TSTP Solution File: KLE066+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 02:15:01 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 44 unt; 0 def)
% Number of atoms : 128 ( 127 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 98 ( 49 ~; 44 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 43 ( 1 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
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(domain4,axiom,
domain(zero) = zero ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_1,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_3,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X0,X1] :
( multiplication(X0,X1) != zero
& multiplication(X0,domain(X1)) = zero ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != zero
& multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)) = zero ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)) = zero,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
domain(zero) = zero,
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_9,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_11,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != zero,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_0:[bind(X0,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_2,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))),
inference(subst,[],[refute_0_2:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_4,plain,
multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)) = zero,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)) != zero
| domain(zero) = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))),domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_6,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| domain(zero) = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)),zero) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
domain(zero) = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))),domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
domain(zero) = zero,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( domain(zero) != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| domain(zero) != zero
| zero = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(zero),domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) ),[0],$fot(zero)]]) ).
cnf(refute_0_10,plain,
( domain(zero) != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| zero = domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) ),
inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1)))
| domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(domain(multiplication(X0,X1)))),bind(Y,$fot(domain(multiplication(X0,domain(X1)))))]]) ).
cnf(refute_0_15,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,X1)),domain(multiplication(X0,domain(X1)))) )],[refute_0_2,refute_0_14]) ).
cnf(refute_0_16,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_15:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_17,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) = domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))),
inference(subst,[],[refute_0_15:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_18,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) != domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)))
| domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) != domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))))),bind(Y,$fot(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))))),bind(Z,$fot(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_21,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))) != domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))),domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1)))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X1))),domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))) != domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| zero != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| zero = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) ),[1],$fot(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_24,plain,
( zero != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| zero = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1)))),domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( domain(zero) != domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))
| zero = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(zero,domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) )],[refute_0_10,refute_0_24]) ).
cnf(refute_0_26,plain,
zero = domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(domain(zero),domain(multiplication(skolemFOFtoCNF_X0,domain(domain(skolemFOFtoCNF_X1))))) )],[refute_0_7,refute_0_25]) ).
cnf(refute_0_27,plain,
( zero != domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero ),
inference(subst,[],[refute_0_13:[bind(X,$fot(zero)),bind(Y,$fot(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_28,plain,
domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero,
inference(resolve,[$cnf( $equal(zero,domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_30,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),zero) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_1,refute_0_30]) ).
cnf(refute_0_32,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_33,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
inference(subst,[],[refute_0_32:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_34,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_35,plain,
multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero,
inference(subst,[],[refute_0_34:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_36,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),
introduced(tautology,[refl,[$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_37,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_38,plain,
( multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero),
inference(resolve,[$cnf( $equal(multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),zero) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero)
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) != multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero))),bind(Z,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_41,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) != multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) )],[refute_0_33,refute_0_41]) ).
cnf(refute_0_43,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[0],$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_44,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_46,plain,
( domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_47,plain,
( domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),zero) )],[refute_0_28,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero ),
inference(subst,[],[refute_0_19:[bind(X,$fot(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))),bind(Y,$fot(multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_50,plain,
( multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = zero,
inference(resolve,[$cnf( $equal(multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),zero) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != zero
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[1],$fot(zero)]]) ).
cnf(refute_0_53,plain,
( multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero ),
inference(resolve,[$cnf( $equal(multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),zero) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_44,refute_0_53]) ).
cnf(refute_0_55,plain,
multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),multiplication(zero,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),multiplication(domain(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_31,refute_0_54]) ).
cnf(refute_0_56,plain,
multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != zero,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_57,plain,
$false,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) )],[refute_0_55,refute_0_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 15:25:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------