TSTP Solution File: NUM472+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM472+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:26:58 EDT 2022
% Result : Theorem 0.38s 0.58s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 63 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 25 ~; 14 |; 20 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 3 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1324_04,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W0) )
& doDivides0(xl,sdtpldt0(xm,xn)) ) ).
fof(m__,conjecture,
( ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn)) ) ).
fof(subgoal_0,plain,
( ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = sdtpldt0(xm,xn) )
=> sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = sdtpldt0(xm,xn) )
=> sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
& ! [W0] :
( sdtpldt0(xm,W0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( sdtpldt0(xm,W0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( sdtpldt0(xm,W0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(W0) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm)
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[m__1324_04]) ).
fof(normalize_0_4,plain,
? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0)
& aNaturalNumber0(skolemFOFtoCNF_W0) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(canonicalize,[],[m__1324]) ).
fof(normalize_0_8,plain,
aNaturalNumber0(xn),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( sdtpldt0(xm,W0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(W0) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( sdtpldt0(xm,W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtpldt0(xm,W0),sdtpldt0(xm,xn)) ),[1],$fot(sdtasdt0(xl,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_3,plain,
( sdtpldt0(xm,W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( sdtpldt0(xm,W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| ~ aNaturalNumber0(W0) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,W0),sdtpldt0(xm,xn)) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| ~ aNaturalNumber0(xn) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xn))]]) ).
cnf(refute_0_6,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) ),[1],$fot(sdtasdt0(xl,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_7,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| ~ aNaturalNumber0(xn) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0) = sdtasdt0(xl,skolemFOFtoCNF_W0),
introduced(tautology,[refl,[$fot(sdtasdt0(xl,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_10,plain,
~ aNaturalNumber0(xn),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
aNaturalNumber0(xn),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( aNaturalNumber0(xn) )],[refute_0_11,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM472+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.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 Jul 7 15:52:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.58
% 0.38/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.38/0.58
%------------------------------------------------------------------------------