%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU203+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:52:21 PM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 10 unt; 4 def)
% Number of atoms : 222 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 254 ( 109 ~; 117 |; 9 &)
% ( 14 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 122 ( 0 sgn 112 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f35,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<~> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(sK1(X0,X1,X3),X1)
| ~ in(X3,X2)
| relation_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK1(X0,X1,X3),X3),X0)
| ~ in(X3,X2)
| relation_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X2)
| relation_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f35]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f77,plain,
! [X3] :
( ~ in(X3,sK12)
| ~ in(ordered_pair(X3,sK11),sK13)
| ~ in(X3,relation_dom(sK13))
| ~ in(sK11,relation_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f78,plain,
( in(sK14,sK12)
| in(sK11,relation_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
( in(ordered_pair(sK14,sK11),sK13)
| in(sK11,relation_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
relation(sK13),
inference(cnf_transformation,[],[f40]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| in(X3,X2)
| relation_image(X0,X1) != X2 ),
inference(definition_unfolding,[],[f55,f60]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X3),X3),singleton(sK1(X0,X1,X3))),X0)
| ~ in(X3,X2)
| relation_image(X0,X1) != X2 ),
inference(definition_unfolding,[],[f54,f60]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f56,f60]) ).
fof(f96,plain,
( in(unordered_pair(unordered_pair(sK14,sK11),singleton(sK14)),sK13)
| in(sK11,relation_image(sK13,sK12)) ),
inference(definition_unfolding,[],[f79,f60]) ).
fof(f97,plain,
! [X3] :
( ~ in(X3,sK12)
| ~ in(unordered_pair(unordered_pair(X3,sK11),singleton(X3)),sK13)
| ~ in(X3,relation_dom(sK13))
| ~ in(sK11,relation_image(sK13,sK12)) ),
inference(definition_unfolding,[],[f77,f60]) ).
fof(f98,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| in(X3,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f87]) ).
fof(f99,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X3),X3),singleton(sK1(X0,X1,X3))),X0)
| ~ in(X3,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f88]) ).
fof(f100,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| in(sK1(X0,X1,X3),X1)
| ~ in(X3,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f53]) ).
fof(f102,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f94]) ).
fof(f104,plain,
! [X3,X0,X1,X4] :
( relation(X0)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| in(X3,relation_image(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f105,plain,
! [X3,X0,X1] :
( relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X3),X3),singleton(sK1(X0,X1,X3))),X0)
| ~ in(X3,relation_image(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f106,plain,
! [X3,X0,X1] :
( ~ in(X3,relation_image(X0,X1))
| in(sK1(X0,X1,X3),X1)
| relation(X0) ),
inference(consistent_polarity_flipping,[],[f100]) ).
fof(f113,plain,
! [X2,X3,X0] :
( relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f129,plain,
~ relation(sK13),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f135,definition,
( spl15_1
<=> in(sK11,relation_image(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f136,plain,
( in(sK11,relation_image(sK13,sK12))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl15_2
<=> ! [X3] :
( ~ in(X3,sK12)
| ~ in(X3,relation_dom(sK13))
| ~ in(unordered_pair(unordered_pair(X3,sK11),singleton(X3)),sK13) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f140,plain,
( ! [X3] :
( ~ in(X3,sK12)
| ~ in(X3,relation_dom(sK13))
| ~ in(unordered_pair(unordered_pair(X3,sK11),singleton(X3)),sK13) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( ~ spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f97,f139,f135]) ).
fof(f143,definition,
( spl15_3
<=> in(sK14,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f145,plain,
( in(sK14,sK12)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f78,f143,f135]) ).
fof(f148,definition,
( spl15_4
<=> in(unordered_pair(unordered_pair(sK14,sK11),singleton(sK14)),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f150,plain,
( in(unordered_pair(unordered_pair(sK14,sK11),singleton(sK14)),sK13)
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl15_1
| spl15_4 ),
inference(avatar_split_clause,[],[f96,f148,f135]) ).
fof(f171,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,sK11)),sK13)
| ~ spl15_4 ),
inference(superposition,[],[f150,f49]) ).
fof(f173,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK11,sK14)),sK13)
| ~ spl15_4 ),
inference(forward_demodulation,[],[f171,f49]) ).
fof(f190,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
| relation(X0)
| in(X2,relation_dom(X0)) ),
inference(forward_demodulation,[],[f113,f49]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| relation(X2)
| in(X1,relation_dom(X2)) ),
inference(superposition,[],[f190,f49]) ).
fof(f200,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X3)),X0)
| relation(X0)
| ~ in(X4,X1)
| in(X3,relation_image(X0,X1)) ),
inference(forward_demodulation,[],[f104,f49]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| relation(X2)
| ~ in(X1,X3)
| in(X0,relation_image(X2,X3)) ),
inference(superposition,[],[f200,f49]) ).
fof(f211,plain,
! [X3,X0,X1] :
( in(unordered_pair(singleton(sK1(X0,X1,X3)),unordered_pair(sK1(X0,X1,X3),X3)),X0)
| relation(X0)
| ~ in(X3,relation_image(X0,X1)) ),
inference(forward_demodulation,[],[f105,f49]) ).
fof(f212,plain,
! [X3,X0,X1] :
( ~ in(X3,relation_image(X0,X1))
| relation(X0)
| in(unordered_pair(singleton(sK1(X0,X1,X3)),unordered_pair(X3,sK1(X0,X1,X3))),X0) ),
inference(forward_demodulation,[],[f211,f49]) ).
fof(f341,plain,
( ! [X0] :
( relation(sK13)
| ~ in(sK14,X0)
| in(sK11,relation_image(sK13,X0)) )
| ~ spl15_4 ),
inference(resolution,[],[f201,f173]) ).
fof(f348,plain,
( ! [X0] :
( ~ in(sK14,X0)
| in(sK11,relation_image(sK13,X0)) )
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f341,f129]) ).
fof(f355,plain,
( in(sK11,relation_image(sK13,sK12))
| ~ spl15_3
| ~ spl15_4 ),
inference(resolution,[],[f348,f145]) ).
fof(f359,plain,
( ! [X3] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK11)),sK13)
| ~ in(X3,sK12)
| ~ in(X3,relation_dom(sK13)) )
| ~ spl15_2 ),
inference(forward_demodulation,[],[f140,f49]) ).
fof(f360,plain,
( spl15_1
| ~ spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f355,f148,f143,f135]) ).
fof(f361,plain,
( relation(sK13)
| in(unordered_pair(singleton(sK1(sK13,sK12,sK11)),unordered_pair(sK11,sK1(sK13,sK12,sK11))),sK13)
| ~ spl15_1 ),
inference(resolution,[],[f136,f212]) ).
fof(f362,plain,
( in(sK1(sK13,sK12,sK11),sK12)
| relation(sK13)
| ~ spl15_1 ),
inference(resolution,[],[f136,f106]) ).
fof(f365,plain,
( in(sK1(sK13,sK12,sK11),sK12)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f362,f129]) ).
fof(f366,plain,
( in(unordered_pair(singleton(sK1(sK13,sK12,sK11)),unordered_pair(sK11,sK1(sK13,sK12,sK11))),sK13)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f361,f129]) ).
fof(f367,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK11,X0)),sK13)
| ~ in(X0,sK12)
| ~ in(X0,relation_dom(sK13)) )
| ~ spl15_2 ),
inference(superposition,[],[f359,f49]) ).
fof(f372,plain,
( relation(sK13)
| in(sK1(sK13,sK12,sK11),relation_dom(sK13))
| ~ spl15_1 ),
inference(resolution,[],[f366,f191]) ).
fof(f375,plain,
( in(sK1(sK13,sK12,sK11),relation_dom(sK13))
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f372,f129]) ).
fof(f378,plain,
( ~ in(sK1(sK13,sK12,sK11),sK12)
| ~ in(sK1(sK13,sK12,sK11),relation_dom(sK13))
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f367,f366]) ).
fof(f381,plain,
( ~ in(sK1(sK13,sK12,sK11),relation_dom(sK13))
| ~ spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f378,f365]) ).
fof(f526,plain,
( $false
| ~ spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f381,f375]) ).
fof(f527,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f526]) ).
cnf(s1,plain,
( ~ spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f141]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f146]) ).
cnf(s3,plain,
( spl15_1
| spl15_4 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( spl15_1
| ~ spl15_3
| ~ spl15_4 ),
inference(sat_conversion,[],[f360]) ).
cnf(s11,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f527]) ).
cnf(s12,plain,
spl15_1,
inference(rat,[],[s6,s2,s3]) ).
cnf(s13,plain,
~ spl15_2,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s12]) ).
fof(f528,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:59:26 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 % (2013377)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (2013383)% WARNING: option uhcvi not known.
% 0.19/0.48 % (2013383)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=564424509:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48 % (2013384)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=873262109:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48 % (2013387)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=546590059:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48 % (2013386)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1493573247:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48 % (2013385)dis+10_1_sil=32000:sp=arity:random_seed=2921715714:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (2013382)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=816673116_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48 % (2013388)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1615339487:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48 % (2013383) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2013377-2013383"...
% 0.19/0.48 % (2013383)...printing done.
% 0.19/0.48 % (2013383)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (2013383)------------------------------
% 0.19/0.49 % (2013383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (2013383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (2013383)CaDiCaL version: 2.1.3
% 0.19/0.49 % (2013383)Termination reason: Refutation
% 0.19/0.49 % (2013383)Time elapsed: 0.018 s
% 0.19/0.49 % (2013383)Peak memory usage: 13 MB
% 0.19/0.49 % (2013383)Instructions burned: 31 (million)
% 0.19/0.49 % (2013377)Success in time 0.044 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------