%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM556+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 : n003.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 12:24:48 PM UTC 2026
% Result : Theorem 2.50s 0.98s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 116 ( 27 unt; 8 def)
% Number of atoms : 348 ( 62 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 376 ( 144 ~; 138 |; 70 &)
% ( 12 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 49 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/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(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,axiom,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
fof(f72,conjecture,
( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f73,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f81,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(f83,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f110]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f135]) ).
fof(f166,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(f167,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) ),
inference(ennf_transformation,[],[f73]) ).
fof(f221,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,[],[f81]) ).
fof(f222,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,[],[f221]) ).
fof(f223,plain,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& 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)) ) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f224,plain,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& 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)) ) ) ),
inference(flattening,[],[f223]) ).
fof(f225,plain,
( ( ~ aElementOf0(sK19,xS)
& aElementOf0(sK19,xP)
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f167]) ).
fof(f226,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f270,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f294,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f295,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f338,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f366,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f370,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f166]) ).
fof(f372,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f373,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f374,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f375,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f376,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f379,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f222]) ).
fof(f380,plain,
! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1
| ~ aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f222]) ).
fof(f391,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f224]) ).
fof(f394,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f224]) ).
fof(f395,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f224]) ).
fof(f397,plain,
( aElementOf0(sK19,xP)
| xk != sbrdtbr0(xP) ),
inference(cnf_transformation,[],[f225]) ).
fof(f398,plain,
( ~ aElementOf0(sK19,xS)
| xk != sbrdtbr0(xP) ),
inference(cnf_transformation,[],[f225]) ).
fof(f424,definition,
sF20 = sbrdtbr0(xP),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f425,plain,
sbrdtbr0(xP) = sF20,
inference(reorient_equations,[],[f424]) ).
fof(f426,plain,
( ~ aElementOf0(sK19,xS)
| xk != sF20 ),
inference(definition_folding,[],[f398,f425]) ).
fof(f427,plain,
( aElementOf0(sK19,xP)
| xk != sF20 ),
inference(definition_folding,[],[f397,f425]) ).
fof(f431,definition,
( spl21_1
<=> xk = sF20 ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f433,plain,
( xk != sF20
| spl21_1 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f440,definition,
( spl21_3
<=> aElementOf0(sK19,xP) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f442,plain,
( aElementOf0(sK19,xP)
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,plain,
( ~ spl21_1
| spl21_3 ),
inference(avatar_split_clause,[],[f427,f440,f431]) ).
fof(f445,definition,
( spl21_4
<=> aElementOf0(sK19,xS) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f447,plain,
( ~ aElementOf0(sK19,xS)
| spl21_4 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
( ~ spl21_1
| ~ spl21_4 ),
inference(avatar_split_clause,[],[f426,f445,f431]) ).
fof(f449,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ),
inference(forward_demodulation,[],[f380,f379]) ).
fof(f469,plain,
sF20 = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(forward_demodulation,[],[f425,f379]) ).
fof(f471,definition,
( spl21_8
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
fof(f472,plain,
( aElement0(xx)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f473,plain,
( ~ aElement0(xx)
| spl21_8 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f501,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f226,f366]) ).
fof(f508,plain,
( ~ aSet0(xS)
| spl21_8 ),
inference(forward_subsumption_resolution,[],[f501,f473]) ).
fof(f509,plain,
( $false
| spl21_8 ),
inference(forward_subsumption_resolution,[],[f508,f338]) ).
fof(f510,plain,
spl21_8,
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f1721,plain,
( ~ isFinite0(xQ)
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ aSet0(xQ) ),
inference(resolution,[],[f295,f375]) ).
fof(f1732,plain,
( sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f1721,f373]) ).
fof(f1740,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),
inference(forward_subsumption_resolution,[],[f1732,f374]) ).
fof(f2035,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(resolution,[],[f294,f395]) ).
fof(f2044,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f2035,f472]) ).
fof(f2055,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f2044,f394]) ).
fof(f2443,plain,
xk = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),
inference(forward_demodulation,[],[f1740,f372]) ).
fof(f2445,definition,
( spl21_83
<=> isFinite0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl21_83])],[avatar_definition]) ).
fof(f2447,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| spl21_83 ),
inference(avatar_component_clause,[],[f2445]) ).
fof(f2453,plain,
( sF20 = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl21_8 ),
inference(forward_demodulation,[],[f2055,f469]) ).
fof(f2459,plain,
( xk = sF20
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ spl21_8 ),
inference(forward_demodulation,[],[f2453,f2443]) ).
fof(f2460,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| spl21_1
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f2459,f433]) ).
fof(f2461,plain,
( ~ spl21_83
| spl21_1
| ~ spl21_8 ),
inference(avatar_split_clause,[],[f2460,f471,f431,f2445]) ).
fof(f2535,plain,
( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ~ aElement0(xy)
| spl21_83 ),
inference(resolution,[],[f2447,f270]) ).
fof(f2536,plain,
( ~ isFinite0(xQ)
| ~ aElement0(xy)
| spl21_83 ),
inference(forward_subsumption_resolution,[],[f2535,f374]) ).
fof(f2537,plain,
( ~ aElement0(xy)
| spl21_83 ),
inference(forward_subsumption_resolution,[],[f2536,f373]) ).
fof(f2538,plain,
( $false
| spl21_83 ),
inference(forward_subsumption_resolution,[],[f2537,f376]) ).
fof(f2539,plain,
spl21_83,
inference(avatar_contradiction_clause,[],[f2538]) ).
fof(f2541,plain,
( aElementOf0(sK19,sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ spl21_3 ),
inference(forward_demodulation,[],[f442,f379]) ).
fof(f2694,plain,
( aElementOf0(sK19,sdtmndt0(xQ,xy))
| xx = sK19
| ~ spl21_3 ),
inference(resolution,[],[f2541,f449]) ).
fof(f2705,definition,
( spl21_103
<=> xx = sK19 ),
introduced(definition,[new_symbols(definition,[spl21_103])],[avatar_definition]) ).
fof(f2707,plain,
( xx = sK19
| ~ spl21_103 ),
inference(avatar_component_clause,[],[f2705]) ).
fof(f2709,definition,
( spl21_104
<=> aElementOf0(sK19,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[spl21_104])],[avatar_definition]) ).
fof(f2711,plain,
( aElementOf0(sK19,sdtmndt0(xQ,xy))
| ~ spl21_104 ),
inference(avatar_component_clause,[],[f2709]) ).
fof(f2712,plain,
( spl21_103
| spl21_104
| ~ spl21_3 ),
inference(avatar_split_clause,[],[f2694,f440,f2709,f2705]) ).
fof(f2724,plain,
( ~ aElementOf0(xx,xS)
| spl21_4
| ~ spl21_103 ),
inference(superposition,[],[f447,f2707]) ).
fof(f2725,plain,
( $false
| spl21_4
| ~ spl21_103 ),
inference(forward_subsumption_resolution,[],[f2724,f366]) ).
fof(f2726,plain,
( spl21_4
| ~ spl21_103 ),
inference(avatar_contradiction_clause,[],[f2725]) ).
fof(f2854,plain,
( aElementOf0(sK19,xQ)
| ~ spl21_104 ),
inference(resolution,[],[f2711,f391]) ).
fof(f2890,plain,
( aElementOf0(sK19,xS)
| ~ spl21_104 ),
inference(resolution,[],[f2854,f370]) ).
fof(f2896,plain,
( $false
| spl21_4
| ~ spl21_104 ),
inference(forward_subsumption_resolution,[],[f2890,f447]) ).
fof(f2897,plain,
( spl21_4
| ~ spl21_104 ),
inference(avatar_contradiction_clause,[],[f2896]) ).
cnf(s2,plain,
( ~ spl21_1
| spl21_3 ),
inference(sat_conversion,[],[f443]) ).
cnf(s3,plain,
( ~ spl21_1
| ~ spl21_4 ),
inference(sat_conversion,[],[f448]) ).
cnf(s8,plain,
spl21_8,
inference(sat_conversion,[],[f510]) ).
cnf(s77,plain,
( spl21_1
| ~ spl21_8
| ~ spl21_83 ),
inference(sat_conversion,[],[f2461]) ).
cnf(s78,plain,
spl21_83,
inference(sat_conversion,[],[f2539]) ).
cnf(s97,plain,
( ~ spl21_3
| spl21_103
| spl21_104 ),
inference(sat_conversion,[],[f2712]) ).
cnf(s99,plain,
( spl21_4
| ~ spl21_103 ),
inference(sat_conversion,[],[f2726]) ).
cnf(s100,plain,
( spl21_4
| ~ spl21_104 ),
inference(sat_conversion,[],[f2897]) ).
cnf(s101,plain,
( spl21_1
| ~ spl21_8 ),
inference(rat,[],[s77,s78]) ).
cnf(s126,plain,
spl21_1,
inference(rat,[],[s101,s8]) ).
cnf(s133,plain,
~ spl21_4,
inference(rat,[],[s3,s126]) ).
cnf(s134,plain,
~ spl21_104,
inference(rat,[],[s100,s133]) ).
cnf(s135,plain,
~ spl21_103,
inference(rat,[],[s99,s133]) ).
cnf(s136,plain,
~ spl21_3,
inference(rat,[],[s97,s134,s135]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s2,s136,s126]) ).
fof(f2900,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:30:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.42 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
% 2.50/0.98 % (896743)Will run a generic schedule for satisfiability detection.
% 2.50/0.98 % (896748)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=339895584_2999 on theBenchmark for (2999ds/0Mi)
% 2.50/0.98 % (896749)% WARNING: option uhcvi not known.
% 2.50/0.98 % TRYING [1]
% 2.50/0.98 % TRYING [2]
% 2.50/0.98 % (896750)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2611908266:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.50/0.98 % (896749)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2982586471:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.50/0.98 % (896751)dis+10_1_sil=32000:sp=arity:random_seed=4038849760:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.50/0.98 % (896752)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=786170350:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.50/0.98 % (896753)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=508023657:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.50/0.98 % (896754)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2597936488:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.50/0.98 % TRYING [3]
% 2.50/0.98 % TRYING [4]
% 2.50/0.98 % TRYING [5]
% 2.50/0.98 % TRYING [6]
% 2.50/0.98 % (896751)Instruction limit reached!
% 2.50/0.98 % (896751)------------------------------
% 2.50/0.98 % (896751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896751)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896751)Termination reason: Instruction limit
% 2.50/0.98 % (896751)Termination phase: Saturation
% 2.50/0.98 % (896751)Time elapsed: 0.066 s
% 2.50/0.98 % (896751)Peak memory usage: 13 MB
% 2.50/0.98 % (896751)Instructions burned: 103 (million)
% 2.50/0.98 % (896752)Instruction limit reached!
% 2.50/0.98 % (896752)------------------------------
% 2.50/0.98 % (896752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896752)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896752)Termination reason: Instruction limit
% 2.50/0.98 % (896752)Termination phase: Saturation
% 2.50/0.98 % (896752)Time elapsed: 0.072 s
% 2.50/0.98 % (896752)Peak memory usage: 13 MB
% 2.50/0.98 % (896752)Instructions burned: 116 (million)
% 2.50/0.98 % (896753)Instruction limit reached!
% 2.50/0.98 % (896753)------------------------------
% 2.50/0.98 % (896753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896753)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896753)Termination reason: Instruction limit
% 2.50/0.98 % (896753)Termination phase: Saturation
% 2.50/0.98 % (896753)Time elapsed: 0.081 s
% 2.50/0.98 % (896753)Peak memory usage: 14 MB
% 2.50/0.98 % (896753)Instructions burned: 132 (million)
% 2.50/0.98 % (896762)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1659200664:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.50/0.98 % (896763)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4086256520:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.50/0.98 % TRYING [1]
% 2.50/0.98 % (896754)Instruction limit reached!
% 2.50/0.98 % (896754)------------------------------
% 2.50/0.98 % (896754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896754)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896754)Termination reason: Instruction limit
% 2.50/0.98 % (896754)Termination phase: Saturation
% 2.50/0.98 % (896754)Time elapsed: 0.097 s
% 2.50/0.98 % (896754)Peak memory usage: 15 MB
% 2.50/0.98 % (896754)Instructions burned: 159 (million)
% 2.50/0.98 % TRYING [2]
% 2.50/0.98 % TRYING [3]
% 2.50/0.98 % (896764)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=2465568647:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.50/0.98 % TRYING [4]
% 2.50/0.98 % (896767)ott-21_1_sil=16000:fs=off:random_seed=1583508594:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.50/0.98 % TRYING [7]
% 2.50/0.98 % TRYING [5]
% 2.50/0.98 % (896763)Instruction limit reached!
% 2.50/0.98 % (896763)------------------------------
% 2.50/0.98 % (896763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896763)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896763)Termination reason: Instruction limit
% 2.50/0.98 % (896763)Termination phase: Saturation
% 2.50/0.98 % (896763)Time elapsed: 0.087 s
% 2.50/0.98 % (896763)Peak memory usage: 13 MB
% 2.50/0.98 % (896763)Instructions burned: 131 (million)
% 2.50/0.98 % TRYING [6]
% 2.50/0.98 % (896770)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4283115117:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.50/0.98 % (896767)Instruction limit reached!
% 2.50/0.98 % (896767)------------------------------
% 2.50/0.98 % (896767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896767)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896767)Termination reason: Instruction limit
% 2.50/0.98 % (896767)Termination phase: Saturation
% 2.50/0.98 % (896767)Time elapsed: 0.095 s
% 2.50/0.98 % (896767)Peak memory usage: 13 MB
% 2.50/0.98 % (896767)Instructions burned: 180 (million)
% 2.50/0.98 % (896772)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2371908860:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.50/0.98 % TRYING [1]
% 2.50/0.98 % TRYING [2]
% 2.50/0.98 % TRYING [3]
% 2.50/0.98 % TRYING [4]
% 2.50/0.98 % TRYING [8]
% 2.50/0.98 % TRYING [5]
% 2.50/0.98 % (896762)Instruction limit reached!
% 2.50/0.98 % (896762)------------------------------
% 2.50/0.98 % (896762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896762)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896762)Termination reason: Instruction limit
% 2.50/0.98 % (896762)Termination phase: Finite model building SAT solving
% 2.50/0.98 % (896762)Time elapsed: 0.338 s
% 2.50/0.98 % (896762)Peak memory usage: 27 MB
% 2.50/0.98 % (896762)Instructions burned: 714 (million)
% 2.50/0.98 % (896774)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=685730352:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 2.50/0.98 % (896774) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-896743-896774"...
% 2.50/0.98 % (896774)...printing done.
% 2.50/0.98 % (896774)Refutation found. Thanks to Tanya!
% 2.50/0.98 % SZS status Theorem for theBenchmark
% 2.50/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/0.98 % (896774)------------------------------
% 2.50/0.98 % (896774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.50/0.98 % (896774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.98 % (896774)CaDiCaL version: 2.1.3
% 2.50/0.98 % (896774)Termination reason: Refutation
% 2.50/0.98 % (896774)Time elapsed: 0.063 s
% 2.50/0.98 % (896774)Peak memory usage: 14 MB
% 2.50/0.98 % (896774)Instructions burned: 99 (million)
% 2.50/0.98 % (896743)Success in time 0.555 s
% 2.50/0.98 % Vampire exiting
%------------------------------------------------------------------------------