%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU429+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:48:58 PM UTC 2026
% Result : Theorem 0.17s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 12 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 28 ( 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( ~ v1_xboole_0(X0)
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
& m2_relset_1(X3,X0,X1) )
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_38__relset_2) ).
fof(f61,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0))) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f96,plain,
( ~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(sK3,sK0,sK1)
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f61]) ).
fof(f113,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f96]) ).
fof(f114,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f96]) ).
fof(f115,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f96]) ).
fof(f116,plain,
~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f96]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f226,plain,
( v1_xboole_0(sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(resolution,[],[f161,f116]) ).
fof(f227,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f226,f113]) ).
fof(f228,plain,
~ m2_relset_1(sK3,sK0,sK1),
inference(forward_subsumption_resolution,[],[f227,f114]) ).
fof(f229,plain,
$false,
inference(forward_subsumption_resolution,[],[f228,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU429+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 05:22:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.17/1.31 % (3691339)Detected formulas, will run a generic FOF schedule.
% 0.17/1.31 % (3691349)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1102366309:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.31 % (3691349)First to succeed.
% 0.17/1.31 % (3691349)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3691339"
% 0.17/1.31 % (3691346)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=2550563395:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.31 % (3691348)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1505504146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.31 % (3691348)Also succeeded, but the first one will report.
% 0.17/1.31 % (3691345)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=3798663633:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.31 % (3691344)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=3369030312:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.31 % (3691347)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=573373565:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.31 % (3691347)Also succeeded, but the first one will report.
% 0.17/1.31 % (3691350)dis-21_1_sil=8000:lcm=predicate:random_seed=38744737: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)
% 0.17/1.31 % (3691350)Also succeeded, but the first one will report.
% 0.17/1.31 % (3691349)Refutation found. Thanks to Tanya!
% 0.17/1.31 % SZS status Theorem for theBenchmark
% 0.17/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.31 % (3691349)------------------------------
% 0.17/1.31 % (3691349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (3691349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (3691349)CaDiCaL version: 2.1.3
% 0.17/1.31 % (3691349)Termination reason: Refutation
% 0.17/1.31 % (3691349)Time elapsed: 0.003 s
% 0.17/1.31 % (3691349)Peak memory usage: 89 MB
% 0.17/1.31 % (3691349)Instructions burned: 6 (million)
% 0.17/1.31 % (3691349)------------------------------
% 0.17/1.31 % (3691349)------------------------------
% 0.17/1.31 % (3691339)Success in time 0.269 s
% 0.17/1.31 % Vampire exiting
%------------------------------------------------------------------------------