%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM539+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 : n012.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 12:24:44 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 171 ( 23 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 197 ( 61 ~; 40 |; 77 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 48 ( 37 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f49,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X0] :
( aElementOf0(X0,xT)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& ~ ( ~ ? [X0] : aElementOf0(X0,xS)
| xS = slcrc0 )
& ~ ( ~ ? [X0] : aElementOf0(X0,xT)
| xT = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1779) ).
fof(f50,axiom,
( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xT),X0) )
& aElementOf0(szmzizndt0(xT),xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1802) ).
fof(f51,conjecture,
( ( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
| szmzizndt0(xS) = szmzizndt0(xT) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
| szmzizndt0(xS) = szmzizndt0(xT) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f59,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& ~ ( ~ ? [X2] : aElementOf0(X2,xS)
| xS = slcrc0 )
& ~ ( ~ ? [X3] : aElementOf0(X3,xT)
| xT = slcrc0 ) ),
inference(rectify,[],[f49]) ).
fof(f60,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xT),X1) )
& aElementOf0(szmzizndt0(xT),xS) ),
inference(rectify,[],[f50]) ).
fof(f61,plain,
~ ( ( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) ) )
=> ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xS),X1) )
| szmzizndt0(xS) = szmzizndt0(xT) ) ),
inference(rectify,[],[f52]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f104]) ).
fof(f125,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xT) )
& aSubsetOf0(xT,szNzAzT0)
& ? [X2] : aElementOf0(X2,xS)
& slcrc0 != xS
& ? [X3] : aElementOf0(X3,xT)
& slcrc0 != xT ),
inference(ennf_transformation,[],[f59]) ).
fof(f126,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xT) )
& aSubsetOf0(xT,szNzAzT0)
& ? [X2] : aElementOf0(X2,xS)
& slcrc0 != xS
& ? [X3] : aElementOf0(X3,xT)
& slcrc0 != xT ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,xS) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xT),X1)
| ~ aElementOf0(X1,xT) )
& aElementOf0(szmzizndt0(xT),xS) ),
inference(ennf_transformation,[],[f60]) ).
fof(f128,plain,
( ? [X1] :
( ~ sdtlseqdt0(szmzizndt0(xS),X1)
& aElementOf0(X1,xT) )
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,xS) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f129,plain,
( ? [X1] :
( ~ sdtlseqdt0(szmzizndt0(xS),X1)
& aElementOf0(X1,xT) )
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(szmzizndt0(xS),xS)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,xS) ) ),
inference(flattening,[],[f128]) ).
fof(f169,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xT) )
& aSubsetOf0(xT,szNzAzT0)
& aElementOf0(sK12,xS)
& slcrc0 != xS
& aElementOf0(sK13,xT)
& slcrc0 != xT ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12),skolemize(X3,sK13)],[f126]) ).
fof(f170,plain,
( ? [X0] :
( ~ sdtlseqdt0(szmzizndt0(xS),X0)
& aElementOf0(X0,xT) )
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xS),X1)
| ~ aElementOf0(X1,xS) ) ),
inference(rectify,[],[f129]) ).
fof(f171,plain,
( ~ sdtlseqdt0(szmzizndt0(xS),sK14)
& aElementOf0(sK14,xT)
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xS),X1)
| ~ aElementOf0(X1,xS) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f170]) ).
fof(f232,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f258,plain,
! [X1] :
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f263,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(cnf_transformation,[],[f127]) ).
fof(f264,plain,
! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(szmzizndt0(xT),X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f265,plain,
aElementOf0(szmzizndt0(xT),xT),
inference(cnf_transformation,[],[f127]) ).
fof(f266,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(cnf_transformation,[],[f127]) ).
fof(f269,plain,
! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(szmzizndt0(xS),X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f271,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(cnf_transformation,[],[f171]) ).
fof(f276,plain,
sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)),
inference(resolution,[],[f263,f269]) ).
fof(f286,plain,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(resolution,[],[f258,f265]) ).
fof(f287,plain,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(resolution,[],[f258,f266]) ).
fof(f312,plain,
sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(resolution,[],[f264,f266]) ).
fof(f1110,plain,
( szmzizndt0(xS) = szmzizndt0(xT)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(resolution,[],[f232,f276]) ).
fof(f1124,plain,
( ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1110,f271]) ).
fof(f1132,plain,
( ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1124,f312]) ).
fof(f1148,plain,
~ aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(forward_subsumption_resolution,[],[f1132,f287]) ).
fof(f1154,plain,
$false,
inference(forward_subsumption_resolution,[],[f1148,f286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM539+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:24:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.37 % (2707008)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (2707014)% WARNING: option uhcvi not known.
% 0.07/0.37 % (2707015)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1421996662:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (2707013)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3797026347_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (2707014)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3558816642:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (2707016)dis+10_1_sil=32000:sp=arity:random_seed=2358057573:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (2707017)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1068469022:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (2707018)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1454946196:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (2707019)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3839761660:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % TRYING [4]
% 0.07/0.37 % (2707018) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2707008-2707018"...
% 0.07/0.37 % (2707018)...printing done.
% 0.07/0.37 % (2707018)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Theorem for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (2707018)------------------------------
% 0.07/0.37 % (2707018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (2707018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (2707018)CaDiCaL version: 2.1.3
% 0.07/0.37 % (2707018)Termination reason: Refutation
% 0.07/0.37 % (2707018)Time elapsed: 0.010 s
% 0.07/0.37 % (2707018)Peak memory usage: 12 MB
% 0.07/0.37 % (2707018)Instructions burned: 29 (million)
% 0.07/0.37 % (2707008)Success in time 0.035 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------