TSTP Solution File: NUM528+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM528+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n029.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 : Thu Aug 31 12:10:56 EDT 2023
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 22
% Syntax : Number of formulae : 138 ( 22 unt; 0 def)
% Number of atoms : 532 ( 189 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 665 ( 271 ~; 287 |; 79 &)
% ( 9 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 144 (; 134 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1293,plain,
$false,
inference(subsumption_resolution,[],[f1274,f238]) ).
fof(f238,plain,
~ isPrime0(sz10),
inference(subsumption_resolution,[],[f226,f157]) ).
fof(f157,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mSortsC_01) ).
fof(f226,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(equality_resolution,[],[f171]) ).
fof(f171,plain,
! [X0] :
( sz10 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK0(X0) != X0
& sz10 != sK0(X0)
& doDivides0(sK0(X0),X0)
& aNaturalNumber0(sK0(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f124,f125]) ).
fof(f125,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK0(X0) != X0
& sz10 != sK0(X0)
& doDivides0(sK0(X0),X0)
& aNaturalNumber0(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0] :
( ( ( isPrime0(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 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ( ( isPrime0(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 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( ( isPrime0(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 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,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/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mDefPrime) ).
fof(f1274,plain,
isPrime0(sz10),
inference(superposition,[],[f142,f1273]) ).
fof(f1273,plain,
sz10 = xp,
inference(subsumption_resolution,[],[f1270,f146]) ).
fof(f146,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
( sz00 != xp
& sz00 != xm
& sz00 != xn
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__2987) ).
fof(f1270,plain,
( sz10 = xp
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f1240,f159]) ).
fof(f159,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mLERefl) ).
fof(f1240,plain,
( ~ sdtlseqdt0(xn,xn)
| sz10 = xp ),
inference(duplicate_literal_removal,[],[f1239]) ).
fof(f1239,plain,
( ~ sdtlseqdt0(xn,xn)
| sz10 = xp
| sz10 = xp ),
inference(superposition,[],[f1207,f1208]) ).
fof(f1208,plain,
( xn = xm
| sz10 = xp ),
inference(resolution,[],[f1207,f291]) ).
fof(f291,plain,
( sdtlseqdt0(xn,xm)
| xn = xm ),
inference(subsumption_resolution,[],[f290,f146]) ).
fof(f290,plain,
( sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| xn = xm ),
inference(subsumption_resolution,[],[f287,f147]) ).
fof(f147,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f287,plain,
( sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xn = xm ),
inference(resolution,[],[f185,f141]) ).
fof(f141,plain,
( ~ sdtlseqdt0(xm,xn)
| xn = xm ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( ~ sdtlseqdt0(xm,xn)
| xn = xm ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xn != xm ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
( sdtlseqdt0(xm,xn)
& xn != xm ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mLETotal) ).
fof(f1207,plain,
( ~ sdtlseqdt0(xn,xm)
| sz10 = xp ),
inference(subsumption_resolution,[],[f1206,f1190]) ).
fof(f1190,plain,
( sz00 != sdtasdt0(xn,xn)
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f1189,f147]) ).
fof(f1189,plain,
( sz00 != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f1176,f150]) ).
fof(f150,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f1176,plain,
( sz00 != sdtasdt0(xn,xn)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,xm) ),
inference(duplicate_literal_removal,[],[f1170]) ).
fof(f1170,plain,
( sz00 != sdtasdt0(xn,xn)
| sz00 = xm
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,xm) ),
inference(superposition,[],[f192,f717]) ).
fof(f717,plain,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f563,f715]) ).
fof(f715,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(subsumption_resolution,[],[f261,f714]) ).
fof(f714,plain,
aNaturalNumber0(xq),
inference(subsumption_resolution,[],[f713,f148]) ).
fof(f148,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f713,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f712,f146]) ).
fof(f712,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f711,f151]) ).
fof(f151,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f711,plain,
( aNaturalNumber0(xq)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f710,f153]) ).
fof(f153,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3046) ).
fof(f710,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f234,f143]) ).
fof(f143,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3059) ).
fof(f234,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f199]) ).
fof(f199,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mDefQuot) ).
fof(f261,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq) ),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f260,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[],[f259,f181]) ).
fof(f181,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mSortsB_02) ).
fof(f259,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(subsumption_resolution,[],[f258,f148]) ).
fof(f258,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f181,f144]) ).
fof(f144,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3082) ).
fof(f563,plain,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f562,f456]) ).
fof(f456,plain,
( sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(subsumption_resolution,[],[f455,f148]) ).
fof(f455,plain,
( sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f447,f151]) ).
fof(f447,plain,
( sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f421,f145]) ).
fof(f145,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3014) ).
fof(f421,plain,
! [X2,X3] :
( sdtlseqdt0(X2,sdtasdt0(X3,X2))
| sz00 = X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(duplicate_literal_removal,[],[f412]) ).
fof(f412,plain,
! [X2,X3] :
( sdtlseqdt0(X2,sdtasdt0(X3,X2))
| sz00 = X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(superposition,[],[f186,f183]) ).
fof(f183,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mMulComm) ).
fof(f186,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mMonMul2) ).
fof(f562,plain,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f537,f267]) ).
fof(f267,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(subsumption_resolution,[],[f266,f147]) ).
fof(f266,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xm) ),
inference(duplicate_literal_removal,[],[f265]) ).
fof(f265,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f263,f181]) ).
fof(f263,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(subsumption_resolution,[],[f262,f148]) ).
fof(f262,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f181,f145]) ).
fof(f537,plain,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(resolution,[],[f203,f154]) ).
fof(f154,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3152) ).
fof(f203,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mLEAsym) ).
fof(f192,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X0
| sz00 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mZeroMul) ).
fof(f1206,plain,
( sz10 = xp
| ~ sdtlseqdt0(xn,xm)
| sz00 = sdtasdt0(xn,xn) ),
inference(subsumption_resolution,[],[f1202,f267]) ).
fof(f1202,plain,
( sz10 = xp
| ~ sdtlseqdt0(xn,xm)
| sz00 = sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[],[f1192,f792]) ).
fof(f792,plain,
! [X5] :
( sz10 = sdtsldt0(X5,X5)
| sz00 = X5
| ~ aNaturalNumber0(X5) ),
inference(subsumption_resolution,[],[f787,f157]) ).
fof(f787,plain,
! [X5] :
( sz10 = sdtsldt0(X5,X5)
| ~ aNaturalNumber0(sz10)
| sz00 = X5
| ~ aNaturalNumber0(X5) ),
inference(duplicate_literal_removal,[],[f774]) ).
fof(f774,plain,
! [X5] :
( sz10 = sdtsldt0(X5,X5)
| ~ aNaturalNumber0(sz10)
| sz00 = X5
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X5) ),
inference(superposition,[],[f243,f164]) ).
fof(f164,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m_MulUnit) ).
fof(f243,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f241,f242]) ).
fof(f242,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f235,f181]) ).
fof(f235,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f134,f135]) ).
fof(f135,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',mDefDiv) ).
fof(f241,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f232,f181]) ).
fof(f232,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f201]) ).
fof(f201,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f1192,plain,
( xp = sdtsldt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f924,f1190]) ).
fof(f924,plain,
( xp = sdtsldt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn))
| sz00 = sdtasdt0(xn,xn)
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f923,f267]) ).
fof(f923,plain,
( xp = sdtsldt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn))
| sz00 = sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(subsumption_resolution,[],[f907,f148]) ).
fof(f907,plain,
( xp = sdtsldt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| sz00 = sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(superposition,[],[f790,f725]) ).
fof(f725,plain,
( sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(superposition,[],[f145,f717]) ).
fof(f790,plain,
! [X0,X1] :
( sdtsldt0(sdtasdt0(X1,X0),X0) = X1
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f771]) ).
fof(f771,plain,
! [X0,X1] :
( sdtsldt0(sdtasdt0(X1,X0),X0) = X1
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(superposition,[],[f243,f183]) ).
fof(f142,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238',m__3025) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM528+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.20/0.36 % Computer : n029.cluster.edu
% 0.20/0.36 % Model : x86_64 x86_64
% 0.20/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.36 % Memory : 8042.1875MB
% 0.20/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.36 % CPULimit : 300
% 0.20/0.36 % WCLimit : 300
% 0.20/0.36 % DateTime : Fri Aug 25 12:04:24 EDT 2023
% 0.20/0.36 % CPUTime :
% 0.20/0.36 This is a FOF_CAX_RFO_SEQ problem
% 0.20/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.J3QrSUxWeK/Vampire---4.8_32238
% 0.20/0.37 % (32347)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40 % (32349)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (32348)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (32351)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (32350)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.43 % (32352)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (32353)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.43 % (32354)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.46 % (32348)First to succeed.
% 0.22/0.47 % (32348)Refutation found. Thanks to Tanya!
% 0.22/0.47 % SZS status Theorem for Vampire---4
% 0.22/0.47 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.47 % (32348)------------------------------
% 0.22/0.47 % (32348)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.47 % (32348)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.47 % (32348)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (32348)Memory used [KB]: 1663
% 0.22/0.47 % (32348)Time elapsed: 0.041 s
% 0.22/0.47 % (32348)------------------------------
% 0.22/0.47 % (32348)------------------------------
% 0.22/0.47 % (32347)Success in time 0.101 s
% 0.22/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------