%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM618+3 : 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 : n010.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 12:16:01 PM UTC 2026
% Result : Theorem 2.58s 1.32s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 74 ( 25 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 79 ( 26 ~; 17 |; 33 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 25 ( 17 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f97,axiom,
! [X0] :
( ( ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
| aElementOf0(X0,xO) )
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
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(f113,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f115,conjecture,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& xx = sdtlpdtrp0(xe,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f116,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& xx = sdtlpdtrp0(xe,X0) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f128,plain,
! [X0] :
( ( ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
| aElementOf0(X0,xO) )
=> ? [X2] :
( aElementOf0(X2,szNzAzT0)
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X0 ) ),
inference(rectify,[],[f97]) ).
fof(f166,plain,
! [X0] :
( ? [X2] :
( aElementOf0(X2,szNzAzT0)
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X0 )
| ( ! [X1] :
( ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X1) != X0 )
& ~ aElementOf0(X0,xO) ) ),
inference(ennf_transformation,[],[f128]) ).
fof(f168,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(f177,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,X0) != xx ),
inference(ennf_transformation,[],[f116]) ).
fof(f384,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,szNzAzT0)
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
| ( ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X0 )
& ~ aElementOf0(X0,xO) ) ),
inference(rectify,[],[f166]) ).
fof(f385,plain,
! [X0] :
( ( aElementOf0(sK51(X0),szNzAzT0)
& szDzizrdt0(xd) = sdtlpdtrp0(xd,sK51(X0))
& aElementOf0(sK51(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,sK51(X0)) = X0 )
| ( ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X0 )
& ~ aElementOf0(X0,xO) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f384]) ).
fof(f673,plain,
! [X0] :
( sdtlpdtrp0(xe,sK51(X0)) = X0
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f385]) ).
fof(f679,plain,
! [X0] :
( aElementOf0(sK51(X0),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f385]) ).
fof(f686,plain,
! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f168]) ).
fof(f725,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f730,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f1127,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(sK51(X0),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(superposition,[],[f730,f673]) ).
fof(f1128,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(X0,xO) ),
inference(forward_subsumption_resolution,[],[f1127,f679]) ).
fof(f1129,plain,
~ aElementOf0(xx,xO),
inference(equality_resolution,[],[f1128]) ).
fof(f1131,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f1129,f686]) ).
fof(f1132,plain,
$false,
inference(forward_subsumption_resolution,[],[f1131,f725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM618+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:47:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.58/1.32 % (1295666)Detected formulas, will run a generic FOF schedule.
% 2.58/1.32 % (1295675)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3019430464:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.32 % (1295675)First to succeed.
% 2.58/1.32 % (1295675)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1295666"
% 2.58/1.32 % (1295673)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=3084065599:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.32 % (1295672)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=3525112174:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.32 % (1295674)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=337029959:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.32 % (1295671)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=314113464:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.32 % (1295676)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3509458604:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.32 % (1295677)dis-21_1_sil=8000:lcm=predicate:random_seed=1884639265: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)
% 2.58/1.32 % (1295677)Also succeeded, but the first one will report.
% 2.58/1.32 % (1295676)Also succeeded, but the first one will report.
% 2.58/1.32 % (1295674)Also succeeded, but the first one will report.
% 2.58/1.32 % (1295675)Refutation found. Thanks to Tanya!
% 2.58/1.32 % SZS status Theorem for theBenchmark
% 2.58/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.32 % (1295675)------------------------------
% 2.58/1.32 % (1295675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.32 % (1295675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.32 % (1295675)CaDiCaL version: 2.1.3
% 2.58/1.32 % (1295675)Termination reason: Refutation
% 2.58/1.32 % (1295675)Time elapsed: 0.010 s
% 2.58/1.32 % (1295675)Peak memory usage: 89 MB
% 2.58/1.32 % (1295675)Instructions burned: 27 (million)
% 2.58/1.32 % (1295675)------------------------------
% 2.58/1.32 % (1295675)------------------------------
% 2.58/1.32 % (1295666)Success in time 0.286 s
% 2.58/1.32 % Vampire exiting
%------------------------------------------------------------------------------