TSTP Solution File: KLE056+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 29 unt; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 34 ~; 29 |; 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 : 27 ( 1 sgn 12 !; 1 ?)
% 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(goals,conjecture,
! [X0] :
( domain(X0) = zero
=> X0 = zero ) ).
fof(subgoal_0,plain,
! [X0] :
( domain(X0) = zero
=> X0 = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] :
( domain(X0) = zero
=> X0 = 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] :
( X0 != zero
& domain(X0) = zero ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( skolemFOFtoCNF_X0 != zero
& domain(skolemFOFtoCNF_X0) = zero ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
domain(skolemFOFtoCNF_X0) = zero,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_6,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_8,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_X0 != zero,
inference(conjunct,[],[normalize_0_3]) ).
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(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_0:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_2,plain,
domain(skolemFOFtoCNF_X0) = zero,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) != zero
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_4,plain,
( addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),zero) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
addition(skolemFOFtoCNF_X0,zero) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_8,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
multiplication(zero,skolemFOFtoCNF_X0) = zero,
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_10,plain,
addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),
introduced(tautology,[refl,[$fot(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_11,plain,
( addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0))
| multiplication(zero,skolemFOFtoCNF_X0) != zero
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = addition(skolemFOFtoCNF_X0,zero) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_12,plain,
( multiplication(zero,skolemFOFtoCNF_X0) != zero
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = addition(skolemFOFtoCNF_X0,zero) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = addition(skolemFOFtoCNF_X0,zero),
inference(resolve,[$cnf( $equal(multiplication(zero,skolemFOFtoCNF_X0),zero) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != addition(skolemFOFtoCNF_X0,zero)
| addition(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = skolemFOFtoCNF_X0 ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)))),bind(Y,$fot(addition(skolemFOFtoCNF_X0,zero))),bind(Z,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_20,plain,
( addition(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X0,zero)) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) = skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,zero),skolemFOFtoCNF_X0) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
( addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_23,plain,
( addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),skolemFOFtoCNF_X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_25,plain,
( domain(skolemFOFtoCNF_X0) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = multiplication(zero,skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_26,plain,
( domain(skolemFOFtoCNF_X0) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = multiplication(zero,skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = multiplication(zero,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),zero) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != multiplication(zero,skolemFOFtoCNF_X0)
| multiplication(zero,skolemFOFtoCNF_X0) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = zero ),
inference(subst,[],[refute_0_18:[bind(X,$fot(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0))),bind(Y,$fot(multiplication(zero,skolemFOFtoCNF_X0))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_29,plain,
( multiplication(zero,skolemFOFtoCNF_X0) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = zero ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),multiplication(zero,skolemFOFtoCNF_X0)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = zero,
inference(resolve,[$cnf( $equal(multiplication(zero,skolemFOFtoCNF_X0),zero) )],[refute_0_9,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != zero
| skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| skolemFOFtoCNF_X0 = zero ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[1],$fot(zero)]]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| skolemFOFtoCNF_X0 = zero ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)
| skolemFOFtoCNF_X0 = zero ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_23,refute_0_32]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_X0 = zero,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(zero,skolemFOFtoCNF_X0)),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_5,refute_0_33]) ).
cnf(refute_0_35,plain,
skolemFOFtoCNF_X0 != zero,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,zero) )],[refute_0_34,refute_0_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 14:07:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------