TSTP Solution File: NUM494+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : 300s
% DateTime : Sun May 5 08:32:48 EDT 2024
% Result : Theorem 13.58s 2.37s
% Output : Refutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 108 ( 22 unt; 0 def)
% Number of atoms : 448 ( 178 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 562 ( 222 ~; 201 |; 114 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 143 ( 124 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f68085,plain,
$false,
inference(resolution,[],[f68084,f216]) ).
fof(f216,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f68084,plain,
~ aNaturalNumber0(sz00),
inference(resolution,[],[f42046,f305]) ).
fof(f305,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[],[f303,f239]) ).
fof(f239,plain,
! [X0] :
( sP5(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( sP5(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f66,f127,f126]) ).
fof(f126,plain,
! [X0] :
( sP4(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f127,plain,
! [X0] :
( ( isPrime0(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f66,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f303,plain,
( ~ sP5(sz00)
| ~ isPrime0(sz00) ),
inference(resolution,[],[f230,f289]) ).
fof(f289,plain,
~ sP4(sz00),
inference(equality_resolution,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sz00 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ( sP4(X0)
| ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& aNaturalNumber0(sK14(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f156,f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& aNaturalNumber0(sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(rectify,[],[f155]) ).
fof(f155,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f230,plain,
! [X0] :
( sP4(X0)
| ~ isPrime0(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ( ( isPrime0(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ isPrime0(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f42046,plain,
isPrime0(sz00),
inference(backward_demodulation,[],[f189,f42039]) ).
fof(f42039,plain,
sz00 = xp,
inference(resolution,[],[f42038,f216]) ).
fof(f42038,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = xp ),
inference(resolution,[],[f42037,f178]) ).
fof(f178,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f42037,plain,
( ~ aNaturalNumber0(xn)
| sz00 = xp
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[],[f42036,f179]) ).
fof(f179,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f42036,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| sz00 = xp
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f42033,f244]) ).
fof(f244,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f42033,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sz00) ),
inference(backward_demodulation,[],[f41951,f42026]) ).
fof(f42026,plain,
xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm)),
inference(resolution,[],[f42025,f180]) ).
fof(f180,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f42025,plain,
( ~ aNaturalNumber0(xp)
| xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm)) ),
inference(resolution,[],[f42024,f178]) ).
fof(f42024,plain,
( ~ aNaturalNumber0(xn)
| xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f42022,f179]) ).
fof(f42022,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f41931,f244]) ).
fof(f41931,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literal_removal,[],[f41820]) ).
fof(f41820,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[],[f5899,f29245]) ).
fof(f29245,plain,
sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(resolution,[],[f29244,f180]) ).
fof(f29244,plain,
( ~ aNaturalNumber0(xp)
| sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(equality_resolution,[],[f26792]) ).
fof(f26792,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[],[f26784,f26783]) ).
fof(f26783,plain,
sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xm,xr),xp),
inference(forward_demodulation,[],[f26768,f851]) ).
fof(f851,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[],[f568,f179]) ).
fof(f568,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xn) = sdtpldt0(xn,X0) ),
inference(resolution,[],[f246,f178]) ).
fof(f246,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f26768,plain,
sdtpldt0(xm,xn) = sdtpldt0(sdtpldt0(xm,xr),xp),
inference(resolution,[],[f26734,f179]) ).
fof(f26734,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xn) = sdtpldt0(sdtpldt0(X0,xr),xp) ),
inference(forward_demodulation,[],[f26718,f934]) ).
fof(f934,plain,
xn = sdtpldt0(xr,xp),
inference(forward_demodulation,[],[f920,f176]) ).
fof(f176,plain,
xn = sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& xn = sdtpldt0(xp,xr)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f920,plain,
sdtpldt0(xp,xr) = sdtpldt0(xr,xp),
inference(resolution,[],[f570,f175]) ).
fof(f175,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f570,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) = sdtpldt0(X0,xp) ),
inference(resolution,[],[f246,f180]) ).
fof(f26718,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,xr),xp) = sdtpldt0(X0,sdtpldt0(xr,xp)) ),
inference(resolution,[],[f3470,f175]) ).
fof(f3470,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X1,X0),xp) = sdtpldt0(X1,sdtpldt0(X0,xp)) ),
inference(resolution,[],[f274,f180]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f26784,plain,
! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xm,xr),xp),X0)
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[],[f901,f26783]) ).
fof(f901,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xm,xr),xp),X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xm,xr),xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[],[f899,f885]) ).
fof(f885,plain,
sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
inference(resolution,[],[f569,f175]) ).
fof(f569,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xm) = sdtpldt0(xm,X0) ),
inference(resolution,[],[f246,f179]) ).
fof(f899,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xm,xr),xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[],[f173,f885]) ).
fof(f173,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f5899,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sdtpldt0(X1,X0))
| sdtmndt0(sdtpldt0(X1,X0),X1) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f5778]) ).
fof(f5778,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| sdtmndt0(sdtpldt0(X1,X0),X1) = X0
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X1) ),
inference(resolution,[],[f291,f298]) ).
fof(f298,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f272]) ).
fof(f272,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK17(X0,X1)) = X1
& aNaturalNumber0(sK17(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f170,f171]) ).
fof(f171,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK17(X0,X1)) = X1
& aNaturalNumber0(sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f170,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f291,plain,
! [X2,X0] :
( ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f252]) ).
fof(f252,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f41951,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sz00 = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sz00) ),
inference(duplicate_literal_removal,[],[f41799]) ).
fof(f41799,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sz00 = sdtmndt0(sdtpldt0(xn,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[],[f5899,f21651]) ).
fof(f21651,plain,
sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xn,xm),sz00),
inference(resolution,[],[f14199,f179]) ).
fof(f14199,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(sdtpldt0(xn,X0),sz00) ),
inference(resolution,[],[f433,f178]) ).
fof(f433,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) = sdtpldt0(sdtpldt0(X1,X0),sz00) ),
inference(resolution,[],[f244,f224]) ).
fof(f224,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f189,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f54,f131]) ).
fof(f131,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 15:09:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (22330)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (22333)WARNING: value z3 for option sas not known
% 0.15/0.37 % (22334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (22332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (22337)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37 % (22336)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37 % (22331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (22335)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37 % (22333)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 Detected minimum model sizes of [3]
% 0.15/0.38 Detected maximum model sizes of [max]
% 0.15/0.38 TRYING [3]
% 0.21/0.42 Detected minimum model sizes of [3]
% 0.21/0.42 Detected maximum model sizes of [max]
% 0.21/0.42 TRYING [4]
% 0.21/0.42 TRYING [3]
% 0.21/0.49 TRYING [4]
% 0.21/0.53 TRYING [5]
% 2.10/0.70 TRYING [5]
% 2.71/0.76 TRYING [6]
% 6.28/1.26 TRYING [7]
% 6.84/1.36 TRYING [6]
% 7.94/1.49 Detected minimum model sizes of [3]
% 7.94/1.49 Detected maximum model sizes of [max]
% 7.94/1.49 TRYING [3]
% 8.22/1.54 TRYING [4]
% 9.95/1.78 TRYING [5]
% 13.58/2.37 % (22336)First to succeed.
% 13.58/2.37 % (22336)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22330"
% 13.58/2.37 % (22336)Refutation found. Thanks to Tanya!
% 13.58/2.37 % SZS status Theorem for theBenchmark
% 13.58/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 13.58/2.37 % (22336)------------------------------
% 13.58/2.37 % (22336)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 13.58/2.37 % (22336)Termination reason: Refutation
% 13.58/2.37
% 13.58/2.37 % (22336)Memory used [KB]: 28298
% 13.58/2.37 % (22336)Time elapsed: 1.998 s
% 13.58/2.37 % (22336)Instructions burned: 6421 (million)
% 13.58/2.37 % (22330)Success in time 2.002 s
%------------------------------------------------------------------------------