%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU236+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 : n006.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 12:52:32 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 103 ( 16 unt; 6 def)
% Number of atoms : 248 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 247 ( 102 ~; 105 |; 12 &)
% ( 17 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 68 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f10,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f11,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f12,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f27,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f43,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f46,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f50,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f51,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f58,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f71,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f80,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f81,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f85,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f87,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f88,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f87]) ).
fof(f94,plain,
? [X0] :
( ? [X1] :
( ( in(X0,X1)
<~> ordinal_subset(succ(X0),X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f102,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f101]) ).
fof(f106,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f114,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f116,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f119,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| subset(X1,X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f175,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f176,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f179,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f183,plain,
( ordinal_subset(succ(sK16),sK17)
| in(sK16,sK17) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
( ~ ordinal_subset(succ(sK16),sK17)
| ~ in(sK16,sK17) ),
inference(cnf_transformation,[],[f94]) ).
fof(f185,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f94]) ).
fof(f186,plain,
ordinal(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f194,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f199,plain,
! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f138,f114]) ).
fof(f200,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f179,f114]) ).
fof(f201,plain,
( ~ ordinal_subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ in(sK16,sK17) ),
inference(definition_unfolding,[],[f184,f114]) ).
fof(f202,plain,
( ordinal_subset(set_union2(sK16,singleton(sK16)),sK17)
| in(sK16,sK17) ),
inference(definition_unfolding,[],[f183,f114]) ).
fof(f203,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f116]) ).
fof(f207,definition,
( spl18_1
<=> in(sK16,sK17) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f208,plain,
( ~ in(sK16,sK17)
| spl18_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( in(sK16,sK17)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl18_2
<=> ordinal_subset(set_union2(sK16,singleton(sK16)),sK17) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f212,plain,
( ~ ordinal_subset(set_union2(sK16,singleton(sK16)),sK17)
| spl18_2 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( ordinal_subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f202,f211,f207]) ).
fof(f215,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f201,f211,f207]) ).
fof(f305,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f119,f106]) ).
fof(f340,plain,
( ~ ordinal(set_union2(sK16,singleton(sK16)))
| subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ ordinal(sK17)
| ~ spl18_2 ),
inference(resolution,[],[f176,f213]) ).
fof(f349,plain,
( ~ ordinal(set_union2(sK16,singleton(sK16)))
| subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f340,f185]) ).
fof(f351,definition,
( spl18_5
<=> subset(set_union2(sK16,singleton(sK16)),sK17) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f352,plain,
( ~ subset(set_union2(sK16,singleton(sK16)),sK17)
| spl18_5 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f355,definition,
( spl18_6
<=> ordinal(set_union2(sK16,singleton(sK16))) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f356,plain,
( ordinal(set_union2(sK16,singleton(sK16)))
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
( ~ ordinal(set_union2(sK16,singleton(sK16)))
| spl18_6 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f358,plain,
( spl18_5
| ~ spl18_6
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f349,f211,f355,f351]) ).
fof(f359,plain,
( ~ ordinal(sK16)
| spl18_6 ),
inference(resolution,[],[f357,f199]) ).
fof(f361,plain,
( $false
| spl18_6 ),
inference(forward_subsumption_resolution,[],[f359,f186]) ).
fof(f362,plain,
spl18_6,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f380,plain,
( ! [X0] :
( ~ in(X0,set_union2(sK16,singleton(sK16)))
| in(X0,sK17) )
| ~ spl18_5 ),
inference(resolution,[],[f353,f122]) ).
fof(f385,plain,
( in(sK16,sK17)
| ~ spl18_5 ),
inference(resolution,[],[f380,f200]) ).
fof(f389,plain,
( $false
| spl18_1
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f385,f208]) ).
fof(f390,plain,
( spl18_1
| ~ spl18_5 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f392,plain,
( ~ ordinal(set_union2(sK16,singleton(sK16)))
| ~ subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ ordinal(sK17)
| spl18_2 ),
inference(resolution,[],[f212,f175]) ).
fof(f397,plain,
( ~ subset(set_union2(sK16,singleton(sK16)),sK17)
| ~ ordinal(sK17)
| spl18_2
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f392,f356]) ).
fof(f400,plain,
( ~ subset(set_union2(sK16,singleton(sK16)),sK17)
| spl18_2
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f397,f185]) ).
fof(f401,plain,
( ~ spl18_5
| spl18_2
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f400,f355,f211,f351]) ).
fof(f405,plain,
( ~ subset(sK16,sK17)
| ~ subset(singleton(sK16),sK17)
| spl18_5 ),
inference(resolution,[],[f352,f194]) ).
fof(f407,definition,
( spl18_7
<=> subset(singleton(sK16),sK17) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f409,plain,
( ~ subset(singleton(sK16),sK17)
| spl18_7 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f411,definition,
( spl18_8
<=> subset(sK16,sK17) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f413,plain,
( ~ subset(sK16,sK17)
| spl18_8 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f414,plain,
( ~ spl18_7
| ~ spl18_8
| spl18_5 ),
inference(avatar_split_clause,[],[f405,f351,f411,f407]) ).
fof(f417,plain,
( ~ in(sK2(singleton(sK16),sK17),sK17)
| spl18_7 ),
inference(resolution,[],[f409,f124]) ).
fof(f418,plain,
( in(sK2(singleton(sK16),sK17),singleton(sK16))
| spl18_7 ),
inference(resolution,[],[f409,f123]) ).
fof(f456,plain,
( sK16 = sK2(singleton(sK16),sK17)
| spl18_7 ),
inference(resolution,[],[f418,f203]) ).
fof(f474,plain,
( ~ in(sK16,sK17)
| spl18_7 ),
inference(superposition,[],[f417,f456]) ).
fof(f475,plain,
( $false
| ~ spl18_1
| spl18_7 ),
inference(forward_subsumption_resolution,[],[f474,f209]) ).
fof(f476,plain,
( ~ spl18_1
| spl18_7 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f482,plain,
( ~ in(sK16,sK17)
| ~ ordinal(sK17)
| spl18_8 ),
inference(resolution,[],[f413,f305]) ).
fof(f486,plain,
( ~ ordinal(sK17)
| ~ spl18_1
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f482,f209]) ).
fof(f488,plain,
( $false
| ~ spl18_1
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f486,f185]) ).
fof(f489,plain,
( ~ spl18_1
| spl18_8 ),
inference(avatar_contradiction_clause,[],[f488]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f214]) ).
cnf(s2,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f215]) ).
cnf(s4,plain,
( ~ spl18_2
| spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f358]) ).
cnf(s5,plain,
spl18_6,
inference(sat_conversion,[],[f362]) ).
cnf(s6,plain,
( spl18_1
| ~ spl18_5 ),
inference(sat_conversion,[],[f390]) ).
cnf(s7,plain,
( spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f401]) ).
cnf(s8,plain,
( spl18_5
| ~ spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f414]) ).
cnf(s9,plain,
( ~ spl18_1
| spl18_7 ),
inference(sat_conversion,[],[f476]) ).
cnf(s10,plain,
( ~ spl18_1
| spl18_8 ),
inference(sat_conversion,[],[f489]) ).
cnf(s11,plain,
( ~ spl18_2
| spl18_5 ),
inference(rat,[],[s4,s5]) ).
cnf(s12,plain,
spl18_1,
inference(rat,[],[s11,s1,s6]) ).
cnf(s13,plain,
spl18_8,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
spl18_7,
inference(rat,[],[s9,s12]) ).
cnf(s15,plain,
~ spl18_2,
inference(rat,[],[s2,s12]) ).
cnf(s16,plain,
spl18_5,
inference(rat,[],[s8,s13,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s7,s5,s16,s15]) ).
fof(f490,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU236+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:14:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (3574745)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (3574754)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=576749400:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (3574751)% WARNING: option uhcvi not known.
% 0.10/0.45 % (3574754) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3574745-3574754"...
% 0.10/0.45 % (3574752)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1636128549:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (3574750)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2135457653_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (3574751)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=514359992:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (3574753)dis+10_1_sil=32000:sp=arity:random_seed=1346129977:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (3574754)...printing done.
% 0.10/0.45 % (3574756)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3710936576:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (3574755)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4167351031:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (3574754)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (3574754)------------------------------
% 0.10/0.45 % (3574754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (3574754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (3574754)CaDiCaL version: 2.1.3
% 0.10/0.45 % (3574754)Termination reason: Refutation
% 0.10/0.45 % (3574754)Time elapsed: 0.006 s
% 0.10/0.45 % (3574754)Peak memory usage: 12 MB
% 0.10/0.45 % (3574754)Instructions burned: 14 (million)
% 0.10/0.45 % (3574745)Success in time 0.043 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------