%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU435+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 : n006.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 12:49:02 PM UTC 2026
% Result : Theorem 0.18s 1.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 30 ( 13 ~; 7 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-6 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f43,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
fof(f53,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ~ m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(flattening,[],[f56]) ).
fof(f73,plain,
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
& m1_subset_1(sK5,k1_zfmisc_1(sK3))
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f53]) ).
fof(f82,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))),
inference(cnf_transformation,[],[f73]) ).
fof(f83,plain,
m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(cnf_transformation,[],[f73]) ).
fof(f84,plain,
~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4))),
inference(cnf_transformation,[],[f73]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f149,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))))
| ~ m1_subset_1(sK5,k1_zfmisc_1(sK3)) ),
inference(resolution,[],[f87,f84]) ).
fof(f152,plain,
~ m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(forward_subsumption_resolution,[],[f149,f82]) ).
fof(f153,plain,
$false,
inference(forward_subsumption_resolution,[],[f152,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU435+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 05:26:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.18/1.30 % (3660996)Detected formulas, will run a generic FOF schedule.
% 0.18/1.30 % (3661005)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2674171167:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.30 % (3661005)First to succeed.
% 0.18/1.30 % (3661005)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3660996"
% 0.18/1.30 % (3661001)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=3075082742:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.30 % (3661006)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3952727363:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.30 % (3661002)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=1479440697:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.30 % (3661003)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=578297518:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.30 % (3661007)dis-21_1_sil=8000:lcm=predicate:random_seed=3718837114: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)
% 0.18/1.30 % (3661004)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4218410322:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.30 % (3661004)Also succeeded, but the first one will report.
% 0.18/1.30 % (3661006)Also succeeded, but the first one will report.
% 0.18/1.30 % (3661007)Also succeeded, but the first one will report.
% 0.18/1.30 % (3661005)Refutation found. Thanks to Tanya!
% 0.18/1.30 % SZS status Theorem for theBenchmark
% 0.18/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.30 % (3661005)------------------------------
% 0.18/1.30 % (3661005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (3661005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (3661005)CaDiCaL version: 2.1.3
% 0.18/1.30 % (3661005)Termination reason: Refutation
% 0.18/1.30 % (3661005)Time elapsed: 0.002 s
% 0.18/1.30 % (3661005)Peak memory usage: 88 MB
% 0.18/1.30 % (3661005)Instructions burned: 4 (million)
% 0.18/1.30 % (3661005)------------------------------
% 0.18/1.30 % (3661005)------------------------------
% 0.18/1.30 % (3660996)Success in time 0.268 s
% 0.18/1.30 % Vampire exiting
%------------------------------------------------------------------------------