%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:15:43 PM UTC 2026
% Result : Theorem 2.29s 1.18s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 140 ( 30 unt; 12 def)
% Number of atoms : 431 ( 41 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 488 ( 197 ~; 207 |; 58 &)
% ( 14 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 46 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
fof(f43,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( isFinite0(X0)
& aElementOf0(X1,X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f69,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
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/sandbox/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/sandbox/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(f80,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(f81,plain,
( ( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f112]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f125]) ).
fof(f139,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xQ)
| xy = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(nnf_transformation,[],[f74]) ).
fof(f140,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xQ)
| xy = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
( ( ( ~ aElementOf0(sK8,xS)
& aElementOf0(sK8,xP)
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f81]) ).
fof(f173,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f201,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f205,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f80]) ).
fof(f207,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f208,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f209,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f210,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f211,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f213,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f69]) ).
fof(f214,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f140]) ).
fof(f215,plain,
! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1
| ~ aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f140]) ).
fof(f221,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f140]) ).
fof(f224,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f140]) ).
fof(f227,plain,
( aElementOf0(sK8,xP)
| xk != sbrdtbr0(xP) ),
inference(cnf_transformation,[],[f141]) ).
fof(f228,plain,
( ~ aElementOf0(sK8,xS)
| xk != sbrdtbr0(xP) ),
inference(cnf_transformation,[],[f141]) ).
fof(f266,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f267,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f284,plain,
! [X0,X1] :
( sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f285,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f325,definition,
~ sP29(xk),
introduced(definition,[new_symbols(definition,[sP29])],[inequality_splitting_name_introduction]) ).
fof(f326,plain,
( ~ aElementOf0(sK8,xS)
| sP29(sbrdtbr0(xP)) ),
inference(inequality_splitting,[],[f228,f325]) ).
fof(f327,definition,
~ sP30(xk),
introduced(definition,[new_symbols(definition,[sP30])],[inequality_splitting_name_introduction]) ).
fof(f328,plain,
( aElementOf0(sK8,xP)
| sP30(sbrdtbr0(xP)) ),
inference(inequality_splitting,[],[f227,f327]) ).
fof(f370,definition,
( spl42_3
<=> sP30(sbrdtbr0(xP)) ),
introduced(definition,[new_symbols(definition,[spl42_3])],[avatar_definition]) ).
fof(f372,plain,
( sP30(sbrdtbr0(xP))
| ~ spl42_3 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f374,definition,
( spl42_4
<=> aElementOf0(sK8,xP) ),
introduced(definition,[new_symbols(definition,[spl42_4])],[avatar_definition]) ).
fof(f376,plain,
( aElementOf0(sK8,xP)
| ~ spl42_4 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f377,plain,
( spl42_3
| spl42_4 ),
inference(avatar_split_clause,[],[f328,f374,f370]) ).
fof(f379,definition,
( spl42_5
<=> sP29(sbrdtbr0(xP)) ),
introduced(definition,[new_symbols(definition,[spl42_5])],[avatar_definition]) ).
fof(f381,plain,
( sP29(sbrdtbr0(xP))
| ~ spl42_5 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f383,definition,
( spl42_6
<=> aElementOf0(sK8,xS) ),
introduced(definition,[new_symbols(definition,[spl42_6])],[avatar_definition]) ).
fof(f385,plain,
( ~ aElementOf0(sK8,xS)
| spl42_6 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f386,plain,
( spl42_5
| ~ spl42_6 ),
inference(avatar_split_clause,[],[f326,f383,f379]) ).
fof(f387,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ),
inference(forward_demodulation,[],[f215,f214]) ).
fof(f394,plain,
( sP30(sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)))
| ~ spl42_3 ),
inference(forward_demodulation,[],[f372,f214]) ).
fof(f419,plain,
( sP30(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_3 ),
inference(superposition,[],[f394,f267]) ).
fof(f422,plain,
( sP30(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_3 ),
inference(forward_subsumption_resolution,[],[f419,f224]) ).
fof(f434,definition,
( spl42_13
<=> isFinite0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl42_13])],[avatar_definition]) ).
fof(f435,plain,
( isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_13 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f436,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| spl42_13 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f438,definition,
( spl42_14
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl42_14])],[avatar_definition]) ).
fof(f439,plain,
( aElement0(xx)
| ~ spl42_14 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f440,plain,
( ~ aElement0(xx)
| spl42_14 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f442,definition,
( spl42_15
<=> aElementOf0(xx,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl42_15])],[avatar_definition]) ).
fof(f443,plain,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
| spl42_15 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f444,plain,
( aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ spl42_15 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f446,definition,
( spl42_16
<=> sP30(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))) ),
introduced(definition,[new_symbols(definition,[spl42_16])],[avatar_definition]) ).
fof(f448,plain,
( sP30(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| ~ spl42_16 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f449,plain,
( ~ spl42_13
| ~ spl42_14
| spl42_15
| spl42_16
| ~ spl42_3 ),
inference(avatar_split_clause,[],[f422,f370,f446,f442,f438,f434]) ).
fof(f499,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f201,f266]) ).
fof(f505,plain,
( ~ aSet0(xS)
| spl42_14 ),
inference(forward_subsumption_resolution,[],[f499,f440]) ).
fof(f506,plain,
( $false
| spl42_14 ),
inference(forward_subsumption_resolution,[],[f505,f173]) ).
fof(f507,plain,
spl42_14,
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f536,plain,
( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ~ aElement0(xy)
| spl42_13 ),
inference(resolution,[],[f436,f285]) ).
fof(f539,plain,
( ~ isFinite0(xQ)
| ~ aElement0(xy)
| spl42_13 ),
inference(forward_subsumption_resolution,[],[f536,f209]) ).
fof(f540,plain,
( ~ aElement0(xy)
| spl42_13 ),
inference(forward_subsumption_resolution,[],[f539,f208]) ).
fof(f541,plain,
( $false
| spl42_13 ),
inference(forward_subsumption_resolution,[],[f540,f211]) ).
fof(f542,plain,
spl42_13,
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f831,plain,
( aElementOf0(xx,xQ)
| ~ spl42_15 ),
inference(resolution,[],[f221,f444]) ).
fof(f842,plain,
( $false
| ~ spl42_15 ),
inference(forward_subsumption_resolution,[],[f831,f213]) ).
fof(f843,plain,
~ spl42_15,
inference(avatar_contradiction_clause,[],[f842]) ).
fof(f912,plain,
( sP30(sbrdtbr0(xQ))
| ~ isFinite0(xQ)
| ~ aElementOf0(xy,xQ)
| ~ aSet0(xQ)
| ~ spl42_16 ),
inference(superposition,[],[f448,f284]) ).
fof(f913,plain,
( sP30(sbrdtbr0(xQ))
| ~ aElementOf0(xy,xQ)
| ~ aSet0(xQ)
| ~ spl42_16 ),
inference(forward_subsumption_resolution,[],[f912,f208]) ).
fof(f916,plain,
( sP30(sbrdtbr0(xQ))
| ~ aSet0(xQ)
| ~ spl42_16 ),
inference(forward_subsumption_resolution,[],[f913,f210]) ).
fof(f918,plain,
( sP30(sbrdtbr0(xQ))
| ~ spl42_16 ),
inference(forward_subsumption_resolution,[],[f916,f209]) ).
fof(f920,plain,
( sP30(xk)
| ~ spl42_16 ),
inference(forward_demodulation,[],[f918,f207]) ).
fof(f921,plain,
( $false
| ~ spl42_16 ),
inference(forward_subsumption_resolution,[],[f920,f327]) ).
fof(f922,plain,
~ spl42_16,
inference(avatar_contradiction_clause,[],[f921]) ).
fof(f924,plain,
( aElementOf0(sK8,sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ spl42_4 ),
inference(forward_demodulation,[],[f376,f214]) ).
fof(f1750,plain,
( aElementOf0(sK8,sdtmndt0(xQ,xy))
| xx = sK8
| ~ spl42_4 ),
inference(resolution,[],[f387,f924]) ).
fof(f1770,definition,
( spl42_80
<=> xx = sK8 ),
introduced(definition,[new_symbols(definition,[spl42_80])],[avatar_definition]) ).
fof(f1772,plain,
( xx = sK8
| ~ spl42_80 ),
inference(avatar_component_clause,[],[f1770]) ).
fof(f1774,definition,
( spl42_81
<=> aElementOf0(sK8,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl42_81])],[avatar_definition]) ).
fof(f1776,plain,
( aElementOf0(sK8,sdtmndt0(xQ,xy))
| ~ spl42_81 ),
inference(avatar_component_clause,[],[f1774]) ).
fof(f1778,plain,
( spl42_80
| spl42_81
| ~ spl42_4 ),
inference(avatar_split_clause,[],[f1750,f374,f1774,f1770]) ).
fof(f1794,plain,
( ~ aElementOf0(xx,xS)
| spl42_6
| ~ spl42_80 ),
inference(superposition,[],[f385,f1772]) ).
fof(f1795,plain,
( $false
| spl42_6
| ~ spl42_80 ),
inference(forward_subsumption_resolution,[],[f1794,f201]) ).
fof(f1796,plain,
( spl42_6
| ~ spl42_80 ),
inference(avatar_contradiction_clause,[],[f1795]) ).
fof(f1884,plain,
( aElementOf0(sK8,xQ)
| ~ spl42_81 ),
inference(resolution,[],[f1776,f221]) ).
fof(f1913,plain,
( aElementOf0(sK8,xS)
| ~ spl42_81 ),
inference(resolution,[],[f1884,f205]) ).
fof(f1918,plain,
( $false
| spl42_6
| ~ spl42_81 ),
inference(forward_subsumption_resolution,[],[f1913,f385]) ).
fof(f1919,plain,
( spl42_6
| ~ spl42_81 ),
inference(avatar_contradiction_clause,[],[f1918]) ).
fof(f1920,plain,
( sP29(sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)))
| ~ spl42_5 ),
inference(forward_demodulation,[],[f381,f214]) ).
fof(f1970,plain,
( sP29(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_5 ),
inference(superposition,[],[f1920,f267]) ).
fof(f1972,plain,
( sP29(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_5
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1970,f443]) ).
fof(f1975,plain,
( sP29(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_5
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1972,f439]) ).
fof(f1976,plain,
( sP29(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl42_5
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1975,f224]) ).
fof(f1977,plain,
( sP29(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1976,f435]) ).
fof(f1980,plain,
( sP29(sbrdtbr0(xQ))
| ~ isFinite0(xQ)
| ~ aElementOf0(xy,xQ)
| ~ aSet0(xQ)
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(superposition,[],[f1977,f284]) ).
fof(f1981,plain,
( sP29(sbrdtbr0(xQ))
| ~ aElementOf0(xy,xQ)
| ~ aSet0(xQ)
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1980,f208]) ).
fof(f1984,plain,
( sP29(sbrdtbr0(xQ))
| ~ aSet0(xQ)
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1981,f210]) ).
fof(f1990,plain,
( sP29(sbrdtbr0(xQ))
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1984,f209]) ).
fof(f1991,plain,
( sP29(xk)
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_demodulation,[],[f1990,f207]) ).
fof(f1992,plain,
( $false
| ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(forward_subsumption_resolution,[],[f1991,f325]) ).
fof(f1993,plain,
( ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(avatar_contradiction_clause,[],[f1992]) ).
cnf(s2,plain,
( spl42_3
| spl42_4 ),
inference(sat_conversion,[],[f377]) ).
cnf(s3,plain,
( spl42_5
| ~ spl42_6 ),
inference(sat_conversion,[],[f386]) ).
cnf(s8,plain,
( ~ spl42_3
| ~ spl42_13
| ~ spl42_14
| spl42_15
| spl42_16 ),
inference(sat_conversion,[],[f449]) ).
cnf(s12,plain,
spl42_14,
inference(sat_conversion,[],[f507]) ).
cnf(s15,plain,
spl42_13,
inference(sat_conversion,[],[f542]) ).
cnf(s33,plain,
~ spl42_15,
inference(sat_conversion,[],[f843]) ).
cnf(s40,plain,
~ spl42_16,
inference(sat_conversion,[],[f922]) ).
cnf(s88,plain,
( ~ spl42_4
| spl42_80
| spl42_81 ),
inference(sat_conversion,[],[f1778]) ).
cnf(s92,plain,
( spl42_6
| ~ spl42_80 ),
inference(sat_conversion,[],[f1796]) ).
cnf(s98,plain,
( spl42_6
| ~ spl42_81 ),
inference(sat_conversion,[],[f1919]) ).
cnf(s105,plain,
( ~ spl42_5
| ~ spl42_13
| ~ spl42_14
| spl42_15 ),
inference(sat_conversion,[],[f1993]) ).
cnf(s113,plain,
~ spl42_5,
inference(rat,[],[s105,s33,s15,s12]) ).
cnf(s119,plain,
~ spl42_3,
inference(rat,[],[s8,s40,s33,s12,s15]) ).
cnf(s122,plain,
~ spl42_6,
inference(rat,[],[s3,s113]) ).
cnf(s123,plain,
~ spl42_81,
inference(rat,[],[s98,s122]) ).
cnf(s124,plain,
~ spl42_80,
inference(rat,[],[s92,s122]) ).
cnf(s125,plain,
~ spl42_4,
inference(rat,[],[s88,s123,s124]) ).
cnf(s126,plain,
$false,
inference(rat,[],[s2,s125,s119]) ).
fof(f1994,plain,
$false,
inference(avatar_sat_refutation,[],[s126]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n004.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 27 20:28:22 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/1.18 % (3855542)Detected formulas, will run a generic FOF schedule.
% 2.29/1.18 % (3855550)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2079236457:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.29/1.18 % (3855550)First to succeed.
% 2.29/1.18 % (3855550)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3855542"
% 2.29/1.18 % (3855547)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=957646699:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.29/1.18 % (3855549)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2771537106:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.29/1.18 % (3855548)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2807573699:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.29/1.18 % (3855553)dis-21_1_sil=8000:lcm=predicate:random_seed=2058540435:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.29/1.18 % (3855552)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=325882801:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.29/1.18 % (3855551)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=899168135:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.29/1.18 % (3855552)Also succeeded, but the first one will report.
% 2.29/1.18 % (3855553)Instruction limit reached!
% 2.29/1.18 % (3855553)------------------------------
% 2.29/1.18 % (3855553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.18 % (3855553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.18 % (3855553)CaDiCaL version: 2.1.3
% 2.29/1.18 % (3855553)Termination reason: Instruction limit
% 2.29/1.18 % (3855553)Termination phase: Saturation
% 2.29/1.18 % (3855553)Time elapsed: 0.060 s
% 2.29/1.18 % (3855553)Peak memory usage: 88 MB
% 2.29/1.18 % (3855553)Instructions burned: 129 (million)
% 2.29/1.18 % (3855551)Instruction limit reached!
% 2.29/1.18 % (3855551)------------------------------
% 2.29/1.18 % (3855551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.18 % (3855551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.18 % (3855551)CaDiCaL version: 2.1.3
% 2.29/1.18 % (3855551)Termination reason: Instruction limit
% 2.29/1.18 % (3855551)Termination phase: Saturation
% 2.29/1.18 % (3855551)Time elapsed: 0.070 s
% 2.29/1.18 % (3855551)Peak memory usage: 88 MB
% 2.29/1.18 % (3855551)Instructions burned: 119 (million)
% 2.29/1.18 % (3855550)Refutation found. Thanks to Tanya!
% 2.29/1.18 % SZS status Theorem for theBenchmark
% 2.29/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.37 % (3855550)------------------------------
% 2.83/1.37 % (3855550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.37 % (3855550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.37 % (3855550)CaDiCaL version: 2.1.3
% 2.83/1.37 % (3855550)Termination reason: Refutation
% 2.83/1.37 % (3855550)Time elapsed: 0.023 s
% 2.83/1.37 % (3855550)Peak memory usage: 90 MB
% 2.83/1.37 % (3855550)Instructions burned: 58 (million)
% 2.83/1.37 % (3855550)------------------------------
% 2.83/1.37 % (3855550)------------------------------
% 2.83/1.37 % (3855542)Success in time 0.315 s
% 2.83/1.37 % Vampire exiting
%------------------------------------------------------------------------------