%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM615+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 : 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 12:16:00 PM UTC 2026
% Result : Theorem 2.72s 1.38s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 1 def)
% Number of atoms : 31 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 29 ( 13 ~; 8 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f106,axiom,
? [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X0) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5182) ).
fof(f111,conjecture,
? [X0] :
( ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& sdtlpdtrp0(xe,X0) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f112,negated_conjecture,
~ ? [X0] :
( ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& sdtlpdtrp0(xe,X0) = xp ),
inference(negated_conjecture,[status(cth)],[f111]) ).
fof(f272,plain,
! [X0] :
( ( ( ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sdtlpdtrp0(xe,X0) != xp ),
inference(ennf_transformation,[],[f112]) ).
fof(f456,plain,
( aElementOf0(sK72,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& xp = sdtlpdtrp0(xe,sK72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(X0,sK72)],[f106]) ).
fof(f875,plain,
xp = sdtlpdtrp0(xe,sK72),
inference(cnf_transformation,[],[f456]) ).
fof(f876,plain,
aElementOf0(sK72,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f456]) ).
fof(f883,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X0) != xp ),
inference(cnf_transformation,[],[f272]) ).
fof(f944,definition,
! [X0,X1] :
( sQ73_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ73_eqProxy])],[equality_proxy_definition]) ).
fof(f1088,plain,
sQ73_eqProxy(xp,sdtlpdtrp0(xe,sK72)),
inference(equality_proxy_replacement,[],[f875,f944]) ).
fof(f1091,plain,
! [X0] :
( ~ sQ73_eqProxy(sdtlpdtrp0(xe,X0),xp)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(equality_proxy_replacement,[],[f883,f944]) ).
fof(f1093,plain,
! [X0,X1] :
( sQ73_eqProxy(X1,X0)
| ~ sQ73_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f944]) ).
fof(f1127,plain,
! [X0] :
( ~ sQ73_eqProxy(xp,sdtlpdtrp0(xe,X0))
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(resolution,[],[f1093,f1091]) ).
fof(f1131,plain,
~ aElementOf0(sK72,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(resolution,[],[f1127,f1088]) ).
fof(f1133,plain,
$false,
inference(resolution,[],[f1131,f876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM615+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 20:46:35 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.72/1.38 % (3730805)Detected formulas, will run a generic FOF schedule.
% 2.72/1.38 % (3730816)dis-21_1_sil=8000:lcm=predicate:random_seed=2179872684: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)
% 2.72/1.38 % (3730816)First to succeed.
% 2.72/1.38 % (3730816)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3730805"
% 2.72/1.38 % (3730811)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=34142015:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.38 % (3730812)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=2712248468:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.38 % (3730815)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=335993055:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.38 % (3730813)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=961415290:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.38 % (3730814)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=719269904:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.38 % (3730810)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=200365058:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.38 % (3730814)Also succeeded, but the first one will report.
% 2.72/1.38 % (3730815)Also succeeded, but the first one will report.
% 2.72/1.38 % (3730813)Also succeeded, but the first one will report.
% 2.72/1.38 % (3730816)Refutation found. Thanks to Tanya!
% 2.72/1.38 % SZS status Theorem for theBenchmark
% 2.72/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.38 % (3730816)------------------------------
% 2.72/1.38 % (3730816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.38 % (3730816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.38 % (3730816)CaDiCaL version: 2.1.3
% 2.72/1.38 % (3730816)Termination reason: Refutation
% 2.72/1.38 % (3730816)Time elapsed: 0.008 s
% 2.72/1.38 % (3730816)Peak memory usage: 89 MB
% 2.72/1.38 % (3730816)Instructions burned: 23 (million)
% 2.72/1.38 % (3730816)------------------------------
% 2.72/1.38 % (3730816)------------------------------
% 2.72/1.38 % (3730805)Success in time 0.306 s
% 2.72/1.38 % Vampire exiting
%------------------------------------------------------------------------------