%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:24:33 PM UTC 2026
% Result : Theorem 1.47s 0.90s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 24
% Syntax : Number of formulae : 160 ( 33 unt; 11 def)
% Number of atoms : 442 ( 126 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 486 ( 204 ~; 218 |; 32 &)
% ( 20 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 62 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f44,axiom,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f62,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f72]) ).
fof(f97,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f98,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f99]) ).
fof(f111,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f112,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f117,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f118,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f123,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f130,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f131,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f63]) ).
fof(f142,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f180,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| sz10 = X1
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f182,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 != X0
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f186,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f187,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f188,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f190,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f191,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f197,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f198,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f199,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f118]) ).
fof(f200,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f118]) ).
fof(f201,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f118]) ).
fof(f207,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f167]) ).
fof(f210,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f168]) ).
fof(f211,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f182]) ).
fof(f236,plain,
( ~ aNaturalNumber0(sz00)
| isPrime0(sz00) ),
inference(consistent_polarity_flipping,[],[f211]) ).
fof(f238,plain,
! [X0,X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| sz10 = X1
| isPrime0(X0) ),
inference(consistent_polarity_flipping,[],[f180]) ).
fof(f245,plain,
~ isPrime0(xp),
inference(consistent_polarity_flipping,[],[f191]) ).
fof(f252,definition,
( spl4_1
<=> sz00 = xk ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f254,plain,
( sz00 = xk
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f256,definition,
( spl4_2
<=> sz10 = xk ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f258,plain,
( sz10 = xk
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f259,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f199,f256,f252]) ).
fof(f270,definition,
( spl4_5
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f272,plain,
( isPrime0(sz00)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f274,definition,
( spl4_6
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f275,plain,
( aNaturalNumber0(sz00)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f277,plain,
( spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f236,f274,f270]) ).
fof(f279,plain,
spl4_6,
inference(avatar_split_clause,[],[f119,f274]) ).
fof(f280,plain,
( sz10 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl4_2 ),
inference(forward_demodulation,[],[f198,f258]) ).
fof(f294,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[],[f130,f187]) ).
fof(f300,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f131,f186]) ).
fof(f310,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f133,f186]) ).
fof(f318,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(xn,X0)) ),
inference(resolution,[],[f123,f188]) ).
fof(f336,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f337,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f358,definition,
( spl4_11
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f359,plain,
( sz00 != xp
| spl4_11 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
( sz00 = xp
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f371,definition,
( spl4_14
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f372,plain,
( sz00 != xm
| spl4_14 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f373,plain,
( sz00 = xm
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f380,definition,
( spl4_16
<=> sz10 = xn ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
fof(f381,plain,
( sz10 != xn
| spl4_16 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f382,plain,
( sz10 = xn
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f384,definition,
( spl4_17
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f385,plain,
( sz00 != xn
| spl4_17 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f386,plain,
( sz00 = xn
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f472,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f207,f123]) ).
fof(f483,plain,
( ~ isPrime0(sz00)
| ~ spl4_11 ),
inference(superposition,[],[f245,f360]) ).
fof(f493,plain,
( $false
| ~ spl4_5
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f483,f272]) ).
fof(f494,plain,
( ~ spl4_5
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f493]) ).
fof(f593,plain,
( ~ doDivides0(xp,sz00)
| ~ spl4_14 ),
inference(superposition,[],[f200,f373]) ).
fof(f710,plain,
( ~ doDivides0(xp,sz00)
| ~ spl4_17 ),
inference(superposition,[],[f201,f386]) ).
fof(f814,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(resolution,[],[f210,f190]) ).
fof(f821,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[],[f814,f186]) ).
fof(f822,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f821,f359]) ).
fof(f1195,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f472,f310]) ).
fof(f1197,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f1195,f593]) ).
fof(f1200,plain,
( ~ aNaturalNumber0(xp)
| ~ spl4_6
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f1197,f275]) ).
fof(f1203,plain,
( $false
| ~ spl4_6
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f1200,f186]) ).
fof(f1204,plain,
( ~ spl4_6
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f1203]) ).
fof(f1217,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1195,f275]) ).
fof(f1225,plain,
( doDivides0(xp,sz00)
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1217,f186]) ).
fof(f1419,definition,
( spl4_57
<=> xp = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[spl4_57])],[avatar_definition]) ).
fof(f1421,plain,
( xp = sdtasdt0(xn,xm)
| ~ spl4_57 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f1431,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_2
| spl4_11 ),
inference(forward_demodulation,[],[f822,f280]) ).
fof(f1437,plain,
( xp = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_2
| spl4_11 ),
inference(forward_demodulation,[],[f1431,f300]) ).
fof(f1869,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolution,[],[f318,f187]) ).
fof(f1878,plain,
spl4_7,
inference(avatar_split_clause,[],[f1869,f336]) ).
fof(f1935,definition,
( spl4_68
<=> sz00 = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[spl4_68])],[avatar_definition]) ).
fof(f1937,plain,
( sz00 = sdtasdt0(xn,xm)
| ~ spl4_68 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f1961,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ spl4_57 ),
inference(superposition,[],[f472,f1421]) ).
fof(f1962,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f1961,f187]) ).
fof(f1973,plain,
( doDivides0(xn,xp)
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f1962,f188]) ).
fof(f2070,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_7
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f822,f337]) ).
fof(f2073,plain,
( sz00 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl4_1 ),
inference(forward_demodulation,[],[f198,f254]) ).
fof(f2365,plain,
( $false
| ~ spl4_6
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f710,f1225]) ).
fof(f2366,plain,
( ~ spl4_6
| ~ spl4_17 ),
inference(avatar_contradiction_clause,[],[f2365]) ).
fof(f2600,plain,
( doDivides0(xp,sdtasdt0(sz10,xm))
| ~ spl4_16 ),
inference(superposition,[],[f190,f382]) ).
fof(f2646,plain,
( doDivides0(xp,xm)
| ~ spl4_16 ),
inference(forward_demodulation,[],[f2600,f294]) ).
fof(f2651,plain,
( $false
| ~ spl4_16 ),
inference(forward_subsumption_resolution,[],[f2646,f200]) ).
fof(f2652,plain,
~ spl4_16,
inference(avatar_contradiction_clause,[],[f2651]) ).
fof(f3953,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl4_1
| ~ spl4_7
| spl4_11 ),
inference(forward_demodulation,[],[f2070,f2073]) ).
fof(f3954,plain,
( sz00 = sdtasdt0(xn,xm)
| ~ spl4_1
| ~ spl4_7
| spl4_11 ),
inference(forward_demodulation,[],[f3953,f310]) ).
fof(f3955,plain,
( spl4_68
| ~ spl4_1
| ~ spl4_7
| spl4_11 ),
inference(avatar_split_clause,[],[f3954,f358,f336,f252,f1935]) ).
fof(f30122,plain,
( sz00 != sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| sz00 = xn
| ~ spl4_68 ),
inference(superposition,[],[f142,f1937]) ).
fof(f30129,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| sz00 = xn
| ~ spl4_68 ),
inference(trivial_inequality_removal,[],[f30122]) ).
fof(f30135,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xm
| sz00 = xn
| ~ spl4_68 ),
inference(forward_subsumption_resolution,[],[f30129,f188]) ).
fof(f30153,plain,
( sz00 = xm
| sz00 = xn
| ~ spl4_68 ),
inference(forward_subsumption_resolution,[],[f30135,f187]) ).
fof(f30165,plain,
( sz00 = xn
| spl4_14
| ~ spl4_68 ),
inference(forward_subsumption_resolution,[],[f30153,f372]) ).
fof(f30173,plain,
( $false
| spl4_14
| spl4_17
| ~ spl4_68 ),
inference(forward_subsumption_resolution,[],[f30165,f385]) ).
fof(f30174,plain,
( spl4_14
| spl4_17
| ~ spl4_68 ),
inference(avatar_contradiction_clause,[],[f30173]) ).
fof(f30176,plain,
( xp = sdtasdt0(xn,xm)
| ~ spl4_2
| ~ spl4_7
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f1437,f337]) ).
fof(f30191,plain,
( spl4_57
| ~ spl4_2
| ~ spl4_7
| spl4_11 ),
inference(avatar_split_clause,[],[f30176,f358,f336,f256,f1419]) ).
fof(f30810,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xn = xp
| sz10 = xn
| isPrime0(xp)
| ~ spl4_57 ),
inference(resolution,[],[f1973,f238]) ).
fof(f30811,plain,
( ~ aNaturalNumber0(xn)
| xn = xp
| sz10 = xn
| isPrime0(xp)
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f30810,f186]) ).
fof(f30820,plain,
( xn = xp
| sz10 = xn
| isPrime0(xp)
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f30811,f188]) ).
fof(f30829,plain,
( sz10 = xn
| isPrime0(xp)
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f30820,f197]) ).
fof(f30833,plain,
( isPrime0(xp)
| spl4_16
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f30829,f381]) ).
fof(f30834,plain,
( $false
| spl4_16
| ~ spl4_57 ),
inference(forward_subsumption_resolution,[],[f30833,f245]) ).
fof(f30835,plain,
( spl4_16
| ~ spl4_57 ),
inference(avatar_contradiction_clause,[],[f30834]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f259]) ).
cnf(s3,plain,
( spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f277]) ).
cnf(s5,plain,
spl4_6,
inference(sat_conversion,[],[f279]) ).
cnf(s16,plain,
( ~ spl4_5
| ~ spl4_11 ),
inference(sat_conversion,[],[f494]) ).
cnf(s36,plain,
( ~ spl4_6
| ~ spl4_14 ),
inference(sat_conversion,[],[f1204]) ).
cnf(s67,plain,
spl4_7,
inference(sat_conversion,[],[f1878]) ).
cnf(s82,plain,
( ~ spl4_6
| ~ spl4_17 ),
inference(sat_conversion,[],[f2366]) ).
cnf(s129,plain,
~ spl4_16,
inference(sat_conversion,[],[f2652]) ).
cnf(s254,plain,
( ~ spl4_1
| ~ spl4_7
| spl4_11
| spl4_68 ),
inference(sat_conversion,[],[f3955]) ).
cnf(s3245,plain,
( spl4_14
| spl4_17
| ~ spl4_68 ),
inference(sat_conversion,[],[f30174]) ).
cnf(s3250,plain,
( ~ spl4_2
| ~ spl4_7
| spl4_11
| spl4_57 ),
inference(sat_conversion,[],[f30191]) ).
cnf(s3290,plain,
( spl4_16
| ~ spl4_57 ),
inference(sat_conversion,[],[f30835]) ).
cnf(s3296,plain,
~ spl4_57,
inference(rat,[],[s3290,s129]) ).
cnf(s3310,plain,
~ spl4_17,
inference(rat,[],[s82,s5]) ).
cnf(s3314,plain,
~ spl4_14,
inference(rat,[],[s36,s5]) ).
cnf(s3326,plain,
~ spl4_68,
inference(rat,[],[s3245,s3310,s3314]) ).
cnf(s3352,plain,
spl4_5,
inference(rat,[],[s3,s5]) ).
cnf(s3355,plain,
~ spl4_11,
inference(rat,[],[s16,s3352]) ).
cnf(s3369,plain,
~ spl4_2,
inference(rat,[],[s3250,s3296,s67,s3355]) ).
cnf(s3370,plain,
~ spl4_1,
inference(rat,[],[s254,s3326,s67,s3355]) ).
cnf(s3434,plain,
$false,
inference(rat,[],[s1,s3369,s3370]) ).
fof(f30836,plain,
$false,
inference(avatar_sat_refutation,[],[s3434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:12:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.47/0.90 % (521975)Will run a generic schedule for satisfiability detection.
% 1.47/0.90 % (521980)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2078462839_2999 on theBenchmark for (2999ds/0Mi)
% 1.47/0.90 % (521981)% WARNING: option uhcvi not known.
% 1.47/0.90 % TRYING [1]
% 1.47/0.90 % TRYING [2]
% 1.47/0.90 % TRYING [3]
% 1.47/0.90 % (521981)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=14358742:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.47/0.90 % (521985)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2154100339:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.47/0.90 % (521982)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1745735597:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.47/0.90 % (521983)dis+10_1_sil=32000:sp=arity:random_seed=2173841917:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.47/0.90 % (521984)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4279284425:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.47/0.90 % (521986)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3453225183:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.47/0.90 % TRYING [4]
% 1.47/0.90 % TRYING [5]
% 1.47/0.90 % TRYING [6]
% 1.47/0.90 % (521983)Instruction limit reached!
% 1.47/0.90 % (521983)------------------------------
% 1.47/0.90 % (521983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521983)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521983)Termination reason: Instruction limit
% 1.47/0.90 % (521983)Termination phase: Saturation
% 1.47/0.90 % (521983)Time elapsed: 0.062 s
% 1.47/0.90 % (521983)Peak memory usage: 13 MB
% 1.47/0.90 % (521983)Instructions burned: 103 (million)
% 1.47/0.90 % (521984)Instruction limit reached!
% 1.47/0.90 % (521984)------------------------------
% 1.47/0.90 % (521984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521984)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521984)Termination reason: Instruction limit
% 1.47/0.90 % (521984)Termination phase: Saturation
% 1.47/0.90 % (521984)Time elapsed: 0.067 s
% 1.47/0.90 % (521984)Peak memory usage: 13 MB
% 1.47/0.90 % (521984)Instructions burned: 117 (million)
% 1.47/0.90 % (521985)Instruction limit reached!
% 1.47/0.90 % (521985)------------------------------
% 1.47/0.90 % (521985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521985)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521985)Termination reason: Instruction limit
% 1.47/0.90 % (521985)Termination phase: Saturation
% 1.47/0.90 % (521985)Time elapsed: 0.077 s
% 1.47/0.90 % (521985)Peak memory usage: 14 MB
% 1.47/0.90 % (521985)Instructions burned: 131 (million)
% 1.47/0.90 % (521994)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3891206602:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.47/0.90 % (521995)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1511599864:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.47/0.90 % TRYING [1]
% 1.47/0.90 % TRYING [2]
% 1.47/0.90 % TRYING [3]
% 1.47/0.90 % (521996)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=324212110:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.47/0.90 % (521986)Instruction limit reached!
% 1.47/0.90 % (521986)------------------------------
% 1.47/0.90 % (521986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521986)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521986)Termination reason: Instruction limit
% 1.47/0.90 % (521986)Termination phase: Saturation
% 1.47/0.90 % (521986)Time elapsed: 0.097 s
% 1.47/0.90 % (521986)Peak memory usage: 14 MB
% 1.47/0.90 % (521986)Instructions burned: 160 (million)
% 1.47/0.90 % TRYING [4]
% 1.47/0.90 % (522000)ott-21_1_sil=16000:fs=off:random_seed=1842671950:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.47/0.90 % TRYING [5]
% 1.47/0.90 % TRYING [7]
% 1.47/0.90 % (521995)Instruction limit reached!
% 1.47/0.90 % (521995)------------------------------
% 1.47/0.90 % (521995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521995)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521995)Termination reason: Instruction limit
% 1.47/0.90 % (521995)Termination phase: Saturation
% 1.47/0.90 % (521995)Time elapsed: 0.070 s
% 1.47/0.90 % (521995)Peak memory usage: 12 MB
% 1.47/0.90 % (521995)Instructions burned: 131 (million)
% 1.47/0.90 % (522002)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2154516874:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.47/0.90 % TRYING [6]
% 1.47/0.90 % (522000)Instruction limit reached!
% 1.47/0.90 % (522000)------------------------------
% 1.47/0.90 % (522000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (522000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (522000)CaDiCaL version: 2.1.3
% 1.47/0.90 % (522000)Termination reason: Instruction limit
% 1.47/0.90 % (522000)Termination phase: Saturation
% 1.47/0.90 % (522000)Time elapsed: 0.096 s
% 1.47/0.90 % (522000)Peak memory usage: 13 MB
% 1.47/0.90 % (522000)Instructions burned: 182 (million)
% 1.47/0.90 % (522004)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1767256928:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.47/0.90 % TRYING [1]
% 1.47/0.90 % TRYING [2]
% 1.47/0.90 % TRYING [3]
% 1.47/0.90 % TRYING [4]
% 1.47/0.90 % (521994)Instruction limit reached!
% 1.47/0.90 % (521994)------------------------------
% 1.47/0.90 % (521994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.90 % (521994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.90 % (521994)CaDiCaL version: 2.1.3
% 1.47/0.90 % (521994)Termination reason: Instruction limit
% 1.47/0.90 % (521994)Termination phase: Finite model building constraint generation
% 1.47/0.90 % (521994)Time elapsed: 0.258 s
% 1.47/0.90 % (521994)Peak memory usage: 33 MB
% 1.47/0.90 % (521994)Instructions burned: 714 (million)
% 1.47/0.90 % TRYING [5]
% 1.47/0.90 % TRYING [8]
% 1.47/0.90 % (522006)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3011098063:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 1.47/0.90 % (521981) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-521975-521981"...
% 1.47/0.90 % (521981)...printing done.
% 1.47/0.90 % (521981)Refutation found. Thanks to Tanya!
% 1.47/0.90 % SZS status Theorem for theBenchmark
% 1.47/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 1.47/0.91 % (521981)------------------------------
% 1.47/0.91 % (521981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.91 % (521981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.91 % (521981)CaDiCaL version: 2.1.3
% 1.47/0.91 % (521981)Termination reason: Refutation
% 1.47/0.91 % (521981)Time elapsed: 0.430 s
% 1.47/0.91 % (521981)Peak memory usage: 27 MB
% 1.47/0.91 % (521981)Instructions burned: 763 (million)
% 1.47/0.91 % (521975)Success in time 0.478 s
% 1.47/0.91 % Vampire exiting
%------------------------------------------------------------------------------