%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 1.18s 0.62s
% Output : Refutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 130 ( 29 unt; 8 def)
% Number of atoms : 401 ( 150 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 425 ( 154 ~; 177 |; 72 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 61 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f44,axiom,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f49,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f50,plain,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xm,X1) )
& sdtlseqdt0(xm,xp) ),
inference(rectify,[],[f44]) ).
fof(f51,plain,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
inference(rectify,[],[f47]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f55]) ).
fof(f66,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f67,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f77,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
fof(f101,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f102,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f101]) ).
fof(f121,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f122,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f121]) ).
fof(f125,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f126,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f138,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f139,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f141,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f67]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f77]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f194,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f195,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f196,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f229,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| xp = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f231,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK10),
inference(cnf_transformation,[],[f122]) ).
fof(f246,plain,
xm != xp,
inference(cnf_transformation,[],[f50]) ).
fof(f248,plain,
xn != xp,
inference(cnf_transformation,[],[f50]) ).
fof(f250,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f252,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f254,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f126]) ).
fof(f255,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f126]) ).
fof(f262,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f175]) ).
fof(f270,plain,
~ aNaturalNumber0(sz00),
inference(consistent_polarity_flipping,[],[f127]) ).
fof(f273,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| aNaturalNumber0(X0)
| aNaturalNumber0(X1) ),
inference(consistent_polarity_flipping,[],[f131]) ).
fof(f280,plain,
! [X0] :
( aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f281,plain,
! [X0] :
( aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(consistent_polarity_flipping,[],[f138]) ).
fof(f282,plain,
! [X0] :
( aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(consistent_polarity_flipping,[],[f141]) ).
fof(f292,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| aNaturalNumber0(X0)
| aNaturalNumber0(X1)
| sz00 = X1
| sz00 = X0 ),
inference(consistent_polarity_flipping,[],[f150]) ).
fof(f315,plain,
! [X2,X0] :
( aNaturalNumber0(sdtasdt0(X0,X2))
| aNaturalNumber0(X0)
| aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f262]) ).
fof(f336,plain,
~ aNaturalNumber0(xn),
inference(consistent_polarity_flipping,[],[f196]) ).
fof(f337,plain,
~ aNaturalNumber0(xm),
inference(consistent_polarity_flipping,[],[f195]) ).
fof(f338,plain,
~ aNaturalNumber0(xp),
inference(consistent_polarity_flipping,[],[f194]) ).
fof(f373,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xp
| aNaturalNumber0(X1)
| aNaturalNumber0(X0)
| xp = X0
| sz10 = X0 ),
inference(consistent_polarity_flipping,[],[f229]) ).
fof(f380,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| aNaturalNumber0(X0) ),
inference(consistent_polarity_flipping,[],[f252]) ).
fof(f383,definition,
( spl13_1
<=> sz00 = xk ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f385,plain,
( sz00 = xk
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f387,definition,
( spl13_2
<=> sz10 = xk ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f389,plain,
( sz10 = xk
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f390,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f254,f387,f383]) ).
fof(f405,definition,
( spl13_6
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f406,plain,
( ~ aNaturalNumber0(sz00)
| spl13_6 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f410,plain,
~ spl13_6,
inference(avatar_split_clause,[],[f270,f405]) ).
fof(f416,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f250,f389]) ).
fof(f417,plain,
( sdtasdt0(xp,sK10) = sdtasdt0(xp,sz10)
| ~ spl13_2 ),
inference(superposition,[],[f416,f231]) ).
fof(f442,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f280,f338]) ).
fof(f450,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[],[f281,f337]) ).
fof(f460,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f282,f338]) ).
fof(f659,definition,
( spl13_9
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f660,plain,
( sz00 != xm
| spl13_9 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f661,plain,
( sz00 = xm
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f674,plain,
( ~ doDivides0(xp,sz00)
| ~ spl13_9 ),
inference(superposition,[],[f255,f661]) ).
fof(f738,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| aNaturalNumber0(X2)
| aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f315,f273]) ).
fof(f811,definition,
( spl13_16
<=> sz00 = sdtasdt0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f813,plain,
( sz00 = sdtasdt0(xp,sz00)
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f996,plain,
( xp != sdtasdt0(xp,sK10)
| aNaturalNumber0(xm)
| aNaturalNumber0(xn)
| xn = xp
| sz10 = xn ),
inference(superposition,[],[f373,f231]) ).
fof(f999,plain,
( xp != sdtasdt0(xp,sK10)
| aNaturalNumber0(xn)
| xn = xp
| sz10 = xn ),
inference(forward_subsumption_resolution,[],[f996,f337]) ).
fof(f1001,plain,
( xp != sdtasdt0(xp,sK10)
| xn = xp
| sz10 = xn ),
inference(forward_subsumption_resolution,[],[f999,f336]) ).
fof(f1003,plain,
( xp != sdtasdt0(xp,sK10)
| sz10 = xn ),
inference(forward_subsumption_resolution,[],[f1001,f248]) ).
fof(f1005,definition,
( spl13_23
<=> sz10 = xn ),
introduced(definition,[new_symbols(definition,[spl13_23])],[avatar_definition]) ).
fof(f1007,plain,
( sz10 = xn
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1014,definition,
( spl13_25
<=> xp = sdtasdt0(xp,sK10) ),
introduced(definition,[new_symbols(definition,[spl13_25])],[avatar_definition]) ).
fof(f1017,plain,
( spl13_23
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f1003,f1014,f1005]) ).
fof(f1040,definition,
( spl13_28
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl13_28])],[avatar_definition]) ).
fof(f1041,plain,
( sz00 != xn
| spl13_28 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1125,plain,
( sz00 != xn
| aNaturalNumber0(sz00)
| ~ spl13_16 ),
inference(superposition,[],[f380,f813]) ).
fof(f1127,plain,
( doDivides0(xp,sz00)
| aNaturalNumber0(sz00)
| aNaturalNumber0(xp)
| ~ spl13_16 ),
inference(superposition,[],[f738,f813]) ).
fof(f1129,plain,
( aNaturalNumber0(sz00)
| aNaturalNumber0(xp)
| ~ spl13_9
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1127,f674]) ).
fof(f1131,plain,
( sz00 != xn
| spl13_6
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1125,f406]) ).
fof(f1132,plain,
( aNaturalNumber0(xp)
| spl13_6
| ~ spl13_9
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1129,f406]) ).
fof(f1135,plain,
( ~ spl13_28
| spl13_6
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f1131,f811,f405,f1040]) ).
fof(f1136,plain,
( $false
| spl13_6
| ~ spl13_9
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1132,f338]) ).
fof(f1137,plain,
( spl13_6
| ~ spl13_9
| ~ spl13_16 ),
inference(avatar_contradiction_clause,[],[f1136]) ).
fof(f1138,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f250,f385]) ).
fof(f1150,plain,
( sz00 != sdtasdt0(xp,sz00)
| aNaturalNumber0(xn)
| aNaturalNumber0(xm)
| sz00 = xm
| sz00 = xn
| ~ spl13_1 ),
inference(superposition,[],[f292,f1138]) ).
fof(f3273,plain,
( xm = sdtasdt0(xn,xm)
| ~ spl13_23 ),
inference(superposition,[],[f450,f1007]) ).
fof(f3395,plain,
( sz00 != sdtasdt0(xp,sz00)
| aNaturalNumber0(xm)
| sz00 = xm
| sz00 = xn
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f1150,f336]) ).
fof(f3416,plain,
spl13_16,
inference(avatar_split_clause,[],[f460,f811]) ).
fof(f3418,plain,
( sz00 != sdtasdt0(xp,sz00)
| sz00 = xm
| sz00 = xn
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f3395,f337]) ).
fof(f3421,plain,
( sz00 != sdtasdt0(xp,sz00)
| sz00 = xn
| ~ spl13_1
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f3418,f660]) ).
fof(f3424,plain,
( sz00 != sdtasdt0(xp,sz00)
| ~ spl13_1
| spl13_9
| spl13_28 ),
inference(forward_subsumption_resolution,[],[f3421,f1041]) ).
fof(f3426,plain,
( ~ spl13_16
| ~ spl13_1
| spl13_9
| spl13_28 ),
inference(avatar_split_clause,[],[f3424,f1040,f659,f383,f811]) ).
fof(f3431,plain,
( xp = sdtasdt0(xn,xm)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f416,f442]) ).
fof(f3432,plain,
( xp = sdtasdt0(xp,sK10)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f417,f442]) ).
fof(f3490,plain,
( spl13_25
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f3432,f387,f1014]) ).
fof(f9008,plain,
( xm = xp
| ~ spl13_2
| ~ spl13_23 ),
inference(forward_demodulation,[],[f3273,f3431]) ).
fof(f9009,plain,
( $false
| ~ spl13_2
| ~ spl13_23 ),
inference(forward_subsumption_resolution,[],[f9008,f246]) ).
fof(f9010,plain,
( ~ spl13_2
| ~ spl13_23 ),
inference(avatar_contradiction_clause,[],[f9009]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f390]) ).
cnf(s5,plain,
~ spl13_6,
inference(sat_conversion,[],[f410]) ).
cnf(s26,plain,
( spl13_23
| ~ spl13_25 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s32,plain,
( spl13_6
| ~ spl13_16
| ~ spl13_28 ),
inference(sat_conversion,[],[f1135]) ).
cnf(s33,plain,
( spl13_6
| ~ spl13_9
| ~ spl13_16 ),
inference(sat_conversion,[],[f1137]) ).
cnf(s104,plain,
spl13_16,
inference(sat_conversion,[],[f3416]) ).
cnf(s106,plain,
( ~ spl13_1
| spl13_9
| ~ spl13_16
| spl13_28 ),
inference(sat_conversion,[],[f3426]) ).
cnf(s114,plain,
( ~ spl13_2
| spl13_25 ),
inference(sat_conversion,[],[f3490]) ).
cnf(s255,plain,
( ~ spl13_2
| ~ spl13_23 ),
inference(sat_conversion,[],[f9010]) ).
cnf(s272,plain,
( spl13_6
| ~ spl13_9 ),
inference(rat,[],[s33,s104]) ).
cnf(s273,plain,
( spl13_6
| ~ spl13_28 ),
inference(rat,[],[s32,s104]) ).
cnf(s284,plain,
~ spl13_9,
inference(rat,[],[s272,s5]) ).
cnf(s285,plain,
~ spl13_28,
inference(rat,[],[s273,s5]) ).
cnf(s286,plain,
~ spl13_1,
inference(rat,[],[s106,s285,s104,s284]) ).
cnf(s296,plain,
spl13_2,
inference(rat,[],[s1,s286]) ).
cnf(s297,plain,
~ spl13_23,
inference(rat,[],[s255,s296]) ).
cnf(s298,plain,
spl13_25,
inference(rat,[],[s114,s296]) ).
cnf(s305,plain,
$false,
inference(rat,[],[s26,s298,s297]) ).
fof(f9011,plain,
$false,
inference(avatar_sat_refutation,[],[s305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 20:12:30 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 Running first-order model finding
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.18/0.62 % (2366552)Will run a generic schedule for satisfiability detection.
% 1.18/0.62 % (2366561)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2589073225:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.18/0.62 % (2366558)% WARNING: option uhcvi not known.
% 1.18/0.62 % (2366560)dis+10_1_sil=32000:sp=arity:random_seed=1796781090:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.18/0.62 % (2366557)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=903863333_2999 on theBenchmark for (2999ds/0Mi)
% 1.18/0.62 % (2366558)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=647270852:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.18/0.62 % (2366559)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2349955092:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.18/0.62 % (2366562)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2690687349:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.62 % (2366563)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=558719886:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.18/0.62 % Detected minimum model sizes of [3]
% 1.18/0.62 % Detected maximum model sizes of [max]
% 1.18/0.62 % TRYING [3]
% 1.18/0.62 % TRYING [4]
% 1.18/0.62 % (2366561)Instruction limit reached!
% 1.18/0.62 % (2366561)------------------------------
% 1.18/0.62 % (2366561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366561)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366561)Termination reason: Instruction limit
% 1.18/0.62 % (2366561)Termination phase: Saturation
% 1.18/0.62 % (2366561)Time elapsed: 0.036 s
% 1.18/0.62 % (2366561)Peak memory usage: 13 MB
% 1.18/0.62 % (2366561)Instructions burned: 118 (million)
% 1.18/0.62 % (2366571)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=301327170:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.18/0.62 % Detected minimum model sizes of [3]
% 1.18/0.62 % Detected maximum model sizes of [max]
% 1.18/0.62 % TRYING [3]
% 1.18/0.62 % TRYING [4]
% 1.18/0.62 % TRYING [5]
% 1.18/0.62 % (2366560)Instruction limit reached!
% 1.18/0.62 % (2366560)------------------------------
% 1.18/0.62 % (2366560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366560)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366560)Termination reason: Instruction limit
% 1.18/0.62 % (2366560)Termination phase: Saturation
% 1.18/0.62 % (2366560)Time elapsed: 0.062 s
% 1.18/0.62 % (2366560)Peak memory usage: 12 MB
% 1.18/0.62 % (2366560)Instructions burned: 104 (million)
% 1.18/0.62 % TRYING [5]
% 1.18/0.62 % (2366562)Instruction limit reached!
% 1.18/0.62 % (2366562)------------------------------
% 1.18/0.62 % (2366562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366562)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366562)Termination reason: Instruction limit
% 1.18/0.62 % (2366562)Termination phase: Saturation
% 1.18/0.62 % (2366562)Time elapsed: 0.080 s
% 1.18/0.62 % (2366562)Peak memory usage: 13 MB
% 1.18/0.62 % (2366562)Instructions burned: 132 (million)
% 1.18/0.62 % (2366573)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1281443329:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.62 % (2366563)Instruction limit reached!
% 1.18/0.62 % (2366563)------------------------------
% 1.18/0.62 % (2366563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366563)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366563)Termination reason: Instruction limit
% 1.18/0.62 % (2366563)Termination phase: Saturation
% 1.18/0.62 % (2366563)Time elapsed: 0.097 s
% 1.18/0.62 % (2366563)Peak memory usage: 15 MB
% 1.18/0.62 % (2366563)Instructions burned: 159 (million)
% 1.18/0.62 % (2366575)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=3896976434:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.18/0.62 % TRYING [6]
% 1.18/0.62 % (2366576)ott-21_1_sil=16000:fs=off:random_seed=2386151369:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.18/0.62 % TRYING [6]
% 1.18/0.62 % (2366573)Instruction limit reached!
% 1.18/0.62 % (2366573)------------------------------
% 1.18/0.62 % (2366573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366573)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366573)Termination reason: Instruction limit
% 1.18/0.62 % (2366573)Termination phase: Saturation
% 1.18/0.62 % (2366573)Time elapsed: 0.069 s
% 1.18/0.62 % (2366573)Peak memory usage: 12 MB
% 1.18/0.62 % (2366573)Instructions burned: 132 (million)
% 1.18/0.62 % (2366579)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3390956698:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.18/0.62 % (2366571)Instruction limit reached!
% 1.18/0.62 % (2366571)------------------------------
% 1.18/0.62 % (2366571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366571)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366571)Termination reason: Instruction limit
% 1.18/0.62 % (2366571)Termination phase: Finite model building constraint generation
% 1.18/0.62 % (2366571)Time elapsed: 0.138 s
% 1.18/0.62 % (2366571)Peak memory usage: 32 MB
% 1.18/0.62 % (2366571)Instructions burned: 715 (million)
% 1.18/0.62 % (2366558) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2366552-2366558"...
% 1.18/0.62 % (2366581)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3172343989:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.18/0.62 % (2366558)...printing done.
% 1.18/0.62 % Detected minimum model sizes of [3]
% 1.18/0.62 % Detected maximum model sizes of [max]
% 1.18/0.62 % (2366558)Refutation found. Thanks to Tanya!
% 1.18/0.62 % SZS status Theorem for theBenchmark
% 1.18/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.18/0.62 % (2366558)------------------------------
% 1.18/0.62 % (2366558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.62 % (2366558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.62 % (2366558)CaDiCaL version: 2.1.3
% 1.18/0.62 % (2366558)Termination reason: Refutation
% 1.18/0.62 % (2366558)Time elapsed: 0.191 s
% 1.18/0.62 % (2366558)Peak memory usage: 16 MB
% 1.18/0.62 % (2366558)Instructions burned: 331 (million)
% 1.18/0.62 % (2366552)Success in time 0.233 s
% 1.18/0.62 % Vampire exiting
%------------------------------------------------------------------------------