TSTP Solution File: KLE054+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE054+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 127 ( 80 unt; 0 def)
% Number of atoms : 196 ( 195 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 144 ( 75 ~; 69 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 157 ( 10 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = 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(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0) ).
fof(subgoal_0,plain,
! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) != domain(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_7,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_9,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_11,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_13,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_15,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_8,plain,
domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),
introduced(tautology,[refl,[$fot(domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_9,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))
| domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))) ),[1,0],$fot(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_10,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
inference(resolve,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_14,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) != domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))
| domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)))),bind(Y,$fot(domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)))),bind(Z,$fot(domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))))]]) ).
cnf(refute_0_19,plain,
( domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)) != domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
inference(resolve,[$cnf( $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)),domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),
inference(resolve,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0)),domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) != domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) ),[0],$fot(domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_22,plain,
( domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)),domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_25,plain,
domain(multiplication(X0,addition(X_42,one))) = domain(multiplication(X0,domain(addition(X_42,one)))),
inference(subst,[],[refute_0_24:[bind(X1,$fot(addition(X_42,one)))]]) ).
cnf(refute_0_26,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_27,plain,
multiplication(X_38,addition(X_39,one)) = addition(multiplication(X_38,X_39),multiplication(X_38,one)),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_38)),bind(B,$fot(X_39)),bind(C,$fot(one))]]) ).
cnf(refute_0_28,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_29,plain,
multiplication(X_38,one) = X_38,
inference(subst,[],[refute_0_28:[bind(A,$fot(X_38))]]) ).
cnf(refute_0_30,plain,
( multiplication(X_38,addition(X_39,one)) != addition(multiplication(X_38,X_39),multiplication(X_38,one))
| multiplication(X_38,one) != X_38
| multiplication(X_38,addition(X_39,one)) = addition(multiplication(X_38,X_39),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_38,addition(X_39,one)),addition(multiplication(X_38,X_39),multiplication(X_38,one))) ),[1,1],$fot(X_38)]]) ).
cnf(refute_0_31,plain,
( multiplication(X_38,addition(X_39,one)) != addition(multiplication(X_38,X_39),multiplication(X_38,one))
| multiplication(X_38,addition(X_39,one)) = addition(multiplication(X_38,X_39),X_38) ),
inference(resolve,[$cnf( $equal(multiplication(X_38,one),X_38) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiplication(X_38,addition(X_39,one)) = addition(multiplication(X_38,X_39),X_38),
inference(resolve,[$cnf( $equal(multiplication(X_38,addition(X_39,one)),addition(multiplication(X_38,X_39),multiplication(X_38,one))) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
addition(multiplication(X_38,X_39),X_38) = addition(X_38,multiplication(X_38,X_39)),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_38)),bind(B,$fot(multiplication(X_38,X_39)))]]) ).
cnf(refute_0_34,plain,
( addition(multiplication(X_38,X_39),X_38) != addition(X_38,multiplication(X_38,X_39))
| multiplication(X_38,addition(X_39,one)) != addition(multiplication(X_38,X_39),X_38)
| multiplication(X_38,addition(X_39,one)) = addition(X_38,multiplication(X_38,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_38,addition(X_39,one)),addition(multiplication(X_38,X_39),X_38)) ),[1],$fot(addition(X_38,multiplication(X_38,X_39)))]]) ).
cnf(refute_0_35,plain,
( multiplication(X_38,addition(X_39,one)) != addition(multiplication(X_38,X_39),X_38)
| multiplication(X_38,addition(X_39,one)) = addition(X_38,multiplication(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_38,X_39),X_38),addition(X_38,multiplication(X_38,X_39))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiplication(X_38,addition(X_39,one)) = addition(X_38,multiplication(X_38,X_39)),
inference(resolve,[$cnf( $equal(multiplication(X_38,addition(X_39,one)),addition(multiplication(X_38,X_39),X_38)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
multiplication(X0,addition(X_42,one)) = addition(X0,multiplication(X0,X_42)),
inference(subst,[],[refute_0_36:[bind(X_38,$fot(X0)),bind(X_39,$fot(X_42))]]) ).
cnf(refute_0_38,plain,
( domain(multiplication(X0,addition(X_42,one))) != domain(multiplication(X0,domain(addition(X_42,one))))
| multiplication(X0,addition(X_42,one)) != addition(X0,multiplication(X0,X_42))
| domain(addition(X0,multiplication(X0,X_42))) = domain(multiplication(X0,domain(addition(X_42,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(X0,addition(X_42,one))),domain(multiplication(X0,domain(addition(X_42,one))))) ),[0,0],$fot(addition(X0,multiplication(X0,X_42)))]]) ).
cnf(refute_0_39,plain,
( domain(multiplication(X0,addition(X_42,one))) != domain(multiplication(X0,domain(addition(X_42,one))))
| domain(addition(X0,multiplication(X0,X_42))) = domain(multiplication(X0,domain(addition(X_42,one)))) ),
inference(resolve,[$cnf( $equal(multiplication(X0,addition(X_42,one)),addition(X0,multiplication(X0,X_42))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
domain(addition(X0,multiplication(X0,X_42))) = domain(multiplication(X0,domain(addition(X_42,one)))),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,addition(X_42,one))),domain(multiplication(X0,domain(addition(X_42,one))))) )],[refute_0_25,refute_0_39]) ).
cnf(refute_0_41,plain,
domain(multiplication(X_25,addition(X_11,one))) = domain(multiplication(X_25,domain(addition(X_11,one)))),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_25)),bind(X1,$fot(addition(X_11,one)))]]) ).
cnf(refute_0_42,plain,
domain(addition(X_11,one)) = addition(domain(X_11),domain(one)),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_11)),bind(X1,$fot(one))]]) ).
cnf(refute_0_43,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_44,plain,
addition(one,multiplication(domain(one),one)) = multiplication(domain(one),one),
inference(subst,[],[refute_0_43:[bind(X0,$fot(one))]]) ).
cnf(refute_0_45,plain,
multiplication(domain(one),one) = domain(one),
inference(subst,[],[refute_0_28:[bind(A,$fot(domain(one)))]]) ).
cnf(refute_0_46,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| multiplication(domain(one),one) != domain(one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) ),[0,1],$fot(domain(one))]]) ).
cnf(refute_0_47,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(resolve,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_50,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_6:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_51,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_52,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
addition(one,domain(one)) = one,
inference(subst,[],[refute_0_53:[bind(X0,$fot(one))]]) ).
cnf(refute_0_55,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| addition(one,domain(one)) != one
| one = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) ),[0],$fot(one)]]) ).
cnf(refute_0_56,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),one) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiplication(domain(one),one) != domain(one)
| one != multiplication(domain(one),one)
| one = domain(one) ),
introduced(tautology,[equality,[$cnf( $equal(one,multiplication(domain(one),one)) ),[1],$fot(domain(one))]]) ).
cnf(refute_0_58,plain,
( one != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_45,refute_0_57]) ).
cnf(refute_0_59,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(one,multiplication(domain(one),one)) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
one = domain(one),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) )],[refute_0_48,refute_0_59]) ).
cnf(refute_0_61,plain,
( one != domain(one)
| domain(one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(domain(one)))]]) ).
cnf(refute_0_62,plain,
domain(one) = one,
inference(resolve,[$cnf( $equal(one,domain(one)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( domain(addition(X_11,one)) != addition(domain(X_11),domain(one))
| domain(one) != one
| domain(addition(X_11,one)) = addition(domain(X_11),one) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(X_11,one)),addition(domain(X_11),domain(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_64,plain,
( domain(addition(X_11,one)) != addition(domain(X_11),domain(one))
| domain(addition(X_11,one)) = addition(domain(X_11),one) ),
inference(resolve,[$cnf( $equal(domain(one),one) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
domain(addition(X_11,one)) = addition(domain(X_11),one),
inference(resolve,[$cnf( $equal(domain(addition(X_11,one)),addition(domain(X_11),domain(one))) )],[refute_0_42,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(one,domain(X_11)) = one,
inference(subst,[],[refute_0_53:[bind(X0,$fot(X_11))]]) ).
cnf(refute_0_67,plain,
addition(domain(X_11),one) = addition(one,domain(X_11)),
inference(subst,[],[refute_0_6:[bind(A,$fot(one)),bind(B,$fot(domain(X_11)))]]) ).
cnf(refute_0_68,plain,
( addition(domain(X_11),one) != addition(one,domain(X_11))
| addition(one,domain(X_11)) != one
| addition(domain(X_11),one) = one ),
inference(subst,[],[refute_0_17:[bind(X,$fot(addition(domain(X_11),one))),bind(Y,$fot(addition(one,domain(X_11)))),bind(Z,$fot(one))]]) ).
cnf(refute_0_69,plain,
( addition(one,domain(X_11)) != one
| addition(domain(X_11),one) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X_11),one),addition(one,domain(X_11))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
addition(domain(X_11),one) = one,
inference(resolve,[$cnf( $equal(addition(one,domain(X_11)),one) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( addition(domain(X_11),one) != one
| domain(addition(X_11,one)) != addition(domain(X_11),one)
| domain(addition(X_11,one)) = one ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(X_11,one)),addition(domain(X_11),one)) ),[1],$fot(one)]]) ).
cnf(refute_0_72,plain,
( domain(addition(X_11,one)) != addition(domain(X_11),one)
| domain(addition(X_11,one)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X_11),one),one) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
domain(addition(X_11,one)) = one,
inference(resolve,[$cnf( $equal(domain(addition(X_11,one)),addition(domain(X_11),one)) )],[refute_0_65,refute_0_72]) ).
cnf(refute_0_74,plain,
( domain(addition(X_11,one)) != one
| domain(multiplication(X_25,addition(X_11,one))) != domain(multiplication(X_25,domain(addition(X_11,one))))
| domain(multiplication(X_25,addition(X_11,one))) = domain(multiplication(X_25,one)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(X_25,addition(X_11,one))),domain(multiplication(X_25,domain(addition(X_11,one))))) ),[1,0,1],$fot(one)]]) ).
cnf(refute_0_75,plain,
( domain(multiplication(X_25,addition(X_11,one))) != domain(multiplication(X_25,domain(addition(X_11,one))))
| domain(multiplication(X_25,addition(X_11,one))) = domain(multiplication(X_25,one)) ),
inference(resolve,[$cnf( $equal(domain(addition(X_11,one)),one) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
domain(multiplication(X_25,addition(X_11,one))) = domain(multiplication(X_25,one)),
inference(resolve,[$cnf( $equal(domain(multiplication(X_25,addition(X_11,one))),domain(multiplication(X_25,domain(addition(X_11,one))))) )],[refute_0_41,refute_0_75]) ).
cnf(refute_0_77,plain,
multiplication(X_25,one) = X_25,
inference(subst,[],[refute_0_28:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_78,plain,
domain(multiplication(X_25,one)) = domain(multiplication(X_25,one)),
introduced(tautology,[refl,[$fot(domain(multiplication(X_25,one)))]]) ).
cnf(refute_0_79,plain,
( domain(multiplication(X_25,one)) != domain(multiplication(X_25,one))
| multiplication(X_25,one) != X_25
| domain(multiplication(X_25,one)) = domain(X_25) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(X_25,one)),domain(multiplication(X_25,one))) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_80,plain,
( multiplication(X_25,one) != X_25
| domain(multiplication(X_25,one)) = domain(X_25) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X_25,one)),domain(multiplication(X_25,one))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
domain(multiplication(X_25,one)) = domain(X_25),
inference(resolve,[$cnf( $equal(multiplication(X_25,one),X_25) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( domain(multiplication(X_25,addition(X_11,one))) != domain(multiplication(X_25,one))
| domain(multiplication(X_25,one)) != domain(X_25)
| domain(multiplication(X_25,addition(X_11,one))) = domain(X_25) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(multiplication(X_25,addition(X_11,one))),domain(X_25)) ),[0],$fot(domain(multiplication(X_25,one)))]]) ).
cnf(refute_0_83,plain,
( domain(multiplication(X_25,addition(X_11,one))) != domain(multiplication(X_25,one))
| domain(multiplication(X_25,addition(X_11,one))) = domain(X_25) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X_25,one)),domain(X_25)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
domain(multiplication(X_25,addition(X_11,one))) = domain(X_25),
inference(resolve,[$cnf( $equal(domain(multiplication(X_25,addition(X_11,one))),domain(multiplication(X_25,one))) )],[refute_0_76,refute_0_83]) ).
cnf(refute_0_85,plain,
domain(multiplication(X0,addition(X_42,one))) = domain(X0),
inference(subst,[],[refute_0_84:[bind(X_11,$fot(X_42)),bind(X_25,$fot(X0))]]) ).
cnf(refute_0_86,plain,
( domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1)))
| domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(multiplication(X0,X1)))),bind(Y,$fot(domain(multiplication(X0,domain(X1)))))]]) ).
cnf(refute_0_87,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,X1)),domain(multiplication(X0,domain(X1)))) )],[refute_0_24,refute_0_86]) ).
cnf(refute_0_88,plain,
domain(multiplication(X0,domain(addition(X_42,one)))) = domain(multiplication(X0,addition(X_42,one))),
inference(subst,[],[refute_0_87:[bind(X1,$fot(addition(X_42,one)))]]) ).
cnf(refute_0_89,plain,
( domain(multiplication(X0,addition(X_42,one))) != domain(X0)
| domain(multiplication(X0,domain(addition(X_42,one)))) != domain(multiplication(X0,addition(X_42,one)))
| domain(multiplication(X0,domain(addition(X_42,one)))) = domain(X0) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(domain(multiplication(X0,domain(addition(X_42,one)))))),bind(Y,$fot(domain(multiplication(X0,addition(X_42,one))))),bind(Z,$fot(domain(X0)))]]) ).
cnf(refute_0_90,plain,
( domain(multiplication(X0,addition(X_42,one))) != domain(X0)
| domain(multiplication(X0,domain(addition(X_42,one)))) = domain(X0) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,domain(addition(X_42,one)))),domain(multiplication(X0,addition(X_42,one)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
domain(multiplication(X0,domain(addition(X_42,one)))) = domain(X0),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,addition(X_42,one))),domain(X0)) )],[refute_0_85,refute_0_90]) ).
cnf(refute_0_92,plain,
( domain(addition(X0,multiplication(X0,X_42))) != domain(multiplication(X0,domain(addition(X_42,one))))
| domain(multiplication(X0,domain(addition(X_42,one)))) != domain(X0)
| domain(addition(X0,multiplication(X0,X_42))) = domain(X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(addition(X0,multiplication(X0,X_42))),domain(X0)) ),[0],$fot(domain(multiplication(X0,domain(addition(X_42,one)))))]]) ).
cnf(refute_0_93,plain,
( domain(addition(X0,multiplication(X0,X_42))) != domain(multiplication(X0,domain(addition(X_42,one))))
| domain(addition(X0,multiplication(X0,X_42))) = domain(X0) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,domain(addition(X_42,one)))),domain(X0)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
domain(addition(X0,multiplication(X0,X_42))) = domain(X0),
inference(resolve,[$cnf( $equal(domain(addition(X0,multiplication(X0,X_42))),domain(multiplication(X0,domain(addition(X_42,one))))) )],[refute_0_40,refute_0_93]) ).
cnf(refute_0_95,plain,
domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_94:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X_42,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_96,plain,
( domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) ),[0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_97,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_97,refute_0_23]) ).
cnf(refute_0_99,plain,
domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_99,refute_0_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE054+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 : n024.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 11:42:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------