%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:47:13 PM UTC 2026
% Result : Theorem 2.64s 6.49s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 155 ( 61 ~; 63 |; 21 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 53 ( 44 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0] :
( ( finite(X0)
& ! [X1] :
( in(X1,X0)
=> finite(X1) ) )
=> finite(union(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l22_finset_1) ).
fof(f48,axiom,
! [X0] : subset(X0,powerset(union(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f49,axiom,
! [X0,X1] :
( ( subset(X0,X1)
& finite(X1) )
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f51,axiom,
! [X0] :
( finite(X0)
<=> finite(powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
fof(f52,conjecture,
! [X0] :
( ( finite(X0)
& ! [X1] :
( in(X1,X0)
=> finite(X1) ) )
<=> finite(union(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
fof(f53,negated_conjecture,
~ ! [X0] :
( ( finite(X0)
& ! [X1] :
( in(X1,X0)
=> finite(X1) ) )
<=> finite(union(X0)) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f61,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f63,plain,
? [X0] :
( ( finite(X0)
& ! [X1] :
( finite(X1)
| ~ in(X1,X0) ) )
<~> finite(union(X0)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f73,plain,
! [X0] :
( finite(union(X0))
| ~ finite(X0)
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f74,plain,
! [X0] :
( finite(union(X0))
| ~ finite(X0)
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) ) ),
inference(flattening,[],[f73]) ).
fof(f81,plain,
! [X0,X1] :
( finite(X0)
| ~ subset(X0,X1)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f82,plain,
! [X0,X1] :
( finite(X0)
| ~ subset(X0,X1)
| ~ finite(X1) ),
inference(flattening,[],[f81]) ).
fof(f87,plain,
? [X0] :
( ( ~ finite(union(X0))
| ~ finite(X0)
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) ) )
& ( finite(union(X0))
| ( finite(X0)
& ! [X1] :
( finite(X1)
| ~ in(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f88,plain,
? [X0] :
( ( ~ finite(union(X0))
| ~ finite(X0)
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) ) )
& ( finite(union(X0))
| ( finite(X0)
& ! [X1] :
( finite(X1)
| ~ in(X1,X0) ) ) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
? [X0] :
( ( ~ finite(union(X0))
| ~ finite(X0)
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) ) )
& ( finite(union(X0))
| ( finite(X0)
& ! [X2] :
( finite(X2)
| ~ in(X2,X0) ) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
( ( ~ finite(union(sK0))
| ~ finite(sK0)
| ( ~ finite(sK1)
& in(sK1,sK0) ) )
& ( finite(union(sK0))
| ( finite(sK0)
& ! [X2] :
( finite(X2)
| ~ in(X2,sK0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f89]) ).
fof(f91,plain,
! [X0] :
( finite(union(X0))
| ~ finite(X0)
| ( ~ finite(sK2(X0))
& in(sK2(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f74]) ).
fof(f92,plain,
! [X0] :
( ( finite(X0)
| ~ finite(powerset(X0)) )
& ( finite(powerset(X0))
| ~ finite(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f103,plain,
! [X2] :
( finite(union(sK0))
| finite(X2)
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f104,plain,
( finite(union(sK0))
| finite(sK0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f105,plain,
( in(sK1,sK0)
| ~ finite(sK0)
| ~ finite(union(sK0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f106,plain,
( ~ finite(union(sK0))
| ~ finite(sK0)
| ~ finite(sK1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f113,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X0] : subset(X0,powerset(union(X0))),
inference(cnf_transformation,[],[f48]) ).
fof(f115,plain,
! [X0] :
( in(sK2(X0),X0)
| ~ finite(X0)
| finite(union(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f116,plain,
! [X0] :
( finite(union(X0))
| ~ finite(X0)
| ~ finite(sK2(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f120,plain,
! [X0] :
( finite(powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f199,plain,
! [X0] :
( ~ finite(powerset(union(X0)))
| finite(X0) ),
inference(resolution,[],[f142,f114]) ).
fof(f200,plain,
! [X0,X1] :
( ~ finite(union(X1))
| finite(X0)
| ~ in(X0,X1) ),
inference(resolution,[],[f142,f113]) ).
fof(f264,plain,
! [X0] :
( ~ finite(union(X0))
| finite(X0) ),
inference(resolution,[],[f199,f120]) ).
fof(f396,plain,
! [X0,X1] :
( ~ in(X1,sK0)
| ~ in(X0,sK0)
| finite(X1)
| finite(X0) ),
inference(resolution,[],[f200,f103]) ).
fof(f490,plain,
! [X0] :
( ~ in(X0,sK0)
| finite(X0)
| finite(X0) ),
inference(factoring,[],[f396]) ).
fof(f491,plain,
! [X0] :
( ~ in(X0,sK0)
| finite(X0) ),
inference(duplicate_literal_removal,[],[f490]) ).
fof(f495,plain,
( finite(sK1)
| ~ finite(sK0)
| ~ finite(union(sK0)) ),
inference(resolution,[],[f491,f105]) ).
fof(f497,plain,
( finite(sK2(sK0))
| ~ finite(sK0)
| finite(union(sK0)) ),
inference(resolution,[],[f491,f115]) ).
fof(f498,plain,
( finite(sK2(sK0))
| finite(union(sK0)) ),
inference(forward_subsumption_resolution,[],[f497,f104]) ).
fof(f500,plain,
( ~ finite(sK0)
| ~ finite(union(sK0)) ),
inference(forward_subsumption_resolution,[],[f495,f106]) ).
fof(f506,plain,
( finite(sK0)
| finite(sK0) ),
inference(resolution,[],[f264,f104]) ).
fof(f510,plain,
finite(sK0),
inference(duplicate_literal_removal,[],[f506]) ).
fof(f528,plain,
~ finite(union(sK0)),
inference(forward_subsumption_resolution,[],[f500,f264]) ).
fof(f536,plain,
( ~ finite(sK0)
| ~ finite(sK2(sK0)) ),
inference(resolution,[],[f528,f116]) ).
fof(f538,plain,
~ finite(sK2(sK0)),
inference(forward_subsumption_resolution,[],[f536,f510]) ).
fof(f546,plain,
finite(union(sK0)),
inference(forward_subsumption_resolution,[],[f498,f538]) ).
fof(f547,plain,
$false,
inference(forward_subsumption_resolution,[],[f546,f528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.60 % Computer : n007.cluster.edu
% 0.12/5.60 % Model : x86_64 x86_64
% 0.12/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.60 % Memory : 8046.5625MB
% 0.12/5.60 % OS : Linux 6.8.0-71-generic
% 0.12/5.60 % CPULimit : 300
% 0.12/5.60 % WCLimit : 300
% 0.12/5.60 % DateTime : Mon Sep 28 03:31:02 UTC 2026
% 0.12/5.61 % CPUTime :
% 0.12/5.61 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.64 Running first-order theorem proving
% 0.12/5.64 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
% 2.64/6.49 % (1999736)Detected formulas, will run a generic FOF schedule.
% 2.64/6.49 % (1999745)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2475370778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/6.49 % (1999745)First to succeed.
% 2.64/6.49 % (1999745)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1999736"
% 2.64/6.49 % (1999743)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=1812147947:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/6.49 % (1999744)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1231822342:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/6.49 % (1999742)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=1717863377:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/6.49 % (1999747)dis-21_1_sil=8000:lcm=predicate:random_seed=1675352396: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)
% 2.64/6.49 % (1999741)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=1641054068:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/6.49 % (1999746)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=776459340:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/6.49 % (1999744)Refutation not found, incomplete strategy
% 2.64/6.49 % (1999744)------------------------------
% 2.64/6.49 % (1999744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/6.49 % (1999744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/6.49 % (1999744)CaDiCaL version: 2.1.3
% 2.64/6.49 % (1999744)Termination reason: Refutation not found, incomplete strategy
% 2.64/6.49 % (1999744)Time elapsed: 0.002 s
% 2.64/6.49 % (1999744)Peak memory usage: 88 MB
% 2.64/6.49 % (1999744)Instructions burned: 1 (million)
% 2.64/6.49 % (1999747)Also succeeded, but the first one will report.
% 2.64/6.49 % (1999746)Also succeeded, but the first one will report.
% 2.64/6.49 % (1999745)Refutation found. Thanks to Tanya!
% 2.64/6.49 % SZS status Theorem for theBenchmark
% 2.64/6.49 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/6.49 % (1999745)------------------------------
% 2.64/6.49 % (1999745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/6.49 % (1999745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/6.49 % (1999745)CaDiCaL version: 2.1.3
% 2.64/6.49 % (1999745)Termination reason: Refutation
% 2.64/6.49 % (1999745)Time elapsed: 0.005 s
% 2.64/6.49 % (1999745)Peak memory usage: 88 MB
% 2.64/6.49 % (1999745)Instructions burned: 11 (million)
% 2.64/6.49 % (1999745)------------------------------
% 2.64/6.49 % (1999745)------------------------------
% 2.64/6.49 % (1999736)Success in time 0.305 s
% 2.64/6.49 % Vampire exiting
%------------------------------------------------------------------------------