%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU424+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 : n013.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 12:48:55 PM UTC 2026
% Result : Theorem 2.55s 1.35s
% Output : Refutation 2.55s
% 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(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( ( ~ v1_xboole_0(X0)
& m1_subset_1(X2,k1_zfmisc_1(X0))
& m2_relset_1(X3,X0,X1) )
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_22__relset_2) ).
fof(f57,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_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(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(flattening,[],[f70]) ).
fof(f83,plain,
( ~ m1_subset_1(a_4_0_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(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)],[f57]) ).
fof(f97,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f83]) ).
fof(f98,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f83]) ).
fof(f99,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f83]) ).
fof(f100,plain,
~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f83]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f176,plain,
( v1_xboole_0(sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(resolution,[],[f128,f100]) ).
fof(f177,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f176,f97]) ).
fof(f178,plain,
~ m2_relset_1(sK3,sK0,sK1),
inference(forward_subsumption_resolution,[],[f177,f98]) ).
fof(f179,plain,
$false,
inference(forward_subsumption_resolution,[],[f178,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU424+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 05:19:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.55/1.35 % (848851)Detected formulas, will run a generic FOF schedule.
% 2.55/1.35 % (848984)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=292988360:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.35 % (848984)First to succeed.
% 2.55/1.35 % (848984)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-848851"
% 2.55/1.35 % (848978)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=1129224233:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.35 % (848977)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=2848324745:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.35 % (848980)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=2923931984:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.35 % (848985)dis-21_1_sil=8000:lcm=predicate:random_seed=1155618008: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)
% 2.55/1.35 % (848981)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=492343726:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.35 % (848983)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3254193083:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.35 % (848981)Also succeeded, but the first one will report.
% 2.55/1.35 % (848983)Also succeeded, but the first one will report.
% 2.55/1.35 % (848985)Also succeeded, but the first one will report.
% 2.55/1.35 % (848984)Refutation found. Thanks to Tanya!
% 2.55/1.35 % SZS status Theorem for theBenchmark
% 2.55/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.35 % (848984)------------------------------
% 2.55/1.35 % (848984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.35 % (848984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.35 % (848984)CaDiCaL version: 2.1.3
% 2.55/1.35 % (848984)Termination reason: Refutation
% 2.55/1.35 % (848984)Time elapsed: 0.003 s
% 2.55/1.35 % (848984)Peak memory usage: 89 MB
% 2.55/1.35 % (848984)Instructions burned: 4 (million)
% 2.55/1.35 % (848984)------------------------------
% 2.55/1.35 % (848984)------------------------------
% 2.55/1.35 % (848851)Success in time 0.29 s
% 2.55/1.35 % Vampire exiting
%------------------------------------------------------------------------------