TSTP Solution File: KLE061+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 02:14:59 EDT 2022
% Result : Theorem 0.39s 0.61s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 103 ( 69 unt; 0 def)
% Number of atoms : 153 ( 152 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 105 ( 55 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 125 ( 3 sgn 36 !; 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(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(goals,conjecture,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0) ).
fof(subgoal_0,plain,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : multiplication(domain(X0),domain(X0)) != domain(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(skolemize,[],[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,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_9,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_11,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_13,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
addition(domain(X_13),multiplication(domain(domain(X_13)),domain(X_13))) = multiplication(domain(domain(X_13)),domain(X_13)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(domain(X_13)))]]) ).
cnf(refute_0_3,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
domain(multiplication(one,X_12)) = domain(multiplication(one,domain(X_12))),
inference(subst,[],[refute_0_3:[bind(X0,$fot(one)),bind(X1,$fot(X_12))]]) ).
cnf(refute_0_5,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
multiplication(one,domain(X_12)) = domain(X_12),
inference(subst,[],[refute_0_5:[bind(A,$fot(domain(X_12)))]]) ).
cnf(refute_0_7,plain,
( domain(multiplication(one,X_12)) != domain(multiplication(one,domain(X_12)))
| multiplication(one,domain(X_12)) != domain(X_12)
| domain(multiplication(one,X_12)) = domain(domain(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_12)),domain(multiplication(one,domain(X_12)))) ),[1,0],$fot(domain(X_12))]]) ).
cnf(refute_0_8,plain,
( domain(multiplication(one,X_12)) != domain(multiplication(one,domain(X_12)))
| domain(multiplication(one,X_12)) = domain(domain(X_12)) ),
inference(resolve,[$cnf( $equal(multiplication(one,domain(X_12)),domain(X_12)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
domain(multiplication(one,X_12)) = domain(domain(X_12)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_12)),domain(multiplication(one,domain(X_12)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
multiplication(one,X_12) = X_12,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_11,plain,
domain(multiplication(one,X_12)) = domain(multiplication(one,X_12)),
introduced(tautology,[refl,[$fot(domain(multiplication(one,X_12)))]]) ).
cnf(refute_0_12,plain,
( domain(multiplication(one,X_12)) != domain(multiplication(one,X_12))
| multiplication(one,X_12) != X_12
| domain(multiplication(one,X_12)) = domain(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_12)),domain(multiplication(one,X_12))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_13,plain,
( multiplication(one,X_12) != X_12
| domain(multiplication(one,X_12)) = domain(X_12) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_12)),domain(multiplication(one,X_12))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
domain(multiplication(one,X_12)) = domain(X_12),
inference(resolve,[$cnf( $equal(multiplication(one,X_12),X_12) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( domain(multiplication(one,X_12)) != domain(X_12)
| domain(multiplication(one,X_12)) != domain(domain(X_12))
| domain(X_12) = domain(domain(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_12)),domain(domain(X_12))) ),[0],$fot(domain(X_12))]]) ).
cnf(refute_0_16,plain,
( domain(multiplication(one,X_12)) != domain(domain(X_12))
| domain(X_12) = domain(domain(X_12)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_12)),domain(X_12)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
domain(X_12) = domain(domain(X_12)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_12)),domain(domain(X_12))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
domain(X_13) = domain(domain(X_13)),
inference(subst,[],[refute_0_17:[bind(X_12,$fot(X_13))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( domain(X_13) != domain(domain(X_13))
| domain(domain(X_13)) = domain(X_13) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(domain(X_13))),bind(Y,$fot(domain(domain(X_13))))]]) ).
cnf(refute_0_23,plain,
domain(domain(X_13)) = domain(X_13),
inference(resolve,[$cnf( $equal(domain(X_13),domain(domain(X_13))) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(domain(X_13),multiplication(domain(domain(X_13)),domain(X_13))) != multiplication(domain(domain(X_13)),domain(X_13))
| domain(domain(X_13)) != domain(X_13)
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(domain(X_13)),domain(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X_13),multiplication(domain(domain(X_13)),domain(X_13))),multiplication(domain(domain(X_13)),domain(X_13))) ),[0,1,0],$fot(domain(X_13))]]) ).
cnf(refute_0_25,plain,
( addition(domain(X_13),multiplication(domain(domain(X_13)),domain(X_13))) != multiplication(domain(domain(X_13)),domain(X_13))
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(domain(X_13)),domain(X_13)) ),
inference(resolve,[$cnf( $equal(domain(domain(X_13)),domain(X_13)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(domain(X_13)),domain(X_13)),
inference(resolve,[$cnf( $equal(addition(domain(X_13),multiplication(domain(domain(X_13)),domain(X_13))),multiplication(domain(domain(X_13)),domain(X_13))) )],[refute_0_2,refute_0_25]) ).
cnf(refute_0_27,plain,
multiplication(domain(domain(X_13)),domain(X_13)) = multiplication(domain(domain(X_13)),domain(X_13)),
introduced(tautology,[refl,[$fot(multiplication(domain(domain(X_13)),domain(X_13)))]]) ).
cnf(refute_0_28,plain,
( domain(domain(X_13)) != domain(X_13)
| multiplication(domain(domain(X_13)),domain(X_13)) != multiplication(domain(domain(X_13)),domain(X_13))
| multiplication(domain(domain(X_13)),domain(X_13)) = multiplication(domain(X_13),domain(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(domain(X_13)),domain(X_13)),multiplication(domain(domain(X_13)),domain(X_13))) ),[1,0],$fot(domain(X_13))]]) ).
cnf(refute_0_29,plain,
( domain(domain(X_13)) != domain(X_13)
| multiplication(domain(domain(X_13)),domain(X_13)) = multiplication(domain(X_13),domain(X_13)) ),
inference(resolve,[$cnf( $equal(multiplication(domain(domain(X_13)),domain(X_13)),multiplication(domain(domain(X_13)),domain(X_13))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplication(domain(domain(X_13)),domain(X_13)) = multiplication(domain(X_13),domain(X_13)),
inference(resolve,[$cnf( $equal(domain(domain(X_13)),domain(X_13)) )],[refute_0_23,refute_0_29]) ).
cnf(refute_0_31,plain,
( addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != multiplication(domain(domain(X_13)),domain(X_13))
| multiplication(domain(domain(X_13)),domain(X_13)) != multiplication(domain(X_13),domain(X_13))
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(X_13),domain(X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),multiplication(domain(X_13),domain(X_13))) ),[0],$fot(multiplication(domain(domain(X_13)),domain(X_13)))]]) ).
cnf(refute_0_32,plain,
( addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != multiplication(domain(domain(X_13)),domain(X_13))
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(X_13),domain(X_13)) ),
inference(resolve,[$cnf( $equal(multiplication(domain(domain(X_13)),domain(X_13)),multiplication(domain(X_13),domain(X_13))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(X_13),domain(X_13)),
inference(resolve,[$cnf( $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),multiplication(domain(domain(X_13)),domain(X_13))) )],[refute_0_26,refute_0_32]) ).
cnf(refute_0_34,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_35,plain,
multiplication(domain(X_13),one) = domain(X_13),
inference(subst,[],[refute_0_34:[bind(A,$fot(domain(X_13)))]]) ).
cnf(refute_0_36,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_37,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_38,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_39,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_39:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_41,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_42,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
addition(one,domain(X_13)) = one,
inference(subst,[],[refute_0_43:[bind(X0,$fot(X_13))]]) ).
cnf(refute_0_45,plain,
multiplication(domain(X_13),addition(one,domain(X_13))) = multiplication(domain(X_13),addition(one,domain(X_13))),
introduced(tautology,[refl,[$fot(multiplication(domain(X_13),addition(one,domain(X_13))))]]) ).
cnf(refute_0_46,plain,
( addition(one,domain(X_13)) != one
| multiplication(domain(X_13),addition(one,domain(X_13))) != multiplication(domain(X_13),addition(one,domain(X_13)))
| multiplication(domain(X_13),addition(one,domain(X_13))) = multiplication(domain(X_13),one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(X_13),addition(one,domain(X_13))),multiplication(domain(X_13),addition(one,domain(X_13)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_47,plain,
( addition(one,domain(X_13)) != one
| multiplication(domain(X_13),addition(one,domain(X_13))) = multiplication(domain(X_13),one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(X_13),addition(one,domain(X_13))),multiplication(domain(X_13),addition(one,domain(X_13)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(domain(X_13),addition(one,domain(X_13))) = multiplication(domain(X_13),one),
inference(resolve,[$cnf( $equal(addition(one,domain(X_13)),one) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_50,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_21,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiplication(domain(X_13),addition(one,domain(X_13))) != multiplication(domain(X_13),one)
| multiplication(domain(X_13),one) != domain(X_13)
| multiplication(domain(X_13),addition(one,domain(X_13))) = domain(X_13) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(multiplication(domain(X_13),addition(one,domain(X_13))))),bind(Y,$fot(multiplication(domain(X_13),one))),bind(Z,$fot(domain(X_13)))]]) ).
cnf(refute_0_52,plain,
( multiplication(domain(X_13),one) != domain(X_13)
| multiplication(domain(X_13),addition(one,domain(X_13))) = domain(X_13) ),
inference(resolve,[$cnf( $equal(multiplication(domain(X_13),addition(one,domain(X_13))),multiplication(domain(X_13),one)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
multiplication(domain(X_13),addition(one,domain(X_13))) = domain(X_13),
inference(resolve,[$cnf( $equal(multiplication(domain(X_13),one),domain(X_13)) )],[refute_0_35,refute_0_52]) ).
cnf(refute_0_54,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_55,plain,
multiplication(X_79,addition(one,X_81)) = addition(multiplication(X_79,one),multiplication(X_79,X_81)),
inference(subst,[],[refute_0_54:[bind(A,$fot(X_79)),bind(B,$fot(one)),bind(C,$fot(X_81))]]) ).
cnf(refute_0_56,plain,
multiplication(X_79,one) = X_79,
inference(subst,[],[refute_0_34:[bind(A,$fot(X_79))]]) ).
cnf(refute_0_57,plain,
( multiplication(X_79,addition(one,X_81)) != addition(multiplication(X_79,one),multiplication(X_79,X_81))
| multiplication(X_79,one) != X_79
| multiplication(X_79,addition(one,X_81)) = addition(X_79,multiplication(X_79,X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_79,addition(one,X_81)),addition(multiplication(X_79,one),multiplication(X_79,X_81))) ),[1,0],$fot(X_79)]]) ).
cnf(refute_0_58,plain,
( multiplication(X_79,addition(one,X_81)) != addition(multiplication(X_79,one),multiplication(X_79,X_81))
| multiplication(X_79,addition(one,X_81)) = addition(X_79,multiplication(X_79,X_81)) ),
inference(resolve,[$cnf( $equal(multiplication(X_79,one),X_79) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiplication(X_79,addition(one,X_81)) = addition(X_79,multiplication(X_79,X_81)),
inference(resolve,[$cnf( $equal(multiplication(X_79,addition(one,X_81)),addition(multiplication(X_79,one),multiplication(X_79,X_81))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiplication(X_79,addition(one,X_81)) != addition(X_79,multiplication(X_79,X_81))
| addition(X_79,multiplication(X_79,X_81)) = multiplication(X_79,addition(one,X_81)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(X_79,addition(one,X_81)))),bind(Y,$fot(addition(X_79,multiplication(X_79,X_81))))]]) ).
cnf(refute_0_61,plain,
addition(X_79,multiplication(X_79,X_81)) = multiplication(X_79,addition(one,X_81)),
inference(resolve,[$cnf( $equal(multiplication(X_79,addition(one,X_81)),addition(X_79,multiplication(X_79,X_81))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = multiplication(domain(X_13),addition(one,domain(X_13))),
inference(subst,[],[refute_0_61:[bind(X_79,$fot(domain(X_13))),bind(X_81,$fot(domain(X_13)))]]) ).
cnf(refute_0_63,plain,
( addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != multiplication(domain(X_13),addition(one,domain(X_13)))
| multiplication(domain(X_13),addition(one,domain(X_13))) != domain(X_13)
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = domain(X_13) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))))),bind(Y,$fot(multiplication(domain(X_13),addition(one,domain(X_13))))),bind(Z,$fot(domain(X_13)))]]) ).
cnf(refute_0_64,plain,
( multiplication(domain(X_13),addition(one,domain(X_13))) != domain(X_13)
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = domain(X_13) ),
inference(resolve,[$cnf( $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),multiplication(domain(X_13),addition(one,domain(X_13)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) = domain(X_13),
inference(resolve,[$cnf( $equal(multiplication(domain(X_13),addition(one,domain(X_13))),domain(X_13)) )],[refute_0_53,refute_0_64]) ).
cnf(refute_0_66,plain,
( addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != domain(X_13)
| addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != multiplication(domain(X_13),domain(X_13))
| domain(X_13) = multiplication(domain(X_13),domain(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),multiplication(domain(X_13),domain(X_13))) ),[0],$fot(domain(X_13))]]) ).
cnf(refute_0_67,plain,
( addition(domain(X_13),multiplication(domain(X_13),domain(X_13))) != multiplication(domain(X_13),domain(X_13))
| domain(X_13) = multiplication(domain(X_13),domain(X_13)) ),
inference(resolve,[$cnf( $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),domain(X_13)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
domain(X_13) = multiplication(domain(X_13),domain(X_13)),
inference(resolve,[$cnf( $equal(addition(domain(X_13),multiplication(domain(X_13),domain(X_13))),multiplication(domain(X_13),domain(X_13))) )],[refute_0_33,refute_0_67]) ).
cnf(refute_0_69,plain,
( domain(X_13) != multiplication(domain(X_13),domain(X_13))
| multiplication(domain(X_13),domain(X_13)) = domain(X_13) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(domain(X_13))),bind(Y,$fot(multiplication(domain(X_13),domain(X_13))))]]) ).
cnf(refute_0_70,plain,
multiplication(domain(X_13),domain(X_13)) = domain(X_13),
inference(resolve,[$cnf( $equal(domain(X_13),multiplication(domain(X_13),domain(X_13))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_70:[bind(X_13,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_72,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) ),[0,0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_73,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_73,refute_0_0]) ).
cnf(refute_0_75,plain,
domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_76,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_75,refute_0_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n021.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 11:57:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.61
% 0.39/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.39/0.62
%------------------------------------------------------------------------------