%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM539+2 : 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 : 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 12:15:39 PM UTC 2026
% Result : Theorem 0.18s 1.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 177 ( 26 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 212 ( 68 ~; 48 |; 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 : 51 ( 40 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f53,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(f54,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(f55,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(f59,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,[],[f53]) ).
fof(f60,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,[],[f59]) ).
fof(f61,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,[],[f54]) ).
fof(f62,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,[],[f55]) ).
fof(f63,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,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f75]) ).
fof(f80,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(sK0,xS)
& slcrc0 != xS
& aElementOf0(sK1,xT)
& slcrc0 != xT ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f60]) ).
fof(f81,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,[],[f63]) ).
fof(f82,plain,
( ~ sdtlseqdt0(szmzizndt0(xS),sK2)
& aElementOf0(sK2,xT)
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xS),X1)
| ~ aElementOf0(X1,xS) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f81]) ).
fof(f100,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xT) ),
inference(cnf_transformation,[],[f80]) ).
fof(f103,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f80]) ).
fof(f105,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(cnf_transformation,[],[f61]) ).
fof(f106,plain,
! [X1] :
( sdtlseqdt0(szmzizndt0(xT),X1)
| ~ aElementOf0(X1,xT) ),
inference(cnf_transformation,[],[f61]) ).
fof(f108,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
! [X1] :
( sdtlseqdt0(szmzizndt0(xS),X1)
| ~ aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f82]) ).
fof(f113,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(cnf_transformation,[],[f82]) ).
fof(f129,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f223,plain,
! [X0] :
( ~ sdtlseqdt0(X0,szmzizndt0(xS))
| szmzizndt0(xS) = X0
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[],[f129,f111]) ).
fof(f231,plain,
! [X0] :
( ~ sdtlseqdt0(X0,szmzizndt0(xS))
| szmzizndt0(xS) = X0
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f223,f103]) ).
fof(f247,plain,
( szmzizndt0(xS) = szmzizndt0(xT)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),xS)
| ~ aElementOf0(szmzizndt0(xS),xT) ),
inference(resolution,[],[f231,f106]) ).
fof(f255,plain,
( szmzizndt0(xS) = szmzizndt0(xT)
| ~ aElementOf0(szmzizndt0(xT),xS)
| ~ aElementOf0(szmzizndt0(xS),xT) ),
inference(forward_subsumption_resolution,[],[f247,f100]) ).
fof(f256,plain,
( ~ aElementOf0(szmzizndt0(xT),xS)
| ~ aElementOf0(szmzizndt0(xS),xT) ),
inference(forward_subsumption_resolution,[],[f255,f113]) ).
fof(f257,plain,
~ aElementOf0(szmzizndt0(xS),xT),
inference(forward_subsumption_resolution,[],[f256,f105]) ).
fof(f258,plain,
$false,
inference(forward_subsumption_resolution,[],[f257,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM539+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:25:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.18/1.50 % (3719933)Detected formulas, will run a generic FOF schedule.
% 0.18/1.50 % (3719939)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=1289332075:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.50 % (3719941)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1448834989:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.50 % (3719944)dis-21_1_sil=8000:lcm=predicate:random_seed=2602036890: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)
% 0.18/1.50 % (3719943)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=667831664:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.50 % (3719942)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1134044922:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.50 % (3719940)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=1411019044:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.50 % (3719938)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=2558701849:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.50 % (3719942)First to succeed.
% 0.18/1.50 % (3719942)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3719933"
% 0.18/1.50 % (3719941)Also succeeded, but the first one will report.
% 0.18/1.50 % (3719943)Also succeeded, but the first one will report.
% 0.18/1.50 % (3719944)Instruction limit reached!
% 0.18/1.50 % (3719944)------------------------------
% 0.18/1.50 % (3719944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (3719944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (3719944)CaDiCaL version: 2.1.3
% 0.18/1.50 % (3719944)Termination reason: Instruction limit
% 0.18/1.50 % (3719944)Termination phase: Saturation
% 0.18/1.50 % (3719944)Time elapsed: 0.053 s
% 0.18/1.50 % (3719944)Peak memory usage: 88 MB
% 0.18/1.50 % (3719944)Instructions burned: 131 (million)
% 0.18/1.50 % (3719952)lrs+10_1_sil=8000:sp=occurrence:random_seed=71466825:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.50 % (3719952)Also succeeded, but the first one will report.
% 0.18/1.50 % (3719942)Refutation found. Thanks to Tanya!
% 0.18/1.50 % SZS status Theorem for theBenchmark
% 0.18/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (3719942)------------------------------
% 0.18/1.50 % (3719942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (3719942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (3719942)CaDiCaL version: 2.1.3
% 0.18/1.50 % (3719942)Termination reason: Refutation
% 0.18/1.50 % (3719942)Time elapsed: 0.005 s
% 0.18/1.50 % (3719942)Peak memory usage: 88 MB
% 0.18/1.50 % (3719942)Instructions burned: 6 (million)
% 0.18/1.50 % (3719942)------------------------------
% 0.18/1.50 % (3719942)------------------------------
% 0.18/1.50 % (3719933)Success in time 0.436 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------