%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:52:31 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 6 unt; 5 def)
% Number of atoms : 230 ( 15 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 255 ( 98 ~; 106 |; 34 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f33,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f35,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f58,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
? [X0] :
( ~ ordinal(X0)
& ! [X1] :
( ( ordinal(X1)
& subset(X1,X0) )
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f75,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( in(sK1(X0),X0)
& in(sK2(X0),X0)
& ~ in(sK1(X0),sK2(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK2(X0),sK1(X0)) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f79]) ).
fof(f96,plain,
( ~ ordinal(sK16)
& ! [X1] :
( ( ordinal(X1)
& subset(X1,sK16) )
| ~ in(X1,sK16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f68]) ).
fof(f105,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f110,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f111,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f114,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f164,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f166,plain,
! [X1] :
( ~ in(X1,sK16)
| subset(X1,sK16) ),
inference(cnf_transformation,[],[f96]) ).
fof(f167,plain,
! [X1] :
( ~ in(X1,sK16)
| ordinal(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f168,plain,
~ ordinal(sK16),
inference(cnf_transformation,[],[f96]) ).
fof(f227,plain,
( epsilon_transitive(sK16)
| subset(sK0(sK16),sK16) ),
inference(resolution,[],[f110,f166]) ).
fof(f236,definition,
( spl17_2
<=> epsilon_transitive(sK16) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f237,plain,
( ~ epsilon_transitive(sK16)
| spl17_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( epsilon_transitive(sK16)
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f241,definition,
( spl17_3
<=> subset(sK0(sK16),sK16) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f243,plain,
( subset(sK0(sK16),sK16)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f244,plain,
( spl17_3
| spl17_2 ),
inference(avatar_split_clause,[],[f227,f236,f241]) ).
fof(f246,plain,
( epsilon_connected(sK16)
| ordinal(sK2(sK16)) ),
inference(resolution,[],[f116,f167]) ).
fof(f250,definition,
( spl17_4
<=> ordinal(sK2(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f252,plain,
( ordinal(sK2(sK16))
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl17_5
<=> epsilon_connected(sK16) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f256,plain,
( epsilon_connected(sK16)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( spl17_4
| spl17_5 ),
inference(avatar_split_clause,[],[f246,f254,f250]) ).
fof(f263,plain,
( ~ epsilon_transitive(sK16)
| ordinal(sK16)
| ~ spl17_5 ),
inference(resolution,[],[f256,f105]) ).
fof(f264,plain,
( ordinal(sK16)
| ~ spl17_2
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f263,f238]) ).
fof(f265,plain,
( $false
| ~ spl17_2
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f264,f168]) ).
fof(f266,plain,
( ~ spl17_2
| ~ spl17_5 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f268,plain,
( epsilon_connected(sK16)
| ordinal(sK1(sK16)) ),
inference(resolution,[],[f117,f167]) ).
fof(f272,definition,
( spl17_7
<=> ordinal(sK1(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f274,plain,
( ordinal(sK1(sK16))
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl17_7
| spl17_5 ),
inference(avatar_split_clause,[],[f268,f254,f272]) ).
fof(f319,plain,
! [X0] :
( in(sK1(X0),sK2(X0))
| sK1(X0) = sK2(X0)
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f164,f113]) ).
fof(f322,plain,
! [X0] :
( sK1(X0) = sK2(X0)
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f319,f115]) ).
fof(f328,plain,
! [X0] :
( ~ ordinal(sK2(X0))
| ~ ordinal(sK1(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f322,f114]) ).
fof(f431,plain,
( ~ ordinal(sK1(sK16))
| epsilon_connected(sK16)
| ~ spl17_4 ),
inference(resolution,[],[f328,f252]) ).
fof(f432,plain,
( epsilon_connected(sK16)
| ~ spl17_4
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f431,f274]) ).
fof(f435,plain,
( spl17_5
| ~ spl17_4
| ~ spl17_7 ),
inference(avatar_split_clause,[],[f432,f272,f250,f254]) ).
fof(f439,plain,
( epsilon_transitive(sK16)
| ~ spl17_3 ),
inference(resolution,[],[f243,f111]) ).
fof(f441,plain,
( $false
| spl17_2
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f439,f237]) ).
fof(f442,plain,
( spl17_2
| ~ spl17_3 ),
inference(avatar_contradiction_clause,[],[f441]) ).
cnf(s2,plain,
( spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f244]) ).
cnf(s3,plain,
( spl17_4
| spl17_5 ),
inference(sat_conversion,[],[f257]) ).
cnf(s5,plain,
( ~ spl17_2
| ~ spl17_5 ),
inference(sat_conversion,[],[f266]) ).
cnf(s6,plain,
( spl17_5
| spl17_7 ),
inference(sat_conversion,[],[f275]) ).
cnf(s13,plain,
( ~ spl17_4
| spl17_5
| ~ spl17_7 ),
inference(sat_conversion,[],[f435]) ).
cnf(s14,plain,
( spl17_2
| ~ spl17_3 ),
inference(sat_conversion,[],[f442]) ).
cnf(s17,plain,
spl17_5,
inference(rat,[],[s13,s3,s6]) ).
cnf(s18,plain,
~ spl17_2,
inference(rat,[],[s5,s17]) ).
cnf(s19,plain,
~ spl17_3,
inference(rat,[],[s14,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s2,s19,s18]) ).
fof(f443,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n014.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:13:46 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.47 % (1426338)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (1426348)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=449401140:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (1426344)% WARNING: option uhcvi not known.
% 0.15/0.47 % (1426346)dis+10_1_sil=32000:sp=arity:random_seed=2509212178:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (1426343)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=997768530_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (1426344)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3222658386:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (1426345)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1091952511:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (1426347)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2011625343:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (1426349)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4035473846:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % TRYING [4]
% 0.15/0.47 % (1426346) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1426338-1426346"...
% 0.15/0.47 % TRYING [5]
% 0.15/0.47 % (1426346)...printing done.
% 0.15/0.47 % (1426346)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (1426346)------------------------------
% 0.15/0.47 % (1426346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (1426346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (1426346)CaDiCaL version: 2.1.3
% 0.15/0.47 % (1426346)Termination reason: Refutation
% 0.15/0.47 % (1426346)Time elapsed: 0.008 s
% 0.15/0.47 % (1426346)Peak memory usage: 12 MB
% 0.15/0.47 % (1426346)Instructions burned: 9 (million)
% 0.15/0.47 % (1426338)Success in time 0.043 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------