%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU250+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 : 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 12:48:00 PM UTC 2026
% Result : Theorem 2.55s 1.34s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 7 unt; 2 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 36 ~; 37 |; 13 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,relation_field(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f34,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f59]) ).
fof(f62,plain,
? [X0,X1] :
( ( ~ subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
| ~ subset(relation_field(relation_restriction(X1,X0)),X0) )
& relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f72]) ).
fof(f80,plain,
( ( ~ subset(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8))
| ~ subset(relation_field(relation_restriction(sK8,sK7)),sK7) )
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f62]) ).
fof(f89,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f90,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f114,plain,
relation(sK8),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
( ~ subset(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8))
| ~ subset(relation_field(relation_restriction(sK8,sK7)),sK7) ),
inference(cnf_transformation,[],[f80]) ).
fof(f139,definition,
( spl10_1
<=> subset(relation_field(relation_restriction(sK8,sK7)),sK7) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f140,plain,
( ~ subset(relation_field(relation_restriction(sK8,sK7)),sK7)
| spl10_1 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl10_2
<=> subset(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8)) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f143,plain,
( ~ subset(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8))
| spl10_2 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f115,f142,f139]) ).
fof(f150,plain,
( in(sK0(relation_field(relation_restriction(sK8,sK7)),sK7),relation_field(relation_restriction(sK8,sK7)))
| spl10_1 ),
inference(resolution,[],[f89,f140]) ).
fof(f154,plain,
( ~ in(sK0(relation_field(relation_restriction(sK8,sK7)),sK7),sK7)
| spl10_1 ),
inference(resolution,[],[f90,f140]) ).
fof(f177,plain,
! [X0,X1] :
( ~ in(X0,relation_field(relation_restriction(sK8,X1)))
| in(X0,X1) ),
inference(resolution,[],[f110,f114]) ).
fof(f178,plain,
( in(sK0(relation_field(relation_restriction(sK8,sK7)),sK7),sK7)
| spl10_1 ),
inference(resolution,[],[f177,f150]) ).
fof(f180,plain,
( $false
| spl10_1 ),
inference(resolution,[],[f178,f154]) ).
fof(f184,plain,
spl10_1,
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f185,plain,
( ~ in(sK0(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8)),relation_field(sK8))
| spl10_2 ),
inference(resolution,[],[f143,f90]) ).
fof(f186,plain,
( in(sK0(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8)),relation_field(relation_restriction(sK8,sK7)))
| spl10_2 ),
inference(resolution,[],[f143,f89]) ).
fof(f204,plain,
! [X0,X1] :
( ~ in(X0,relation_field(relation_restriction(sK8,X1)))
| in(X0,relation_field(sK8)) ),
inference(resolution,[],[f111,f114]) ).
fof(f208,plain,
( in(sK0(relation_field(relation_restriction(sK8,sK7)),relation_field(sK8)),relation_field(sK8))
| spl10_2 ),
inference(resolution,[],[f204,f186]) ).
fof(f209,plain,
( $false
| spl10_2 ),
inference(resolution,[],[f208,f185]) ).
fof(f213,plain,
spl10_2,
inference(avatar_contradiction_clause,[],[f209]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f144]) ).
cnf(s2,plain,
spl10_1,
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
spl10_2,
inference(sat_conversion,[],[f213]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f214,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU250+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n019.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 04:19:34 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 2.55/1.34 % (3653811)Detected formulas, will run a generic FOF schedule.
% 2.55/1.34 % (3653822)dis-21_1_sil=8000:lcm=predicate:random_seed=4130552719: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)
% 2.55/1.34 % (3653822)First to succeed.
% 2.55/1.34 % (3653822)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3653811"
% 2.55/1.34 % (3653816)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=1364096045:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.34 % (3653820)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2766363140:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.34 % (3653817)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=150011528:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.34 % (3653819)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=704228961:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.34 % (3653818)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=3723009532:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.34 % (3653819)Refutation not found, incomplete strategy
% 2.55/1.34 % (3653819)------------------------------
% 2.55/1.34 % (3653819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.34 % (3653819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.34 % (3653819)CaDiCaL version: 2.1.3
% 2.55/1.34 % (3653819)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.34 % (3653819)Time elapsed: 0.001 s
% 2.55/1.34 % (3653819)Peak memory usage: 88 MB
% 2.55/1.34 % (3653820)Also succeeded, but the first one will report.
% 2.55/1.34 % (3653821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=336674767:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.34 % (3653821)Also succeeded, but the first one will report.
% 2.55/1.34 % (3653822)Refutation found. Thanks to Tanya!
% 2.55/1.34 % SZS status Theorem for theBenchmark
% 2.55/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.34 % (3653822)------------------------------
% 2.55/1.34 % (3653822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.34 % (3653822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.34 % (3653822)CaDiCaL version: 2.1.3
% 2.55/1.34 % (3653822)Termination reason: Refutation
% 2.55/1.34 % (3653822)Time elapsed: 0.002 s
% 2.55/1.34 % (3653822)Peak memory usage: 89 MB
% 2.55/1.34 % (3653822)Instructions burned: 4 (million)
% 2.55/1.34 % (3653822)------------------------------
% 2.55/1.34 % (3653822)------------------------------
% 2.55/1.34 % (3653811)Success in time 0.273 s
% 2.55/1.34 % Vampire exiting
%------------------------------------------------------------------------------