%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM612+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 : n020.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 12:25:01 PM UTC 2026
% Result : Theorem 0.17s 0.56s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 21 unt; 2 def)
% Number of atoms : 190 ( 36 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 191 ( 67 ~; 61 |; 46 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
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(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f107,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f109,conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f110,negated_conjecture,
~ ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f132,plain,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(rectify,[],[f104]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f141,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f140]) ).
fof(f182,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f186]) ).
fof(f261,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f266,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f267,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(ennf_transformation,[],[f132]) ).
fof(f268,plain,
( ! [X0] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,xQ) ),
inference(ennf_transformation,[],[f107]) ).
fof(f270,plain,
( sbrdtbr0(xQ) != szszuzczcdt0(sbrdtbr0(xP))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(ennf_transformation,[],[f110]) ).
fof(f326,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f182]) ).
fof(f452,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(nnf_transformation,[],[f267]) ).
fof(f453,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(flattening,[],[f452]) ).
fof(f466,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f520,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f521,plain,
! [X0] :
( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f525,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f600,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f848,plain,
xK = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f261]) ).
fof(f851,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f261]) ).
fof(f862,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f266]) ).
fof(f864,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f266]) ).
fof(f865,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f453]) ).
fof(f871,plain,
aSet0(xP),
inference(cnf_transformation,[],[f453]) ).
fof(f875,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f268]) ).
fof(f879,plain,
( sbrdtbr0(xQ) != szszuzczcdt0(sbrdtbr0(xP))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f941,definition,
( spl73_1
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl73_1])],[avatar_definition]) ).
fof(f943,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| spl73_1 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f945,definition,
( spl73_2
<=> sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)) ),
introduced(definition,[new_symbols(definition,[spl73_2])],[avatar_definition]) ).
fof(f947,plain,
( sbrdtbr0(xQ) != szszuzczcdt0(sbrdtbr0(xP))
| spl73_2 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f948,plain,
( ~ spl73_1
| ~ spl73_2 ),
inference(avatar_split_clause,[],[f879,f945,f941]) ).
fof(f998,plain,
xP = sdtmndt0(xQ,xp),
inference(forward_demodulation,[],[f865,f862]) ).
fof(f1176,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f520,f848]) ).
fof(f1178,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f1176,f600]) ).
fof(f1179,plain,
isFinite0(xQ),
inference(forward_subsumption_resolution,[],[f1178,f851]) ).
fof(f1180,plain,
( ~ isFinite0(xP)
| ~ aSet0(xP)
| spl73_1 ),
inference(resolution,[],[f521,f943]) ).
fof(f1193,plain,
( ~ isFinite0(xP)
| spl73_1 ),
inference(forward_subsumption_resolution,[],[f1180,f871]) ).
fof(f1449,plain,
( isFinite0(xP)
| ~ aSet0(xQ)
| ~ isFinite0(xQ) ),
inference(resolution,[],[f466,f875]) ).
fof(f1452,plain,
( isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(forward_subsumption_resolution,[],[f1449,f851]) ).
fof(f1455,plain,
isFinite0(xP),
inference(forward_subsumption_resolution,[],[f1452,f1179]) ).
fof(f1544,plain,
( xK != szszuzczcdt0(sbrdtbr0(xP))
| spl73_2 ),
inference(forward_demodulation,[],[f947,f848]) ).
fof(f2124,plain,
( $false
| spl73_1 ),
inference(forward_subsumption_resolution,[],[f1455,f1193]) ).
fof(f2125,plain,
spl73_1,
inference(avatar_contradiction_clause,[],[f2124]) ).
fof(f4219,plain,
( ~ isFinite0(xQ)
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp)))
| ~ aSet0(xQ) ),
inference(resolution,[],[f525,f864]) ).
fof(f4225,plain,
( sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp)))
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f4219,f1179]) ).
fof(f4255,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp))),
inference(forward_subsumption_resolution,[],[f4225,f851]) ).
fof(f4290,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)),
inference(forward_demodulation,[],[f4255,f998]) ).
fof(f4307,plain,
xK = szszuzczcdt0(sbrdtbr0(xP)),
inference(forward_demodulation,[],[f4290,f848]) ).
fof(f4309,plain,
( $false
| spl73_2 ),
inference(forward_subsumption_resolution,[],[f4307,f1544]) ).
fof(f4310,plain,
spl73_2,
inference(avatar_contradiction_clause,[],[f4309]) ).
cnf(s1,plain,
( ~ spl73_1
| ~ spl73_2 ),
inference(sat_conversion,[],[f948]) ).
cnf(s91,plain,
spl73_1,
inference(sat_conversion,[],[f2125]) ).
cnf(s230,plain,
spl73_2,
inference(sat_conversion,[],[f4310]) ).
cnf(s289,plain,
$false,
inference(rat,[],[s1,s230,s91]) ).
fof(f4312,plain,
$false,
inference(avatar_sat_refutation,[],[s289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM612+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n020.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:46:05 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.17/0.56 % (3729974)Will run a generic schedule for satisfiability detection.
% 0.17/0.56 % (3729979)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=302376758_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.56 % (3729980)% WARNING: option uhcvi not known.
% 0.17/0.56 % (3729980)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=142054062:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.56 % (3729981)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1045338599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.56 % (3729982)dis+10_1_sil=32000:sp=arity:random_seed=3912722002:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.56 % (3729983)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=93547706:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.56 % (3729984)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1453482701:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.56 % (3729985)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3417082265:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.56 % TRYING [1]
% 0.17/0.56 % TRYING [2]
% 0.17/0.56 % TRYING [3]
% 0.17/0.56 % (3729983)Instruction limit reached!
% 0.17/0.56 % (3729983)------------------------------
% 0.17/0.56 % (3729983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.56 % (3729983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.56 % (3729983)CaDiCaL version: 2.1.3
% 0.17/0.56 % (3729983)Termination reason: Instruction limit
% 0.17/0.56 % (3729983)Termination phase: Saturation
% 0.17/0.56 % (3729983)Time elapsed: 0.066 s
% 0.17/0.56 % (3729983)Peak memory usage: 13 MB
% 0.17/0.56 % (3729983)Instructions burned: 117 (million)
% 0.17/0.56 % TRYING [4]
% 0.17/0.56 % (3729982) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3729974-3729982"...
% 0.17/0.56 % (3729982)...printing done.
% 0.17/0.56 % (3729982)Refutation found. Thanks to Tanya!
% 0.17/0.56 % SZS status Theorem for theBenchmark
% 0.17/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.56 % (3729982)------------------------------
% 0.17/0.56 % (3729982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.56 % (3729982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.56 % (3729982)CaDiCaL version: 2.1.3
% 0.17/0.56 % (3729982)Termination reason: Refutation
% 0.17/0.56 % (3729982)Time elapsed: 0.073 s
% 0.17/0.56 % (3729982)Peak memory usage: 14 MB
% 0.17/0.56 % (3729982)Instructions burned: 104 (million)
% 0.17/0.56 % (3729974)Success in time 0.128 s
% 0.17/0.56 % Vampire exiting
%------------------------------------------------------------------------------