TSTP Solution File: NUM458+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM458+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Mon Jul 18 12:26:50 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 56 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 27 ~; 17 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ) ).
fof(m__718,hypothesis,
aNaturalNumber0(xm) ).
fof(m__,conjecture,
( ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = xm )
| sdtlseqdt0(xm,xm) ) ).
fof(subgoal_0,plain,
( ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = xm )
=> sdtlseqdt0(xm,xm) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = xm )
=> sdtlseqdt0(xm,xm) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ sdtlseqdt0(xm,xm)
& ! [W0] :
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
aNaturalNumber0(xm),
inference(canonicalize,[],[m__718]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
inference(canonicalize,[],[m_AddZero]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ( ~ aNaturalNumber0(W0)
| W0 = sdtpldt0(sz00,W0) )
& ( ~ aNaturalNumber0(W0)
| sdtpldt0(W0,sz00) = W0 ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| sdtpldt0(W0,sz00) = W0 ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
aNaturalNumber0(sz00),
inference(canonicalize,[],[mSortsC]) ).
cnf(refute_0_0,plain,
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( sdtpldt0(xm,sz00) != xm
| ~ aNaturalNumber0(sz00) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(sz00))]]) ).
cnf(refute_0_2,plain,
aNaturalNumber0(xm),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ aNaturalNumber0(W0)
| sdtpldt0(W0,sz00) = W0 ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sz00) = xm ),
inference(subst,[],[refute_0_3:[bind(W0,$fot(xm))]]) ).
cnf(refute_0_5,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolve,[$cnf( aNaturalNumber0(xm) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( sdtpldt0(xm,sz00) != xm
| xm != xm
| sdtpldt0(xm,sz00) = xm ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtpldt0(xm,sz00),xm) ),[0],$fot(xm)]]) ).
cnf(refute_0_7,plain,
( xm != xm
| sdtpldt0(xm,sz00) = xm ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,sz00),xm) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( xm != xm
| ~ aNaturalNumber0(sz00) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,sz00),xm) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
xm = xm,
introduced(tautology,[refl,[$fot(xm)]]) ).
cnf(refute_0_10,plain,
~ aNaturalNumber0(sz00),
inference(resolve,[$cnf( $equal(xm,xm) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
aNaturalNumber0(sz00),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( aNaturalNumber0(sz00) )],[refute_0_11,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM458+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 13:25:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42
% 0.19/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------