%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM538+2 : 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 12:24:43 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 15 unt; 2 def)
% Number of atoms : 157 ( 31 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 173 ( 70 ~; 59 |; 27 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
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,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522) ).
fof(f45,axiom,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522_02) ).
fof(f46,conjecture,
( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f82]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f108,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) ),
inference(flattening,[],[f107]) ).
fof(f139,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f140,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f180,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f185,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f209,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f210,plain,
aSet0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f211,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f45]) ).
fof(f212,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f45]) ).
fof(f213,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f217,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f140]) ).
fof(f218,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnf_transformation,[],[f140]) ).
fof(f227,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(equality_resolution,[],[f213]) ).
fof(f253,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f141,f211]) ).
fof(f255,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f253,f210]) ).
fof(f473,plain,
( xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f180,f211]) ).
fof(f482,plain,
xS = sdtpldt0(sdtmndt0(xS,xx),xx),
inference(forward_subsumption_resolution,[],[f473,f210]) ).
fof(f673,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(resolution,[],[f209,f227]) ).
fof(f688,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(forward_subsumption_resolution,[],[f673,f255]) ).
fof(f692,definition,
( spl9_24
<=> isFinite0(sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f694,plain,
( ~ isFinite0(sdtmndt0(xS,xx))
| spl9_24 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f699,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(forward_subsumption_resolution,[],[f688,f217]) ).
fof(f702,definition,
( spl9_26
<=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl9_26])],[avatar_definition]) ).
fof(f704,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f705,plain,
( ~ spl9_24
| spl9_26 ),
inference(avatar_split_clause,[],[f699,f702,f692]) ).
fof(f707,plain,
( ~ aSet0(xS)
| ~ isFinite0(xS)
| ~ aElement0(xx)
| spl9_24 ),
inference(resolution,[],[f694,f185]) ).
fof(f708,plain,
( ~ isFinite0(xS)
| ~ aElement0(xx)
| spl9_24 ),
inference(forward_subsumption_resolution,[],[f707,f210]) ).
fof(f709,plain,
( ~ aElement0(xx)
| spl9_24 ),
inference(forward_subsumption_resolution,[],[f708,f212]) ).
fof(f710,plain,
( $false
| spl9_24 ),
inference(forward_subsumption_resolution,[],[f709,f255]) ).
fof(f711,plain,
spl9_24,
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f1117,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS)
| ~ spl9_26 ),
inference(superposition,[],[f704,f482]) ).
fof(f1135,plain,
( $false
| ~ spl9_26 ),
inference(forward_subsumption_resolution,[],[f1117,f218]) ).
fof(f1136,plain,
~ spl9_26,
inference(avatar_contradiction_clause,[],[f1135]) ).
cnf(s29,plain,
( ~ spl9_24
| spl9_26 ),
inference(sat_conversion,[],[f705]) ).
cnf(s30,plain,
spl9_24,
inference(sat_conversion,[],[f711]) ).
cnf(s47,plain,
~ spl9_26,
inference(sat_conversion,[],[f1136]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s29,s47,s30]) ).
fof(f1137,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:23:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.47 % (2370298)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2370306)dis+10_1_sil=32000:sp=arity:random_seed=1420567770:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (2370304)% WARNING: option uhcvi not known.
% 0.15/0.47 % (2370304)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=404841463:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (2370303)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1149643461_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (2370307)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=701827031:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (2370305)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1954471898:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (2370309)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3461506573:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (2370308)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=792665309:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % (2370306) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2370298-2370306"...
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (2370306)...printing done.
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (2370306)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2370306)------------------------------
% 0.15/0.47 % (2370306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2370306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2370306)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2370306)Termination reason: Refutation
% 0.15/0.47 % (2370306)Time elapsed: 0.014 s
% 0.15/0.47 % (2370306)Peak memory usage: 12 MB
% 0.15/0.47 % (2370306)Instructions burned: 33 (million)
% 0.15/0.47 % (2370298)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------