TSTP Solution File: NUM503+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM503+3 : 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 : n031.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 12:10:18 EDT 2023
% Result : Theorem 2.09s 0.70s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of formulae : 187 ( 25 unt; 0 def)
% Number of atoms : 746 ( 244 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 924 ( 365 ~; 381 |; 139 &)
% ( 16 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 158 (; 130 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11551,plain,
$false,
inference(avatar_sat_refutation,[],[f345,f356,f773,f1059,f2637,f2645,f2676,f2873,f5460,f5573,f11540]) ).
fof(f11540,plain,
( spl17_4
| ~ spl17_25 ),
inference(avatar_contradiction_clause,[],[f11539]) ).
fof(f11539,plain,
( $false
| spl17_4
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f11538,f198]) ).
fof(f198,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__1837) ).
fof(f11538,plain,
( ~ aNaturalNumber0(xm)
| spl17_4
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f11537,f1466]) ).
fof(f1466,plain,
xm != xk,
inference(subsumption_resolution,[],[f1458,f223]) ).
fof(f223,plain,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( sdtlseqdt0(xp,xk)
& xk = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f50,f148]) ).
fof(f148,plain,
( ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) )
=> ( xk = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
( sdtlseqdt0(xp,xk)
& ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__2389) ).
fof(f1458,plain,
( xm != xk
| ~ aNaturalNumber0(sK8) ),
inference(superposition,[],[f230,f224]) ).
fof(f224,plain,
xk = sdtpldt0(xp,sK8),
inference(cnf_transformation,[],[f149]) ).
fof(f230,plain,
! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ~ sdtlseqdt0(xp,xm)
& ! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
~ ( sdtlseqdt0(xp,xm)
| ? [X0] :
( xm = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__2075) ).
fof(f11537,plain,
( xm = xk
| ~ aNaturalNumber0(xm)
| spl17_4
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f11520,f3316]) ).
fof(f3316,plain,
sdtlseqdt0(xm,xk),
inference(subsumption_resolution,[],[f3304,f198]) ).
fof(f3304,plain,
( sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f399,f207]) ).
fof(f207,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK3)
& aNaturalNumber0(sK3)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK4)
& aNaturalNumber0(sK4)
& xn != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f55,f141,f140]) ).
fof(f140,plain,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xm,sK3)
& aNaturalNumber0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
( ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xn,sK4)
& aNaturalNumber0(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& xn != xp ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__2287) ).
fof(f399,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xp)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f398,f199]) ).
fof(f199,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f398,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f395,f194]) ).
fof(f194,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__2306) ).
fof(f395,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f225,f313]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mLETran) ).
fof(f225,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f149]) ).
fof(f11520,plain,
( ~ sdtlseqdt0(xm,xk)
| xm = xk
| ~ aNaturalNumber0(xm)
| spl17_4
| ~ spl17_25 ),
inference(resolution,[],[f1197,f5626]) ).
fof(f5626,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| spl17_4 ),
inference(forward_demodulation,[],[f344,f195]) ).
fof(f195,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f344,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| spl17_4 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f342,plain,
( spl17_4
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f1197,plain,
( ! [X13] :
( sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X13,xk)
| xk = X13
| ~ aNaturalNumber0(X13) )
| ~ spl17_25 ),
inference(forward_demodulation,[],[f1196,f1183]) ).
fof(f1183,plain,
( xk = sK5
| ~ spl17_25 ),
inference(forward_demodulation,[],[f1182,f196]) ).
fof(f196,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f1182,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f1181,f199]) ).
fof(f1181,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| ~ aNaturalNumber0(xp)
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f1180,f691]) ).
fof(f691,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f690,plain,
( spl17_25
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f1180,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1179,f210]) ).
fof(f210,plain,
sz00 != xp,
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK5)
& aNaturalNumber0(sK5)
& 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,[sK5])],[f65,f143]) ).
fof(f143,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK5)
& aNaturalNumber0(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f65,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,[],[f64]) ).
fof(f64,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,[],[f56]) ).
fof(f56,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/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__1860) ).
fof(f1179,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1178,f217]) ).
fof(f217,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f144]) ).
fof(f1178,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1087,f215]) ).
fof(f215,plain,
aNaturalNumber0(sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f1087,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sK5
| ~ aNaturalNumber0(sK5)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f323,f216]) ).
fof(f216,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f323,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,[],[f293]) ).
fof(f293,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,[],[f172]) ).
fof(f172,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,[],[f171]) ).
fof(f171,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,[],[f108]) ).
fof(f108,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,[],[f107]) ).
fof(f107,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/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mDefQuot) ).
fof(f1196,plain,
( ! [X13] :
( ~ sdtlseqdt0(X13,xk)
| sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| sK5 = X13
| ~ aNaturalNumber0(X13) )
| ~ spl17_25 ),
inference(forward_demodulation,[],[f1148,f1183]) ).
fof(f1148,plain,
! [X13] :
( sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X13,sK5)
| sK5 = X13
| ~ aNaturalNumber0(X13) ),
inference(subsumption_resolution,[],[f1147,f199]) ).
fof(f1147,plain,
! [X13] :
( sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X13,sK5)
| sK5 = X13
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1146,f215]) ).
fof(f1146,plain,
! [X13] :
( sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X13,sK5)
| sK5 = X13
| ~ aNaturalNumber0(sK5)
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1082,f210]) ).
fof(f1082,plain,
! [X13] :
( sdtlseqdt0(sdtasdt0(xp,X13),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X13,sK5)
| sK5 = X13
| sz00 = xp
| ~ aNaturalNumber0(sK5)
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f307,f216]) ).
fof(f307,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& sz00 != X0 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mMonMul) ).
fof(f5573,plain,
( ~ spl17_1
| ~ spl17_25 ),
inference(avatar_contradiction_clause,[],[f5572]) ).
fof(f5572,plain,
( $false
| ~ spl17_1
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f5571,f198]) ).
fof(f5571,plain,
( ~ aNaturalNumber0(xm)
| ~ spl17_1
| ~ spl17_25 ),
inference(subsumption_resolution,[],[f5560,f1466]) ).
fof(f5560,plain,
( xm = xk
| ~ aNaturalNumber0(xm)
| ~ spl17_1
| ~ spl17_25 ),
inference(trivial_inequality_removal,[],[f5526]) ).
fof(f5526,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| xm = xk
| ~ aNaturalNumber0(xm)
| ~ spl17_1
| ~ spl17_25 ),
inference(superposition,[],[f1218,f332]) ).
fof(f332,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f330,plain,
( spl17_1
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f1218,plain,
( ! [X1] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X1)
| xk = X1
| ~ aNaturalNumber0(X1) )
| ~ spl17_25 ),
inference(forward_demodulation,[],[f1095,f1183]) ).
fof(f1095,plain,
! [X1] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X1)
| sK5 = X1
| ~ aNaturalNumber0(X1) ),
inference(subsumption_resolution,[],[f1094,f199]) ).
fof(f1094,plain,
! [X1] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X1)
| sK5 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1093,f210]) ).
fof(f1093,plain,
! [X1] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X1)
| sK5 = X1
| ~ aNaturalNumber0(X1)
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1067,f215]) ).
fof(f1067,plain,
! [X1] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X1)
| sK5 = X1
| ~ aNaturalNumber0(sK5)
| ~ aNaturalNumber0(X1)
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f260,f216]) ).
fof(f260,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mMulCanc) ).
fof(f5460,plain,
( ~ spl17_35
| ~ spl17_105
| ~ spl17_107 ),
inference(avatar_contradiction_clause,[],[f5459]) ).
fof(f5459,plain,
( $false
| ~ spl17_35
| ~ spl17_105
| ~ spl17_107 ),
inference(subsumption_resolution,[],[f5458,f208]) ).
fof(f208,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__2327) ).
fof(f5458,plain,
( sz00 = xk
| ~ spl17_35
| ~ spl17_105
| ~ spl17_107 ),
inference(forward_demodulation,[],[f5457,f2716]) ).
fof(f2716,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl17_107 ),
inference(avatar_component_clause,[],[f2714]) ).
fof(f2714,plain,
( spl17_107
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f5457,plain,
( xk = sdtasdt0(xn,sz00)
| ~ spl17_35
| ~ spl17_105 ),
inference(forward_demodulation,[],[f1047,f2644]) ).
fof(f2644,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ spl17_105 ),
inference(avatar_component_clause,[],[f2642]) ).
fof(f2642,plain,
( spl17_105
<=> sz00 = sdtsldt0(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f1047,plain,
( xk = sdtasdt0(xn,sdtsldt0(sz00,xp))
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f1045]) ).
fof(f1045,plain,
( spl17_35
<=> xk = sdtasdt0(xn,sdtsldt0(sz00,xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f2873,plain,
spl17_107,
inference(avatar_contradiction_clause,[],[f2872]) ).
fof(f2872,plain,
( $false
| spl17_107 ),
inference(subsumption_resolution,[],[f2871,f197]) ).
fof(f197,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f2871,plain,
( ~ aNaturalNumber0(xn)
| spl17_107 ),
inference(trivial_inequality_removal,[],[f2868]) ).
fof(f2868,plain,
( sz00 != sz00
| ~ aNaturalNumber0(xn)
| spl17_107 ),
inference(superposition,[],[f2715,f252]) ).
fof(f252,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m_MulZero) ).
fof(f2715,plain,
( sz00 != sdtasdt0(xn,sz00)
| spl17_107 ),
inference(avatar_component_clause,[],[f2714]) ).
fof(f2676,plain,
spl17_103,
inference(avatar_contradiction_clause,[],[f2675]) ).
fof(f2675,plain,
( $false
| spl17_103 ),
inference(subsumption_resolution,[],[f2674,f199]) ).
fof(f2674,plain,
( ~ aNaturalNumber0(xp)
| spl17_103 ),
inference(trivial_inequality_removal,[],[f2671]) ).
fof(f2671,plain,
( sz00 != sz00
| ~ aNaturalNumber0(xp)
| spl17_103 ),
inference(superposition,[],[f2407,f252]) ).
fof(f2407,plain,
( sz00 != sdtasdt0(xp,sz00)
| spl17_103 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f2406,plain,
( spl17_103
<=> sz00 = sdtasdt0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f2645,plain,
( ~ spl17_36
| spl17_105
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f2640,f2406,f2642,f1049]) ).
fof(f1049,plain,
( spl17_36
<=> doDivides0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f2640,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ doDivides0(xp,sz00)
| ~ spl17_103 ),
inference(subsumption_resolution,[],[f2639,f199]) ).
fof(f2639,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(subsumption_resolution,[],[f2638,f210]) ).
fof(f2638,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ doDivides0(xp,sz00)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(subsumption_resolution,[],[f2612,f248]) ).
fof(f248,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mSortsC) ).
fof(f2612,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ doDivides0(xp,sz00)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(duplicate_literal_removal,[],[f2609]) ).
fof(f2609,plain,
( sz00 = sdtsldt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ doDivides0(xp,sz00)
| sz00 = xp
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(superposition,[],[f323,f2408]) ).
fof(f2408,plain,
( sz00 = sdtasdt0(xp,sz00)
| ~ spl17_103 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f2637,plain,
( spl17_36
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f2636,f2406,f1049]) ).
fof(f2636,plain,
( doDivides0(xp,sz00)
| ~ spl17_103 ),
inference(subsumption_resolution,[],[f2635,f199]) ).
fof(f2635,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(subsumption_resolution,[],[f2611,f248]) ).
fof(f2611,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(duplicate_literal_removal,[],[f2610]) ).
fof(f2610,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl17_103 ),
inference(superposition,[],[f326,f2408]) ).
fof(f326,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f298]) ).
fof(f298,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK15(X0,X1)) = X1
& aNaturalNumber0(sK15(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f174,f175]) ).
fof(f175,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK15(X0,X1)) = X1
& aNaturalNumber0(sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,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/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mDefDiv) ).
fof(f1059,plain,
( spl17_35
| ~ spl17_36
| spl17_2 ),
inference(avatar_split_clause,[],[f1058,f334,f1049,f1045]) ).
fof(f334,plain,
( spl17_2
<=> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f1058,plain,
( ~ doDivides0(xp,sz00)
| xk = sdtasdt0(xn,sdtsldt0(sz00,xp))
| spl17_2 ),
inference(forward_demodulation,[],[f1057,f854]) ).
fof(f854,plain,
( sz00 = xm
| spl17_2 ),
inference(subsumption_resolution,[],[f853,f198]) ).
fof(f853,plain,
( sz00 = xm
| ~ aNaturalNumber0(xm)
| spl17_2 ),
inference(subsumption_resolution,[],[f852,f197]) ).
fof(f852,plain,
( sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl17_2 ),
inference(subsumption_resolution,[],[f851,f199]) ).
fof(f851,plain,
( sz00 = xm
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl17_2 ),
inference(subsumption_resolution,[],[f850,f200]) ).
fof(f200,plain,
xn != xp,
inference(cnf_transformation,[],[f142]) ).
fof(f850,plain,
( xn = xp
| sz00 = xm
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl17_2 ),
inference(subsumption_resolution,[],[f846,f203]) ).
fof(f203,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f142]) ).
fof(f846,plain,
( ~ sdtlseqdt0(xn,xp)
| xn = xp
| sz00 = xm
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl17_2 ),
inference(resolution,[],[f336,f309]) ).
fof(f309,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f336,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| spl17_2 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f1057,plain,
( xk = sdtasdt0(xn,sdtsldt0(sz00,xp))
| ~ doDivides0(xp,xm)
| spl17_2 ),
inference(forward_demodulation,[],[f1056,f854]) ).
fof(f1056,plain,
( xk = sdtasdt0(xn,sdtsldt0(xm,xp))
| ~ doDivides0(xp,xm) ),
inference(subsumption_resolution,[],[f1055,f199]) ).
fof(f1055,plain,
( xk = sdtasdt0(xn,sdtsldt0(xm,xp))
| ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1054,f198]) ).
fof(f1054,plain,
( xk = sdtasdt0(xn,sdtsldt0(xm,xp))
| ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1053,f210]) ).
fof(f1053,plain,
( xk = sdtasdt0(xn,sdtsldt0(xm,xp))
| ~ doDivides0(xp,xm)
| sz00 = xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f1035,f197]) ).
fof(f1035,plain,
( xk = sdtasdt0(xn,sdtsldt0(xm,xp))
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xm)
| sz00 = xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f290,f196]) ).
fof(f290,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mDivAsso) ).
fof(f773,plain,
spl17_25,
inference(avatar_contradiction_clause,[],[f772]) ).
fof(f772,plain,
( $false
| spl17_25 ),
inference(subsumption_resolution,[],[f771,f197]) ).
fof(f771,plain,
( ~ aNaturalNumber0(xn)
| spl17_25 ),
inference(subsumption_resolution,[],[f770,f198]) ).
fof(f770,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl17_25 ),
inference(resolution,[],[f692,f273]) ).
fof(f273,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,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/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',mSortsB_02) ).
fof(f692,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl17_25 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f356,plain,
( spl17_1
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f355,f338,f330]) ).
fof(f338,plain,
( spl17_3
<=> sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f355,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl17_3 ),
inference(forward_demodulation,[],[f340,f195]) ).
fof(f340,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f345,plain,
( spl17_1
| ~ spl17_2
| spl17_3
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f184,f342,f338,f334,f330]) ).
fof(f184,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ! [X0] :
( sdtasdt0(xp,xk) != sdtpldt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ! [X1] :
( sdtasdt0(xp,xm) != sdtpldt0(sdtasdt0(xn,xm),X1)
| ~ aNaturalNumber0(X1) ) )
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
~ ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X1] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(rectify,[],[f52]) ).
fof(f52,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(negated_conjecture,[],[f51]) ).
fof(f51,conjecture,
( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453',m__) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:49:07 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_CAX_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.eEVrDAV10b/Vampire---4.8_32453
% 0.15/0.37 % (32702)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41 % (32703)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.43 % (32706)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.43 % (32705)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.43 % (32708)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.43 % (32707)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.43 % (32704)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43 % (32709)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 2.09/0.69 % (32709)First to succeed.
% 2.09/0.70 % (32709)Refutation found. Thanks to Tanya!
% 2.09/0.70 % SZS status Theorem for Vampire---4
% 2.09/0.70 % SZS output start Proof for Vampire---4
% See solution above
% 2.09/0.70 % (32709)------------------------------
% 2.09/0.70 % (32709)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.09/0.70 % (32709)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.09/0.70 % (32709)Termination reason: Refutation
% 2.09/0.70
% 2.09/0.70 % (32709)Memory used [KB]: 11257
% 2.09/0.70 % (32709)Time elapsed: 0.253 s
% 2.09/0.70 % (32709)------------------------------
% 2.09/0.70 % (32709)------------------------------
% 2.09/0.70 % (32702)Success in time 0.326 s
% 2.09/0.70 % Vampire---4.8 exiting
%------------------------------------------------------------------------------