).
cnf(refute_0_61,plain,
multiplication(addition(X_66,X_67),X_68) = addition(multiplication(X_66,X_68),multiplication(X_67,X_68)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_66)),bind(B,$fot(X_67)),bind(C,$fot(X_68))]]) ).
cnf(refute_0_62,plain,
( multiplication(addition(X_66,X_67),X_68) != addition(multiplication(X_66,X_68),multiplication(X_67,X_68))
| addition(multiplication(X_66,X_68),multiplication(X_67,X_68)) = multiplication(addition(X_66,X_67),X_68) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(addition(X_66,X_67),X_68))),bind(Y,$fot(addition(multiplication(X_66,X_68),multiplication(X_67,X_68))))]]) ).
cnf(refute_0_63,plain,
addition(multiplication(X_66,X_68),multiplication(X_67,X_68)) = multiplication(addition(X_66,X_67),X_68),
inference(resolve,[$cnf( $equal(multiplication(addition(X_66,X_67),X_68),addition(multiplication(X_66,X_68),multiplication(X_67,X_68))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( addition(multiplication(X_66,X_68),multiplication(X_67,X_68)) != multiplication(addition(X_66,X_67),X_68)
| addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) != addition(multiplication(X_66,X_68),multiplication(X_67,X_68))
| addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) = multiplication(addition(X_66,X_67),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(X_67,X_68),multiplication(X_66,X_68)),addition(multiplication(X_66,X_68),multiplication(X_67,X_68))) ),[1],$fot(multiplication(addition(X_66,X_67),X_68))]]) ).
cnf(refute_0_65,plain,
( addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) != addition(multiplication(X_66,X_68),multiplication(X_67,X_68))
| addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) = multiplication(addition(X_66,X_67),X_68) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_66,X_68),multiplication(X_67,X_68)),multiplication(addition(X_66,X_67),X_68)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) = multiplication(addition(X_66,X_67),X_68),
inference(resolve,[$cnf( $equal(addition(multiplication(X_67,X_68),multiplication(X_66,X_68)),addition(multiplication(X_66,X_68),multiplication(X_67,X_68))) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
( multiplication(addition(A,B),C) != addition(multiplication(A,C),multiplication(B,C))
| addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(addition(A,B),C))),bind(Y,$fot(addition(multiplication(A,C),multiplication(B,C))))]]) ).
cnf(refute_0_68,plain,
addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C),
inference(resolve,[$cnf( $equal(multiplication(addition(A,B),C),addition(multiplication(A,C),multiplication(B,C))) )],[refute_0_28,refute_0_67]) ).
cnf(refute_0_69,plain,
addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) = multiplication(addition(X_67,X_66),X_68),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_67)),bind(B,$fot(X_66)),bind(C,$fot(X_68))]]) ).
cnf(refute_0_70,plain,
( addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) != multiplication(addition(X_66,X_67),X_68)
| addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) != multiplication(addition(X_67,X_66),X_68)
| multiplication(addition(X_67,X_66),X_68) = multiplication(addition(X_66,X_67),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(X_67,X_68),multiplication(X_66,X_68)),multiplication(addition(X_66,X_67),X_68)) ),[0],$fot(multiplication(addition(X_67,X_66),X_68))]]) ).
cnf(refute_0_71,plain,
( addition(multiplication(X_67,X_68),multiplication(X_66,X_68)) != multiplication(addition(X_66,X_67),X_68)
| multiplication(addition(X_67,X_66),X_68) = multiplication(addition(X_66,X_67),X_68) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_67,X_68),multiplication(X_66,X_68)),multiplication(addition(X_67,X_66),X_68)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiplication(addition(X_67,X_66),X_68) = multiplication(addition(X_66,X_67),X_68),
inference(resolve,[$cnf( $equal(addition(multiplication(X_67,X_68),multiplication(X_66,X_68)),multiplication(addition(X_66,X_67),X_68)) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
( multiplication(addition(X_67,X_66),X_68) != multiplication(addition(X_66,X_67),X_68)
| multiplication(addition(X_66,X_67),X_68) = multiplication(addition(X_67,X_66),X_68) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiplication(addition(X_67,X_66),X_68))),bind(Y,$fot(multiplication(addition(X_66,X_67),X_68)))]]) ).
cnf(refute_0_74,plain,
multiplication(addition(X_66,X_67),X_68) = multiplication(addition(X_67,X_66),X_68),
inference(resolve,[$cnf( $equal(multiplication(addition(X_67,X_66),X_68),multiplication(addition(X_66,X_67),X_68)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiplication(addition(domain(X0),one),X0) = multiplication(addition(one,domain(X0)),X0),
inference(subst,[],[refute_0_74:[bind(X_66,$fot(domain(X0))),bind(X_67,$fot(one)),bind(X_68,$fot(X0))]]) ).
cnf(refute_0_76,plain,
( multiplication(addition(domain(X0),one),X0) != multiplication(addition(one,domain(X0)),X0)
| multiplication(addition(one,domain(X0)),X0) != X0
| multiplication(addition(domain(X0),one),X0) = X0 ),
inference(subst,[],[refute_0_56:[bind(X,$fot(multiplication(addition(domain(X0),one),X0))),bind(Y,$fot(multiplication(addition(one,domain(X0)),X0))),bind(Z,$fot(X0))]]) ).
cnf(refute_0_77,plain,
( multiplication(addition(one,domain(X0)),X0) != X0
| multiplication(addition(domain(X0),one),X0) = X0 ),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(X0),one),X0),multiplication(addition(one,domain(X0)),X0)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiplication(addition(domain(X0),one),X0) = X0,
inference(resolve,[$cnf( $equal(multiplication(addition(one,domain(X0)),X0),X0) )],[refute_0_59,refute_0_77]) ).
cnf(refute_0_79,plain,
( multiplication(addition(domain(X0),one),X0) != X0
| multiplication(addition(domain(X0),one),X0) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(domain(X0),one),X0),multiplication(domain(X0),X0)) ),[0],$fot(X0)]]) ).
cnf(refute_0_80,plain,
( multiplication(addition(domain(X0),one),X0) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(X0),one),X0),X0) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
X0 = multiplication(domain(X0),X0),
inference(resolve,[$cnf( $equal(multiplication(addition(domain(X0),one),X0),multiplication(domain(X0),X0)) )],[refute_0_44,refute_0_80]) ).
cnf(refute_0_82,plain,
skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_81:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_X0)),bind(Y,$fot(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_84,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( domain(skolemFOFtoCNF_X0) != addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| domain(skolemFOFtoCNF_X0) = addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))) ),[1,1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_86,plain,
( domain(skolemFOFtoCNF_X0) != addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))
| domain(skolemFOFtoCNF_X0) = addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
domain(skolemFOFtoCNF_X0) = addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))) )],[refute_0_26,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_89,plain,
( addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0))
| domain(skolemFOFtoCNF_X0) != addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[1],$fot(addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_90,plain,
( domain(skolemFOFtoCNF_X0) != addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
domain(skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_93,plain,
( domain(skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0))
| addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(domain(skolemFOFtoCNF_X0))),bind(Y,$fot(addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_94,plain,
domain(skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_93,refute_0_92]) ).
cnf(refute_0_95,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X0))) )],[refute_0_91,refute_0_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 11:07:55 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.64/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.83
% 0.64/0.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.64/0.84
%------------------------------------------------------------------------------