%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM554+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 : n002.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 12:24:47 PM UTC 2026
% Result : Theorem 1.20s 0.68s
% Output : Refutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 25
% Syntax : Number of formulae : 155 ( 35 unt; 11 def)
% Number of atoms : 420 ( 58 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 444 ( 179 ~; 184 |; 46 &)
% ( 21 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f18,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aSet0(X1) )
=> ( ~ aElementOf0(X0,X1)
=> sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(f21,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( isFinite0(X0)
& aElementOf0(X1,X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(f65,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(f68,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
fof(f70,axiom,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xQ,xy))
| X0 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(f71,conjecture,
( ( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ( ( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f74,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(rectify,[],[f70]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aElement0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f101,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aElement0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f100]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f108]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f138]) ).
fof(f169,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f170,plain,
( ( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| sdtmndt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f205,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f208,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f209,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f235,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f139]) ).
fof(f278,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f306,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f307,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f169]) ).
fof(f309,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f169]) ).
fof(f311,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f169]) ).
fof(f313,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f315,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f316,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f317,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f319,plain,
! [X1] :
( xx != X1
| ~ aElement0(X1)
| aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f74]) ).
fof(f321,plain,
! [X1] :
( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f74]) ).
fof(f323,plain,
! [X0] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f327,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f74]) ).
fof(f328,plain,
aSet0(xP),
inference(cnf_transformation,[],[f74]) ).
fof(f329,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f74]) ).
fof(f330,plain,
( xk != sbrdtbr0(xP)
| aElementOf0(sK15,xP) ),
inference(cnf_transformation,[],[f170]) ).
fof(f331,plain,
( xk != sbrdtbr0(xP)
| ~ aElementOf0(sK15,xS) ),
inference(cnf_transformation,[],[f170]) ).
fof(f346,plain,
! [X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,sdtmndt0(X0,X1)) ),
inference(equality_resolution,[],[f196]) ).
fof(f365,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[],[f319]) ).
fof(f366,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| ~ aSet0(X0)
| aElement0(X1) ),
inference(consistent_polarity_flipping,[],[f171]) ).
fof(f390,plain,
! [X3,X0,X1] :
( aElementOf0(X3,sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X1) ),
inference(consistent_polarity_flipping,[],[f346]) ).
fof(f393,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(consistent_polarity_flipping,[],[f205]) ).
fof(f396,plain,
! [X0,X1] :
( ~ isFinite0(sdtpldt0(X1,X0))
| isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(consistent_polarity_flipping,[],[f208]) ).
fof(f397,plain,
! [X0,X1] :
( ~ isFinite0(sdtmndt0(X1,X0))
| isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(consistent_polarity_flipping,[],[f209]) ).
fof(f419,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(X1,X0)
| isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f235]) ).
fof(f482,plain,
~ aElementOf0(xx,xS),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f484,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,xQ) ),
inference(consistent_polarity_flipping,[],[f307]) ).
fof(f485,plain,
~ isFinite0(xQ),
inference(consistent_polarity_flipping,[],[f313]) ).
fof(f486,plain,
~ aElementOf0(xy,xQ),
inference(consistent_polarity_flipping,[],[f315]) ).
fof(f487,plain,
aElementOf0(xx,xQ),
inference(consistent_polarity_flipping,[],[f317]) ).
fof(f492,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xQ) ),
inference(consistent_polarity_flipping,[],[f323]) ).
fof(f494,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1
| aElementOf0(X1,xP) ),
inference(consistent_polarity_flipping,[],[f321]) ).
fof(f496,plain,
( ~ aElement0(xx)
| ~ aElementOf0(xx,xP) ),
inference(consistent_polarity_flipping,[],[f365]) ).
fof(f498,plain,
( xk != sbrdtbr0(xP)
| aElementOf0(sK15,xS) ),
inference(consistent_polarity_flipping,[],[f331]) ).
fof(f499,plain,
( xk != sbrdtbr0(xP)
| ~ aElementOf0(sK15,xP) ),
inference(consistent_polarity_flipping,[],[f330]) ).
fof(f503,definition,
( spl16_1
<=> aElementOf0(sK15,xP) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f505,plain,
( ~ aElementOf0(sK15,xP)
| spl16_1 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f507,definition,
( spl16_2
<=> xk = sbrdtbr0(xP) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f510,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f499,f507,f503]) ).
fof(f512,definition,
( spl16_3
<=> aElementOf0(sK15,xS) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f514,plain,
( aElementOf0(sK15,xS)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f515,plain,
( spl16_3
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f498,f507,f512]) ).
fof(f522,definition,
( spl16_5
<=> aElementOf0(xx,xP) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f524,plain,
( ~ aElementOf0(xx,xP)
| spl16_5 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f526,definition,
( spl16_6
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f527,plain,
( aElement0(xx)
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f529,plain,
( ~ spl16_5
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f496,f526,f522]) ).
fof(f559,definition,
( spl16_10
<=> isFinite0(xP) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
fof(f560,plain,
( ~ isFinite0(xP)
| spl16_10 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f606,definition,
( spl16_20
<=> isFinite0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl16_20])],[avatar_definition]) ).
fof(f608,plain,
( isFinite0(sdtmndt0(xQ,xy))
| ~ spl16_20 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f636,plain,
( ~ aSet0(xS)
| aElement0(xx) ),
inference(resolution,[],[f366,f482]) ).
fof(f642,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f636,f278]) ).
fof(f646,plain,
spl16_6,
inference(avatar_split_clause,[],[f642,f526]) ).
fof(f798,plain,
( ~ isFinite0(xP)
| isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(superposition,[],[f396,f327]) ).
fof(f799,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy)
| ~ spl16_20 ),
inference(resolution,[],[f397,f608]) ).
fof(f800,plain,
( ~ aSet0(xQ)
| ~ aElement0(xy)
| ~ spl16_20 ),
inference(forward_subsumption_resolution,[],[f799,f485]) ).
fof(f801,plain,
( ~ aElement0(xy)
| ~ spl16_20 ),
inference(forward_subsumption_resolution,[],[f800,f311]) ).
fof(f802,plain,
( $false
| ~ spl16_20 ),
inference(forward_subsumption_resolution,[],[f801,f316]) ).
fof(f803,plain,
~ spl16_20,
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f808,plain,
( ~ isFinite0(xP)
| isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(forward_subsumption_resolution,[],[f798,f329]) ).
fof(f809,plain,
( ~ isFinite0(xP)
| isFinite0(sdtmndt0(xQ,xy))
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f808,f527]) ).
fof(f810,plain,
( spl16_20
| ~ spl16_10
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f809,f526,f559,f606]) ).
fof(f831,plain,
! [X0] :
( aElementOf0(X0,xP)
| xx = X0
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[],[f494,f492]) ).
fof(f1087,plain,
( ! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(xx,X0)
| sdtmndt0(sdtpldt0(X0,xx),xx) = X0 )
| ~ spl16_6 ),
inference(resolution,[],[f393,f527]) ).
fof(f1341,plain,
! [X0] :
( aElementOf0(X0,xQ)
| isFinite0(xQ)
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,X0))) ),
inference(resolution,[],[f419,f311]) ).
fof(f1342,plain,
! [X0] :
( aElementOf0(X0,xP)
| isFinite0(xP)
| sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,X0))) ),
inference(resolution,[],[f419,f328]) ).
fof(f1345,plain,
( ! [X0] :
( aElementOf0(X0,xP)
| sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,X0))) )
| spl16_10 ),
inference(forward_subsumption_resolution,[],[f1342,f560]) ).
fof(f1346,plain,
! [X0] :
( aElementOf0(X0,xQ)
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,X0))) ),
inference(forward_subsumption_resolution,[],[f1341,f485]) ).
fof(f1351,plain,
! [X0] :
( aElementOf0(X0,xQ)
| xk = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,X0))) ),
inference(forward_demodulation,[],[f1346,f309]) ).
fof(f2657,plain,
xk = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),
inference(resolution,[],[f1351,f486]) ).
fof(f2997,plain,
( sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx)))
| spl16_5
| spl16_10 ),
inference(resolution,[],[f1345,f524]) ).
fof(f3212,plain,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
| sdtmndt0(xQ,xy) = sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx)
| ~ spl16_6 ),
inference(resolution,[],[f1087,f329]) ).
fof(f3300,plain,
( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx)
| ~ aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ spl16_6 ),
inference(forward_demodulation,[],[f3212,f327]) ).
fof(f3303,definition,
( spl16_193
<=> aElementOf0(xx,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl16_193])],[avatar_definition]) ).
fof(f3305,plain,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
| spl16_193 ),
inference(avatar_component_clause,[],[f3303]) ).
fof(f3307,definition,
( spl16_194
<=> sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) ),
introduced(definition,[new_symbols(definition,[spl16_194])],[avatar_definition]) ).
fof(f3309,plain,
( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx)
| ~ spl16_194 ),
inference(avatar_component_clause,[],[f3307]) ).
fof(f3310,plain,
( ~ spl16_193
| spl16_194
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f3300,f526,f3307,f3303]) ).
fof(f12946,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xx,xQ)
| ~ aElement0(xy)
| spl16_193 ),
inference(resolution,[],[f3305,f390]) ).
fof(f12949,plain,
( ~ aElementOf0(xx,xQ)
| ~ aElement0(xy)
| spl16_193 ),
inference(forward_subsumption_resolution,[],[f12946,f311]) ).
fof(f12954,plain,
( ~ aElement0(xy)
| spl16_193 ),
inference(forward_subsumption_resolution,[],[f12949,f487]) ).
fof(f12957,plain,
( $false
| spl16_193 ),
inference(forward_subsumption_resolution,[],[f12954,f316]) ).
fof(f12958,plain,
spl16_193,
inference(avatar_contradiction_clause,[],[f12957]) ).
fof(f17033,plain,
( sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| spl16_5
| spl16_10
| ~ spl16_194 ),
inference(forward_demodulation,[],[f2997,f3309]) ).
fof(f17034,plain,
( xk = sbrdtbr0(xP)
| spl16_5
| spl16_10
| ~ spl16_194 ),
inference(forward_demodulation,[],[f17033,f2657]) ).
fof(f17063,plain,
( spl16_2
| spl16_5
| spl16_10
| ~ spl16_194 ),
inference(avatar_split_clause,[],[f17034,f3307,f559,f522,f507]) ).
fof(f17134,plain,
( xx = sK15
| ~ aElementOf0(sK15,xQ)
| spl16_1 ),
inference(resolution,[],[f505,f831]) ).
fof(f17139,definition,
( spl16_1341
<=> aElementOf0(sK15,xQ) ),
introduced(definition,[new_symbols(definition,[spl16_1341])],[avatar_definition]) ).
fof(f17143,definition,
( spl16_1342
<=> xx = sK15 ),
introduced(definition,[new_symbols(definition,[spl16_1342])],[avatar_definition]) ).
fof(f17145,plain,
( xx = sK15
| ~ spl16_1342 ),
inference(avatar_component_clause,[],[f17143]) ).
fof(f17146,plain,
( ~ spl16_1341
| spl16_1342
| spl16_1 ),
inference(avatar_split_clause,[],[f17134,f503,f17143,f17139]) ).
fof(f17148,plain,
( aElementOf0(sK15,xQ)
| ~ spl16_3 ),
inference(resolution,[],[f514,f484]) ).
fof(f17149,plain,
( spl16_1341
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f17148,f512,f17139]) ).
fof(f17426,plain,
( aElementOf0(xx,xS)
| ~ spl16_3
| ~ spl16_1342 ),
inference(superposition,[],[f514,f17145]) ).
fof(f17428,plain,
( $false
| ~ spl16_3
| ~ spl16_1342 ),
inference(forward_subsumption_resolution,[],[f17426,f482]) ).
fof(f17429,plain,
( ~ spl16_3
| ~ spl16_1342 ),
inference(avatar_contradiction_clause,[],[f17428]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f510]) ).
cnf(s2,plain,
( ~ spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f515]) ).
cnf(s4,plain,
( ~ spl16_5
| ~ spl16_6 ),
inference(sat_conversion,[],[f529]) ).
cnf(s16,plain,
spl16_6,
inference(sat_conversion,[],[f646]) ).
cnf(s29,plain,
~ spl16_20,
inference(sat_conversion,[],[f803]) ).
cnf(s31,plain,
( ~ spl16_6
| ~ spl16_10
| spl16_20 ),
inference(sat_conversion,[],[f810]) ).
cnf(s212,plain,
( ~ spl16_6
| ~ spl16_193
| spl16_194 ),
inference(sat_conversion,[],[f3310]) ).
cnf(s958,plain,
spl16_193,
inference(sat_conversion,[],[f12958]) ).
cnf(s1394,plain,
( spl16_2
| spl16_5
| spl16_10
| ~ spl16_194 ),
inference(sat_conversion,[],[f17063]) ).
cnf(s1407,plain,
( spl16_1
| ~ spl16_1341
| spl16_1342 ),
inference(sat_conversion,[],[f17146]) ).
cnf(s1408,plain,
( ~ spl16_3
| spl16_1341 ),
inference(sat_conversion,[],[f17149]) ).
cnf(s1454,plain,
( ~ spl16_3
| ~ spl16_1342 ),
inference(sat_conversion,[],[f17429]) ).
cnf(s1489,plain,
( ~ spl16_6
| spl16_194 ),
inference(rat,[],[s212,s958]) ).
cnf(s1579,plain,
spl16_194,
inference(rat,[],[s1489,s16]) ).
cnf(s1580,plain,
~ spl16_10,
inference(rat,[],[s31,s29,s16]) ).
cnf(s1697,plain,
~ spl16_5,
inference(rat,[],[s4,s16]) ).
cnf(s1698,plain,
spl16_2,
inference(rat,[],[s1394,s1579,s1580,s1697]) ).
cnf(s1779,plain,
spl16_3,
inference(rat,[],[s2,s1698]) ).
cnf(s1780,plain,
~ spl16_1342,
inference(rat,[],[s1454,s1779]) ).
cnf(s1781,plain,
spl16_1341,
inference(rat,[],[s1408,s1779]) ).
cnf(s1782,plain,
spl16_1,
inference(rat,[],[s1407,s1780,s1781]) ).
cnf(s1783,plain,
$false,
inference(rat,[],[s1,s1698,s1782]) ).
fof(f17430,plain,
$false,
inference(avatar_sat_refutation,[],[s1783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n002.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 20:31:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 1.20/0.68 % (3854119)Will run a generic schedule for satisfiability detection.
% 1.20/0.68 % (3854125)% WARNING: option uhcvi not known.
% 1.20/0.68 % (3854125)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2893749625:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.20/0.68 % (3854127)dis+10_1_sil=32000:sp=arity:random_seed=3808854620:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.20/0.68 % (3854128)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1173639467:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.20/0.68 % (3854130)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1866679400:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.20/0.68 % (3854124)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2689383452_2999 on theBenchmark for (2999ds/0Mi)
% 1.20/0.68 % (3854126)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4153278120:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.20/0.68 % (3854129)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3581317178:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.20/0.68 % TRYING [1]
% 1.20/0.68 % TRYING [2]
% 1.20/0.68 % TRYING [3]
% 1.20/0.68 % TRYING [4]
% 1.20/0.68 % TRYING [5]
% 1.20/0.68 % (3854127)Instruction limit reached!
% 1.20/0.68 % (3854127)------------------------------
% 1.20/0.68 % (3854127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.68 % (3854127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.68 % (3854127)CaDiCaL version: 2.1.3
% 1.20/0.68 % (3854127)Termination reason: Instruction limit
% 1.20/0.68 % (3854127)Termination phase: Saturation
% 1.20/0.68 % (3854127)Time elapsed: 0.067 s
% 1.20/0.68 % (3854127)Peak memory usage: 13 MB
% 1.20/0.68 % (3854127)Instructions burned: 103 (million)
% 1.20/0.68 % (3854128)Instruction limit reached!
% 1.20/0.68 % (3854128)------------------------------
% 1.20/0.68 % (3854128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.68 % (3854128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.68 % (3854128)CaDiCaL version: 2.1.3
% 1.20/0.68 % (3854128)Termination reason: Instruction limit
% 1.20/0.68 % (3854128)Termination phase: Saturation
% 1.20/0.68 % (3854128)Time elapsed: 0.072 s
% 1.20/0.68 % (3854128)Peak memory usage: 13 MB
% 1.20/0.68 % (3854128)Instructions burned: 116 (million)
% 1.20/0.68 % (3854129)Instruction limit reached!
% 1.20/0.68 % (3854129)------------------------------
% 1.20/0.68 % (3854129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.68 % (3854129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.68 % (3854129)CaDiCaL version: 2.1.3
% 1.20/0.68 % (3854129)Termination reason: Instruction limit
% 1.20/0.68 % (3854129)Termination phase: Saturation
% 1.20/0.68 % (3854129)Time elapsed: 0.081 s
% 1.20/0.68 % (3854129)Peak memory usage: 14 MB
% 1.20/0.68 % (3854129)Instructions burned: 132 (million)
% 1.20/0.68 % (3854138)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=592251332:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.20/0.68 % (3854139)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1539814974:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.20/0.68 % TRYING [1]
% 1.20/0.68 % TRYING [2]
% 1.20/0.68 % (3854140)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=3993407718:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.20/0.68 % TRYING [3]
% 1.20/0.68 % (3854130)Instruction limit reached!
% 1.20/0.68 % (3854130)------------------------------
% 1.20/0.68 % (3854130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.68 % (3854130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.68 % (3854130)CaDiCaL version: 2.1.3
% 1.20/0.68 % (3854130)Termination reason: Instruction limit
% 1.20/0.68 % (3854130)Termination phase: Saturation
% 1.20/0.68 % (3854130)Time elapsed: 0.108 s
% 1.20/0.68 % (3854130)Peak memory usage: 15 MB
% 1.20/0.68 % (3854130)Instructions burned: 160 (million)
% 1.20/0.68 % TRYING [6]
% 1.20/0.68 % TRYING [4]
% 1.20/0.68 % (3854144)ott-21_1_sil=16000:fs=off:random_seed=3658742760:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.20/0.68 % TRYING [5]
% 1.20/0.68 % (3854139)Instruction limit reached!
% 1.20/0.68 % (3854139)------------------------------
% 1.20/0.68 % (3854139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.68 % (3854139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.68 % (3854139)CaDiCaL version: 2.1.3
% 1.20/0.68 % (3854139)Termination reason: Instruction limit
% 1.20/0.68 % (3854139)Termination phase: Saturation
% 1.20/0.68 % (3854139)Time elapsed: 0.087 s
% 1.20/0.68 % (3854139)Peak memory usage: 13 MB
% 1.20/0.68 % (3854139)Instructions burned: 131 (million)
% 1.20/0.68 % TRYING [6]
% 1.20/0.68 % (3854146)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1958743237:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.20/0.68 % (3854125) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3854119-3854125"...
% 1.20/0.68 % (3854125)...printing done.
% 1.20/0.68 % (3854125)Refutation found. Thanks to Tanya!
% 1.20/0.68 % SZS status Theorem for theBenchmark
% 1.20/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 1.20/0.69 % (3854125)------------------------------
% 1.20/0.69 % (3854125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.69 % (3854125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.69 % (3854125)CaDiCaL version: 2.1.3
% 1.20/0.69 % (3854125)Termination reason: Refutation
% 1.20/0.69 % (3854125)Time elapsed: 0.238 s
% 1.20/0.69 % (3854125)Peak memory usage: 20 MB
% 1.20/0.69 % (3854125)Instructions burned: 691 (million)
% 1.20/0.69 % (3854119)Success in time 0.272 s
% 1.20/0.69 % Vampire exiting
%------------------------------------------------------------------------------