%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU180+2 : 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 : n018.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 12:47:36 PM UTC 2026
% Result : Theorem 3.55s 1.37s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 13 unt; 2 def)
% Number of atoms : 149 ( 15 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 165 ( 62 ~; 61 |; 31 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 64 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f25,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f99,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f108,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f109,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f172,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f99]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f216]) ).
fof(f226,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f109]) ).
fof(f227,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f226]) ).
fof(f285,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f285]) ).
fof(f287,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f286]) ).
fof(f288,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK10(X0,X1,X2),X0)
& ~ in(sK10(X0,X1,X2),X1) )
| ~ in(sK10(X0,X1,X2),X2) )
& ( in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f287]) ).
fof(f335,plain,
( ( ~ in(sK38,relation_field(sK40))
| ~ in(sK39,relation_field(sK40)) )
& in(ordered_pair(sK38,sK39),sK40)
& relation(sK40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39,sK40]),skolemize(X0,sK38),skolemize(X1,sK39),skolemize(X2,sK40)],[f227]) ).
fof(f389,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f288]) ).
fof(f390,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f288]) ).
fof(f434,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f513,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f217]) ).
fof(f514,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f217]) ).
fof(f525,plain,
relation(sK40),
inference(cnf_transformation,[],[f335]) ).
fof(f526,plain,
in(ordered_pair(sK38,sK39),sK40),
inference(cnf_transformation,[],[f335]) ).
fof(f527,plain,
( ~ in(sK38,relation_field(sK40))
| ~ in(sK39,relation_field(sK40)) ),
inference(cnf_transformation,[],[f335]) ).
fof(f607,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f390]) ).
fof(f608,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f389]) ).
fof(f635,definition,
( spl45_1
<=> in(sK39,relation_field(sK40)) ),
introduced(definition,[new_symbols(definition,[spl45_1])],[avatar_definition]) ).
fof(f639,definition,
( spl45_2
<=> in(sK38,relation_field(sK40)) ),
introduced(definition,[new_symbols(definition,[spl45_2])],[avatar_definition]) ).
fof(f641,plain,
( ~ in(sK38,relation_field(sK40))
| spl45_2 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f642,plain,
( ~ spl45_1
| ~ spl45_2 ),
inference(avatar_split_clause,[],[f527,f639,f635]) ).
fof(f895,plain,
relation_field(sK40) = set_union2(relation_dom(sK40),relation_rng(sK40)),
inference(resolution,[],[f434,f525]) ).
fof(f899,plain,
! [X0] :
( ~ in(X0,relation_rng(sK40))
| in(X0,relation_field(sK40)) ),
inference(superposition,[],[f608,f895]) ).
fof(f900,plain,
! [X0] :
( ~ in(X0,relation_dom(sK40))
| in(X0,relation_field(sK40)) ),
inference(superposition,[],[f607,f895]) ).
fof(f944,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK40)
| in(X1,relation_rng(sK40)) ),
inference(resolution,[],[f513,f525]) ).
fof(f950,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK40)
| in(X0,relation_dom(sK40)) ),
inference(resolution,[],[f514,f525]) ).
fof(f1098,plain,
in(sK39,relation_rng(sK40)),
inference(resolution,[],[f944,f526]) ).
fof(f1111,plain,
in(sK39,relation_field(sK40)),
inference(resolution,[],[f1098,f899]) ).
fof(f1115,plain,
spl45_1,
inference(avatar_split_clause,[],[f1111,f635]) ).
fof(f1150,plain,
in(sK38,relation_dom(sK40)),
inference(resolution,[],[f950,f526]) ).
fof(f1161,plain,
in(sK38,relation_field(sK40)),
inference(resolution,[],[f1150,f900]) ).
fof(f1163,plain,
( $false
| spl45_2 ),
inference(forward_subsumption_resolution,[],[f1161,f641]) ).
fof(f1164,plain,
spl45_2,
inference(avatar_contradiction_clause,[],[f1163]) ).
cnf(s1,plain,
( ~ spl45_1
| ~ spl45_2 ),
inference(sat_conversion,[],[f642]) ).
cnf(s9,plain,
spl45_1,
inference(sat_conversion,[],[f1115]) ).
cnf(s10,plain,
spl45_2,
inference(sat_conversion,[],[f1164]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
fof(f1165,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:57:25 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.55/1.37 % (2981514)Detected formulas, will run a generic FOF schedule.
% 3.55/1.37 % (2981519)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=1423089158:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.37 % (2981521)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=2958219340:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.37 % (2981520)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=1970327996:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.37 % (2981522)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=428575768:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.37 % (2981523)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=145117481:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.37 % (2981525)dis-21_1_sil=8000:lcm=predicate:random_seed=2456984422: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)
% 3.55/1.37 % (2981524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=243137905:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.37 % (2981524)First to succeed.
% 3.55/1.37 % (2981524)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2981514"
% 3.55/1.37 % (2981522)Instruction limit reached!
% 3.55/1.37 % (2981522)------------------------------
% 3.55/1.37 % (2981522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.37 % (2981522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.37 % (2981522)CaDiCaL version: 2.1.3
% 3.55/1.37 % (2981522)Termination reason: Instruction limit
% 3.55/1.37 % (2981522)Termination phase: Saturation
% 3.55/1.37 % (2981522)Time elapsed: 0.072 s
% 3.55/1.37 % (2981522)Peak memory usage: 90 MB
% 3.55/1.37 % (2981522)Instructions burned: 110 (million)
% 3.55/1.37 % (2981523)Instruction limit reached!
% 3.55/1.37 % (2981523)------------------------------
% 3.55/1.37 % (2981523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.37 % (2981523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.37 % (2981523)CaDiCaL version: 2.1.3
% 3.55/1.37 % (2981523)Termination reason: Instruction limit
% 3.55/1.37 % (2981523)Termination phase: Saturation
% 3.55/1.37 % (2981523)Time elapsed: 0.079 s
% 3.55/1.37 % (2981523)Peak memory usage: 89 MB
% 3.55/1.37 % (2981523)Instructions burned: 120 (million)
% 3.55/1.37 % (2981525)Instruction limit reached!
% 3.55/1.37 % (2981525)------------------------------
% 3.55/1.37 % (2981525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.37 % (2981525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.37 % (2981525)CaDiCaL version: 2.1.3
% 3.55/1.37 % (2981525)Termination reason: Instruction limit
% 3.55/1.37 % (2981525)Termination phase: Saturation
% 3.55/1.37 % (2981525)Time elapsed: 0.081 s
% 3.55/1.37 % (2981525)Peak memory usage: 90 MB
% 3.55/1.37 % (2981525)Instructions burned: 130 (million)
% 3.55/1.37 % (2981533)lrs+10_1_sil=8000:sp=occurrence:random_seed=4273054788:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.55/1.37 % (2981535)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3763990910:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.55/1.37 % (2981534)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3427101494:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.55/1.37 % (2981524)Refutation found. Thanks to Tanya!
% 3.55/1.37 % SZS status Theorem for theBenchmark
% 3.55/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.38 % (2981524)------------------------------
% 3.55/1.38 % (2981524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.38 % (2981524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.38 % (2981524)CaDiCaL version: 2.1.3
% 3.55/1.38 % (2981524)Termination reason: Refutation
% 3.55/1.38 % (2981524)Time elapsed: 0.025 s
% 3.55/1.38 % (2981524)Peak memory usage: 90 MB
% 3.55/1.38 % (2981524)Instructions burned: 32 (million)
% 3.55/1.38 % (2981524)------------------------------
% 3.55/1.38 % (2981524)------------------------------
% 3.55/1.38 % (2981514)Success in time 0.436 s
% 3.55/1.38 % Vampire exiting
%------------------------------------------------------------------------------