%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 0.11s 0.46s
% Output : Refutation 0.24s
% 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/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f10,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f11,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f12,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f21,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f38,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f41,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f45,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f53,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f67,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f76,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f77,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f81,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f83,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f84,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f83]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ( in(X0,X1)
<~> ordinal_subset(succ(X0),X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f97,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f98,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f97]) ).
fof(f102,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f112,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f115,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| subset(X1,X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f120,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f134,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f173,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f174,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f177,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f181,plain,
( ordinal_subset(succ(sK17),sK18)
| in(sK17,sK18) ),
inference(cnf_transformation,[],[f90]) ).
fof(f182,plain,
( ~ ordinal_subset(succ(sK17),sK18)
| ~ in(sK17,sK18) ),
inference(cnf_transformation,[],[f90]) ).
fof(f183,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f90]) ).
fof(f184,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f90]) ).
fof(f192,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f197,plain,
! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f134,f110]) ).
fof(f198,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f177,f110]) ).
fof(f199,plain,
( ~ ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ in(sK17,sK18) ),
inference(definition_unfolding,[],[f182,f110]) ).
fof(f200,plain,
( ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
| in(sK17,sK18) ),
inference(definition_unfolding,[],[f181,f110]) ).
fof(f201,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f112]) ).
fof(f205,definition,
( spl19_1
<=> in(sK17,sK18) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f206,plain,
( ~ in(sK17,sK18)
| spl19_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f207,plain,
( in(sK17,sK18)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl19_2
<=> ordinal_subset(set_union2(sK17,singleton(sK17)),sK18) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f210,plain,
( ~ ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
| spl19_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f200,f209,f205]) ).
fof(f213,plain,
( ~ spl19_1
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f199,f209,f205]) ).
fof(f303,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f115,f102]) ).
fof(f338,plain,
( ~ ordinal(set_union2(sK17,singleton(sK17)))
| subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ ordinal(sK18)
| ~ spl19_2 ),
inference(resolution,[],[f174,f211]) ).
fof(f347,plain,
( ~ ordinal(set_union2(sK17,singleton(sK17)))
| subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f338,f183]) ).
fof(f349,definition,
( spl19_5
<=> subset(set_union2(sK17,singleton(sK17)),sK18) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f350,plain,
( ~ subset(set_union2(sK17,singleton(sK17)),sK18)
| spl19_5 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f351,plain,
( subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f353,definition,
( spl19_6
<=> ordinal(set_union2(sK17,singleton(sK17))) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f354,plain,
( ordinal(set_union2(sK17,singleton(sK17)))
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( ~ ordinal(set_union2(sK17,singleton(sK17)))
| spl19_6 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,plain,
( spl19_5
| ~ spl19_6
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f347,f209,f353,f349]) ).
fof(f357,plain,
( ~ ordinal(sK17)
| spl19_6 ),
inference(resolution,[],[f355,f197]) ).
fof(f359,plain,
( $false
| spl19_6 ),
inference(forward_subsumption_resolution,[],[f357,f184]) ).
fof(f360,plain,
spl19_6,
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f378,plain,
( ! [X0] :
( ~ in(X0,set_union2(sK17,singleton(sK17)))
| in(X0,sK18) )
| ~ spl19_5 ),
inference(resolution,[],[f351,f118]) ).
fof(f383,plain,
( in(sK17,sK18)
| ~ spl19_5 ),
inference(resolution,[],[f378,f198]) ).
fof(f387,plain,
( $false
| spl19_1
| ~ spl19_5 ),
inference(forward_subsumption_resolution,[],[f383,f206]) ).
fof(f388,plain,
( spl19_1
| ~ spl19_5 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f390,plain,
( ~ ordinal(set_union2(sK17,singleton(sK17)))
| ~ subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ ordinal(sK18)
| spl19_2 ),
inference(resolution,[],[f210,f173]) ).
fof(f395,plain,
( ~ subset(set_union2(sK17,singleton(sK17)),sK18)
| ~ ordinal(sK18)
| spl19_2
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f390,f354]) ).
fof(f398,plain,
( ~ subset(set_union2(sK17,singleton(sK17)),sK18)
| spl19_2
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f395,f183]) ).
fof(f399,plain,
( ~ spl19_5
| spl19_2
| ~ spl19_6 ),
inference(avatar_split_clause,[],[f398,f353,f209,f349]) ).
fof(f403,plain,
( ~ subset(sK17,sK18)
| ~ subset(singleton(sK17),sK18)
| spl19_5 ),
inference(resolution,[],[f350,f192]) ).
fof(f405,definition,
( spl19_7
<=> subset(singleton(sK17),sK18) ),
introduced(definition,[new_symbols(definition,[spl19_7])],[avatar_definition]) ).
fof(f407,plain,
( ~ subset(singleton(sK17),sK18)
| spl19_7 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,definition,
( spl19_8
<=> subset(sK17,sK18) ),
introduced(definition,[new_symbols(definition,[spl19_8])],[avatar_definition]) ).
fof(f411,plain,
( ~ subset(sK17,sK18)
| spl19_8 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f412,plain,
( ~ spl19_7
| ~ spl19_8
| spl19_5 ),
inference(avatar_split_clause,[],[f403,f349,f409,f405]) ).
fof(f415,plain,
( ~ in(sK2(singleton(sK17),sK18),sK18)
| spl19_7 ),
inference(resolution,[],[f407,f120]) ).
fof(f416,plain,
( in(sK2(singleton(sK17),sK18),singleton(sK17))
| spl19_7 ),
inference(resolution,[],[f407,f119]) ).
fof(f454,plain,
( sK17 = sK2(singleton(sK17),sK18)
| spl19_7 ),
inference(resolution,[],[f416,f201]) ).
fof(f472,plain,
( ~ in(sK17,sK18)
| spl19_7 ),
inference(superposition,[],[f415,f454]) ).
fof(f473,plain,
( $false
| ~ spl19_1
| spl19_7 ),
inference(forward_subsumption_resolution,[],[f472,f207]) ).
fof(f474,plain,
( ~ spl19_1
| spl19_7 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f480,plain,
( ~ in(sK17,sK18)
| ~ ordinal(sK18)
| spl19_8 ),
inference(resolution,[],[f411,f303]) ).
fof(f484,plain,
( ~ ordinal(sK18)
| ~ spl19_1
| spl19_8 ),
inference(forward_subsumption_resolution,[],[f480,f207]) ).
fof(f486,plain,
( $false
| ~ spl19_1
| spl19_8 ),
inference(forward_subsumption_resolution,[],[f484,f183]) ).
fof(f487,plain,
( ~ spl19_1
| spl19_8 ),
inference(avatar_contradiction_clause,[],[f486]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
( ~ spl19_1
| ~ spl19_2 ),
inference(sat_conversion,[],[f213]) ).
cnf(s4,plain,
( ~ spl19_2
| spl19_5
| ~ spl19_6 ),
inference(sat_conversion,[],[f356]) ).
cnf(s5,plain,
spl19_6,
inference(sat_conversion,[],[f360]) ).
cnf(s6,plain,
( spl19_1
| ~ spl19_5 ),
inference(sat_conversion,[],[f388]) ).
cnf(s7,plain,
( spl19_2
| ~ spl19_5
| ~ spl19_6 ),
inference(sat_conversion,[],[f399]) ).
cnf(s8,plain,
( spl19_5
| ~ spl19_7
| ~ spl19_8 ),
inference(sat_conversion,[],[f412]) ).
cnf(s9,plain,
( ~ spl19_1
| spl19_7 ),
inference(sat_conversion,[],[f474]) ).
cnf(s10,plain,
( ~ spl19_1
| spl19_8 ),
inference(sat_conversion,[],[f487]) ).
cnf(s11,plain,
( ~ spl19_2
| spl19_5 ),
inference(rat,[],[s4,s5]) ).
cnf(s12,plain,
spl19_1,
inference(rat,[],[s11,s1,s6]) ).
cnf(s13,plain,
spl19_8,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
spl19_7,
inference(rat,[],[s9,s12]) ).
cnf(s15,plain,
~ spl19_2,
inference(rat,[],[s2,s12]) ).
cnf(s16,plain,
spl19_5,
inference(rat,[],[s8,s13,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s7,s5,s16,s15]) ).
fof(f488,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:16:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (4016658)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (4016667)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=359137507:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (4016664)% WARNING: option uhcvi not known.
% 0.11/0.46 % (4016667) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4016658-4016667"...
% 0.11/0.46 % (4016663)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1808980083_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (4016665)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3925027050:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (4016664)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3841256067:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (4016667)...printing done.
% 0.11/0.46 % (4016666)dis+10_1_sil=32000:sp=arity:random_seed=1612751357:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (4016668)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2943924081:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (4016669)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3856607306:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (4016667)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.46 % (4016667)------------------------------
% 0.24/0.46 % (4016667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.46 % (4016667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.46 % (4016667)CaDiCaL version: 2.1.3
% 0.24/0.46 % (4016667)Termination reason: Refutation
% 0.24/0.46 % (4016667)Time elapsed: 0.006 s
% 0.24/0.46 % (4016667)Peak memory usage: 12 MB
% 0.24/0.46 % (4016667)Instructions burned: 14 (million)
% 0.24/0.46 % (4016658)Success in time 0.037 s
% 0.24/0.46 % Vampire exiting
%------------------------------------------------------------------------------