TSTP Solution File: KLE076+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 02:15:04 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 28 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain4,axiom,
domain(zero) = zero ).
fof(goals,conjecture,
! [X0] : domain(multiplication(X0,domain(zero))) = zero ).
fof(subgoal_0,plain,
! [X0] : domain(multiplication(X0,domain(zero))) = zero,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : domain(multiplication(X0,domain(zero))) = zero,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : domain(multiplication(X0,domain(zero))) != zero,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != zero,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
domain(zero) = zero,
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_3,plain,
! [A] : multiplication(A,zero) = zero,
inference(canonicalize,[],[right_annihilation]) ).
fof(normalize_0_4,plain,
! [A] : multiplication(A,zero) = zero,
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_6,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != zero,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
domain(zero) = zero,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
multiplication(A,zero) = zero,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
multiplication(skolemFOFtoCNF_X0,zero) = zero,
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_4,plain,
domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(multiplication(skolemFOFtoCNF_X0,zero)),
introduced(tautology,[refl,[$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))]]) ).
cnf(refute_0_5,plain,
( domain(multiplication(skolemFOFtoCNF_X0,zero)) != domain(multiplication(skolemFOFtoCNF_X0,zero))
| multiplication(skolemFOFtoCNF_X0,zero) != zero
| domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(multiplication(skolemFOFtoCNF_X0,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_6,plain,
( multiplication(skolemFOFtoCNF_X0,zero) != zero
| domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero) ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( domain(multiplication(skolemFOFtoCNF_X0,zero)) != domain(zero)
| domain(zero) != zero
| domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero ),
inference(subst,[],[refute_0_12:[bind(X,$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))),bind(Y,$fot(domain(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_14,plain,
( domain(zero) != zero
| domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(zero)) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero,
inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_17,plain,
( domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1)))
| domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(domain(multiplication(X0,X1)))),bind(Y,$fot(domain(multiplication(X0,domain(X1)))))]]) ).
cnf(refute_0_18,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,X1)),domain(multiplication(X0,domain(X1)))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = domain(multiplication(skolemFOFtoCNF_X0,zero)),
inference(subst,[],[refute_0_18:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(zero))]]) ).
cnf(refute_0_20,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != domain(multiplication(skolemFOFtoCNF_X0,zero))
| domain(multiplication(skolemFOFtoCNF_X0,zero)) != zero
| domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
inference(subst,[],[refute_0_12:[bind(X,$fot(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))))),bind(Y,$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_21,plain,
( domain(multiplication(skolemFOFtoCNF_X0,zero)) != zero
| domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),domain(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero,
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),zero) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
( domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != zero
| zero != zero
| domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_24,plain,
( zero != zero
| domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
zero != zero,
inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_26,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 10:45:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------