%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU250+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 4.94s 1.68s
% Output : Refutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 7 unt; 2 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 35 |; 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 : 42 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f209,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/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f216,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/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f217,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)],[f216]) ).
fof(f311,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,[],[f217]) ).
fof(f317,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f318,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,[],[f209]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f318]) ).
fof(f325,plain,
( ( ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1))
| ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0) )
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f311]) ).
fof(f326,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,[],[f317]) ).
fof(f327,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,[],[f326]) ).
fof(f328,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f327]) ).
fof(f333,plain,
relation(sK1),
inference(cnf_transformation,[],[f325]) ).
fof(f334,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1))
| ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0) ),
inference(cnf_transformation,[],[f325]) ).
fof(f341,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
fof(f342,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
fof(f346,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f319]) ).
fof(f347,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f319]) ).
fof(f358,definition,
( spl3_1
<=> subset(relation_field(relation_restriction(sK1,sK0)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f360,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f362,definition,
( spl3_2
<=> subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f364,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1))
| spl3_2 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f365,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f334,f362,f358]) ).
fof(f368,plain,
( in(sK2(relation_field(relation_restriction(sK1,sK0)),sK0),relation_field(relation_restriction(sK1,sK0)))
| spl3_1 ),
inference(unit_resulting_resolution,[],[f341,f360]) ).
fof(f370,plain,
( ~ in(sK2(relation_field(relation_restriction(sK1,sK0)),sK0),sK0)
| spl3_1 ),
inference(unit_resulting_resolution,[],[f342,f360]) ).
fof(f397,plain,
( ~ relation(sK1)
| spl3_1 ),
inference(unit_resulting_resolution,[],[f346,f370,f368]) ).
fof(f404,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f397,f333]) ).
fof(f405,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f411,plain,
( ~ in(sK2(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)),relation_field(sK1))
| spl3_2 ),
inference(unit_resulting_resolution,[],[f342,f364]) ).
fof(f412,plain,
( in(sK2(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)),relation_field(relation_restriction(sK1,sK0)))
| spl3_2 ),
inference(unit_resulting_resolution,[],[f341,f364]) ).
fof(f497,plain,
( ~ relation(sK1)
| spl3_2 ),
inference(unit_resulting_resolution,[],[f347,f411,f412]) ).
fof(f506,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f497,f333]) ).
fof(f507,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f506]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f365]) ).
cnf(s5,plain,
spl3_1,
inference(sat_conversion,[],[f405]) ).
cnf(s8,plain,
spl3_2,
inference(sat_conversion,[],[f507]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s5]) ).
fof(f508,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU250+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:25:18 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.94/1.68 % (14966)Detected formulas, will run a generic FOF schedule.
% 4.94/1.68 % (14971)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=1020841791:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.94/1.68 % (14974)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2391094426:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.94/1.68 % (14976)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1665622216:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.94/1.68 % (14973)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=2280583117:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.94/1.68 % (14972)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=1237378742:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.94/1.68 % (14975)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=480201069:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.94/1.68 % (14977)dis-21_1_sil=8000:lcm=predicate:random_seed=3457517822: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)
% 4.94/1.68 % (14974)Instruction limit reached!
% 4.94/1.68 % (14974)------------------------------
% 4.94/1.68 % (14974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14974)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14974)Termination reason: Instruction limit
% 4.94/1.68 % (14974)Termination phase: Saturation
% 4.94/1.68 % (14974)Time elapsed: 0.069 s
% 4.94/1.68 % (14974)Peak memory usage: 90 MB
% 4.94/1.68 % (14974)Instructions burned: 110 (million)
% 4.94/1.68 % (14975)Instruction limit reached!
% 4.94/1.68 % (14975)------------------------------
% 4.94/1.68 % (14975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14975)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14975)Termination reason: Instruction limit
% 4.94/1.68 % (14975)Termination phase: Saturation
% 4.94/1.68 % (14975)Time elapsed: 0.078 s
% 4.94/1.68 % (14975)Peak memory usage: 89 MB
% 4.94/1.68 % (14975)Instructions burned: 119 (million)
% 4.94/1.68 % (14977)Instruction limit reached!
% 4.94/1.68 % (14977)------------------------------
% 4.94/1.68 % (14977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14977)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14977)Termination reason: Instruction limit
% 4.94/1.68 % (14977)Termination phase: Saturation
% 4.94/1.68 % (14977)Time elapsed: 0.078 s
% 4.94/1.68 % (14977)Peak memory usage: 90 MB
% 4.94/1.68 % (14977)Instructions burned: 129 (million)
% 4.94/1.68 % (14976)Instruction limit reached!
% 4.94/1.68 % (14976)------------------------------
% 4.94/1.68 % (14976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14976)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14976)Termination reason: Instruction limit
% 4.94/1.68 % (14976)Termination phase: Saturation
% 4.94/1.68 % (14976)Time elapsed: 0.103 s
% 4.94/1.68 % (14976)Peak memory usage: 91 MB
% 4.94/1.68 % (14976)Instructions burned: 139 (million)
% 4.94/1.68 % (14985)lrs+10_1_sil=8000:sp=occurrence:random_seed=448097125:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.94/1.68 % (14986)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3068551226:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.94/1.68 % (14987)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2918506508:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.94/1.68 % (14986)First to succeed.
% 4.94/1.68 % (14986)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14966"
% 4.94/1.68 % (14988)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1388472423:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.94/1.68 % (14988)Also succeeded, but the first one will report.
% 4.94/1.68 % (14985)Instruction limit reached!
% 4.94/1.68 % (14985)------------------------------
% 4.94/1.68 % (14985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14985)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14985)Termination reason: Instruction limit
% 4.94/1.68 % (14985)Termination phase: Saturation
% 4.94/1.68 % (14985)Time elapsed: 0.188 s
% 4.94/1.68 % (14985)Peak memory usage: 93 MB
% 4.94/1.68 % (14985)Instructions burned: 285 (million)
% 4.94/1.68 % (14987)Instruction limit reached!
% 4.94/1.68 % (14987)------------------------------
% 4.94/1.68 % (14987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14987)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14987)Termination reason: Instruction limit
% 4.94/1.68 % (14987)Termination phase: Saturation
% 4.94/1.68 % (14987)Time elapsed: 0.225 s
% 4.94/1.68 % (14987)Peak memory usage: 93 MB
% 4.94/1.68 % (14987)Instructions burned: 325 (million)
% 4.94/1.68 % (14971)Also succeeded, but the first one will report.
% 4.94/1.68 % (14986)Refutation found. Thanks to Tanya!
% 4.94/1.68 % SZS status Theorem for theBenchmark
% 4.94/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 4.94/1.68 % (14986)------------------------------
% 4.94/1.68 % (14986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.68 % (14986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.68 % (14986)CaDiCaL version: 2.1.3
% 4.94/1.68 % (14986)Termination reason: Refutation
% 4.94/1.68 % (14986)Time elapsed: 0.009 s
% 4.94/1.68 % (14986)Peak memory usage: 90 MB
% 4.94/1.68 % (14986)Instructions burned: 12 (million)
% 4.94/1.68 % (14986)------------------------------
% 4.94/1.68 % (14986)------------------------------
% 4.94/1.68 % (14966)Success in time 0.625 s
% 4.94/1.68 % Vampire exiting
%------------------------------------------------------------------------------