%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM560+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:15:45 PM UTC 2026
% Result : Theorem 2.46s 1.38s
% Output : Refutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 81 ( 13 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 95 ( 28 ~; 16 |; 40 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f68,conjecture,
( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f70,plain,
~ ( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xF,xy))
=> aElementOf0(X1,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
inference(rectify,[],[f69]) ).
fof(f75,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f76,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) ),
inference(flattening,[],[f75]) ).
fof(f90,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X0,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X0) )
& ( ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f91,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X0,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X0) )
& ( ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ? [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
& aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X1,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X1) )
& ( ( aElementOf0(X1,szDzozmdt0(xF))
& xy = sdtlpdtrp0(xF,X1) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
( ~ aElementOf0(sK0,szDzozmdt0(xF))
& aElementOf0(sK0,sdtlbdtrb0(xF,xy))
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X1,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X1) )
& ( ( aElementOf0(X1,szDzozmdt0(xF))
& xy = sdtlpdtrp0(xF,X1) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f92]) ).
fof(f105,plain,
! [X1] :
( ~ aElementOf0(X1,sdtlbdtrb0(xF,xy))
| aElementOf0(X1,szDzozmdt0(xF)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f109,plain,
aElementOf0(sK0,sdtlbdtrb0(xF,xy)),
inference(cnf_transformation,[],[f93]) ).
fof(f110,plain,
~ aElementOf0(sK0,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f93]) ).
fof(f134,plain,
aElementOf0(sK0,szDzozmdt0(xF)),
inference(resolution,[],[f105,f109]) ).
fof(f135,plain,
$false,
inference(forward_subsumption_resolution,[],[f134,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM560+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.43 % Computer : n026.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Sun Sep 27 20:33:20 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.46/1.38 % (3185711)Detected formulas, will run a generic FOF schedule.
% 2.46/1.38 % (3185720)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1122416292:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.46/1.38 % (3185720)First to succeed.
% 2.46/1.38 % (3185720)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3185711"
% 2.46/1.38 % (3185721)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2506313635:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.46/1.38 % (3185717)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=1140572019:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.46/1.38 % (3185719)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3786838118:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.46/1.38 % (3185716)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=1849432708:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.46/1.38 % (3185718)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=3026250831:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.46/1.38 % (3185722)dis-21_1_sil=8000:lcm=predicate:random_seed=4243004055: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)
% 2.46/1.38 % (3185719)Also succeeded, but the first one will report.
% 2.46/1.38 % (3185721)Also succeeded, but the first one will report.
% 2.46/1.38 % (3185722)Also succeeded, but the first one will report.
% 2.46/1.38 % (3185720)Refutation found. Thanks to Tanya!
% 2.46/1.38 % SZS status Theorem for theBenchmark
% 2.46/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.46/1.38 % (3185720)------------------------------
% 2.46/1.38 % (3185720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.46/1.38 % (3185720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/1.38 % (3185720)CaDiCaL version: 2.1.3
% 2.46/1.38 % (3185720)Termination reason: Refutation
% 2.46/1.38 % (3185720)Time elapsed: 0.001 s
% 2.46/1.38 % (3185720)Peak memory usage: 88 MB
% 2.46/1.38 % (3185720)Instructions burned: 2 (million)
% 2.46/1.38 % (3185720)------------------------------
% 2.46/1.38 % (3185720)------------------------------
% 2.46/1.38 % (3185711)Success in time 0.275 s
% 2.46/1.38 % Vampire exiting
%------------------------------------------------------------------------------