%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU264+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:48:04 PM UTC 2026
% Result : Theorem 3.55s 1.48s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 9 unt; 2 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 80 ( 35 ~; 26 |; 9 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 59 ( 0 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f16,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(X0,X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(X0,X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f28]) ).
fof(f34,plain,
( ~ relation_of2_as_subset(sK6,sK5,sK4)
& subset(sK3,sK4)
& relation_of2_as_subset(sK6,sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f27]) ).
fof(f43,plain,
! [X2,X0,X1] :
( subset(relation_rng(X2),X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0] :
( ~ subset(relation_rng(sK6),sK4)
| ~ relation_of2_as_subset(sK6,sK5,X0) ),
inference(resolution,[],[f45,f48]) ).
fof(f56,definition,
( spl7_1
<=> ! [X0] : ~ relation_of2_as_subset(sK6,sK5,X0) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f57,plain,
( ! [X0] : ~ relation_of2_as_subset(sK6,sK5,X0)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl7_2
<=> subset(relation_rng(sK6),sK4) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f61,plain,
( ~ subset(relation_rng(sK6),sK4)
| spl7_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f54,f59,f56]) ).
fof(f64,plain,
( ! [X0] :
( ~ subset(relation_rng(sK6),X0)
| ~ subset(X0,sK4) )
| spl7_2 ),
inference(resolution,[],[f61,f49]) ).
fof(f70,plain,
( ! [X0,X1] :
( ~ relation_of2_as_subset(sK6,X1,X0)
| ~ subset(X0,sK4) )
| spl7_2 ),
inference(resolution,[],[f64,f43]) ).
fof(f74,plain,
( ~ subset(sK3,sK4)
| spl7_2 ),
inference(resolution,[],[f70,f46]) ).
fof(f77,plain,
( $false
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f74,f47]) ).
fof(f78,plain,
spl7_2,
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f79,plain,
( $false
| ~ spl7_1 ),
inference(resolution,[],[f57,f46]) ).
fof(f82,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s1,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
spl7_2,
inference(sat_conversion,[],[f78]) ).
cnf(s3,plain,
~ spl7_1,
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU264+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.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 04:25:52 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
% 3.55/1.48 % (4142960)Detected formulas, will run a generic FOF schedule.
% 3.55/1.48 % (4142968)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3982521678:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.48 % (4142968)Refutation not found, incomplete strategy
% 3.55/1.48 % (4142968)------------------------------
% 3.55/1.48 % (4142968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (4142968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (4142968)CaDiCaL version: 2.1.3
% 3.55/1.48 % (4142968)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.48 % (4142968)Time elapsed: 0.001 s
% 3.55/1.48 % (4142968)Peak memory usage: 88 MB
% 3.55/1.48 % (4142967)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=1896767486:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.48 % (4142965)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=1237141061:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.48 % (4142970)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3558682713:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.48 % (4142966)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=3343324977:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.48 % (4142969)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2458306585:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.48 % (4142969)Refutation not found, incomplete strategy
% 3.55/1.48 % (4142969)------------------------------
% 3.55/1.48 % (4142969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (4142969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (4142969)CaDiCaL version: 2.1.3
% 3.55/1.48 % (4142969)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.48 % (4142969)Time elapsed: 0.001 s
% 3.55/1.48 % (4142969)Peak memory usage: 87 MB
% 3.55/1.48 % (4142970)First to succeed.
% 3.55/1.48 % (4142970)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4142960"
% 3.55/1.48 % (4142971)dis-21_1_sil=8000:lcm=predicate:random_seed=2705420092: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)
% 3.55/1.48 % (4142971)Also succeeded, but the first one will report.
% 3.55/1.48 % (4142968)------------------------------
% 3.55/1.48 % (4142968)------------------------------
% 3.55/1.48 % (4142969)------------------------------
% 3.55/1.48 % (4142969)------------------------------
% 3.55/1.48 % (4142970)Refutation found. Thanks to Tanya!
% 3.55/1.48 % SZS status Theorem for theBenchmark
% 3.55/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.48 % (4142970)------------------------------
% 3.55/1.48 % (4142970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (4142970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (4142970)CaDiCaL version: 2.1.3
% 3.55/1.48 % (4142970)Termination reason: Refutation
% 3.55/1.48 % (4142970)Time elapsed: 0.003 s
% 3.55/1.48 % (4142970)Peak memory usage: 89 MB
% 3.55/1.48 % (4142970)Instructions burned: 2 (million)
% 3.55/1.48 % (4142970)------------------------------
% 3.55/1.48 % (4142970)------------------------------
% 3.55/1.48 % (4142960)Success in time 0.421 s
% 3.55/1.48 % Vampire exiting
%------------------------------------------------------------------------------