%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU238+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 : 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 12:52:33 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 146 ( 15 unt; 8 def)
% Number of atoms : 435 ( 44 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 473 ( 184 ~; 226 |; 27 &)
% ( 17 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 105 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f26,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(f43,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(f46,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f49,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f51,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f53,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f54,conjecture,
! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X1] :
( ordinal(X1)
& X0 = succ(X1) )
& being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f55,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X1] :
( ordinal(X1)
& X0 = succ(X1) )
& being_limit_ordinal(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f64,plain,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& succ(X2) = X0 )
& being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f55]) ).
fof(f65,plain,
! [X0,X1] :
( ( subset(X0,X1)
& X0 != X1 )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f86,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f86]) ).
fof(f91,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f93,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f94,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f93]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f103,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f104,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
? [X0] :
( ( ( ~ being_limit_ordinal(X0)
& ! [X1] :
( X0 != succ(X1)
| ~ ordinal(X1) ) )
| ( ? [X2] :
( ordinal(X2)
& succ(X2) = X0 )
& being_limit_ordinal(X0) ) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f116,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f124,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f125,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f139,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f178,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f181,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f184,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f187,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f190,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0)
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f191,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK13(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f192,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK13(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(succ(sK13(X0)),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
! [X1] :
( being_limit_ordinal(sK14)
| ~ ordinal(X1)
| succ(X1) != sK14 ),
inference(cnf_transformation,[],[f105]) ).
fof(f195,plain,
! [X1] :
( ordinal(sK15)
| ~ ordinal(X1)
| succ(X1) != sK14 ),
inference(cnf_transformation,[],[f105]) ).
fof(f196,plain,
! [X1] :
( sK14 = succ(sK15)
| ~ ordinal(X1)
| succ(X1) != sK14 ),
inference(cnf_transformation,[],[f105]) ).
fof(f197,plain,
( sK14 = succ(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f105]) ).
fof(f198,plain,
( ordinal(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f105]) ).
fof(f199,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f105]) ).
fof(f209,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(set_union2(X0,singleton(X0))) ),
inference(definition_unfolding,[],[f139,f124]) ).
fof(f210,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f181,f124]) ).
fof(f211,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f187,f124]) ).
fof(f213,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0)
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f193,f124]) ).
fof(f214,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,X0)
| in(set_union2(X1,singleton(X1)),X0)
| ~ being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f190,f124]) ).
fof(f215,plain,
( sK14 = set_union2(sK15,singleton(sK15))
| ~ being_limit_ordinal(sK14) ),
inference(definition_unfolding,[],[f197,f124]) ).
fof(f216,plain,
! [X1] :
( sK14 = set_union2(sK15,singleton(sK15))
| ~ ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(definition_unfolding,[],[f196,f124,f124]) ).
fof(f217,plain,
! [X1] :
( ordinal(sK15)
| ~ ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(definition_unfolding,[],[f195,f124]) ).
fof(f218,plain,
! [X1] :
( being_limit_ordinal(sK14)
| ~ ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(definition_unfolding,[],[f194,f124]) ).
fof(f219,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f237,plain,
! [X0] :
( ~ ordinal(set_union2(X0,singleton(X0)))
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f209]) ).
fof(f256,plain,
! [X0,X1] :
( subset(X0,X1)
| ordinal(X0)
| ordinal(X1)
| ordinal_subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f178]) ).
fof(f260,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ordinal(X1)
| epsilon_transitive(X0)
| in(X0,X1) ),
inference(consistent_polarity_flipping,[],[f184]) ).
fof(f262,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X1)
| ~ ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f211]) ).
fof(f266,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0)
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f213]) ).
fof(f267,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| in(sK13(X0),X0)
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f192]) ).
fof(f268,plain,
! [X0] :
( ~ ordinal(sK13(X0))
| ordinal(X0)
| ~ being_limit_ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f191]) ).
fof(f269,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ordinal(X1)
| ordinal(X0)
| in(set_union2(X1,singleton(X1)),X0)
| being_limit_ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f214]) ).
fof(f270,plain,
~ ordinal(sK14),
inference(consistent_polarity_flipping,[],[f199]) ).
fof(f271,plain,
( ~ ordinal(sK15)
| being_limit_ordinal(sK14) ),
inference(consistent_polarity_flipping,[],[f198]) ).
fof(f272,plain,
( sK14 = set_union2(sK15,singleton(sK15))
| being_limit_ordinal(sK14) ),
inference(consistent_polarity_flipping,[],[f215]) ).
fof(f273,plain,
! [X1] :
( sK14 = set_union2(sK15,singleton(sK15))
| ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(consistent_polarity_flipping,[],[f216]) ).
fof(f274,plain,
! [X1] :
( ~ ordinal(sK15)
| ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(consistent_polarity_flipping,[],[f217]) ).
fof(f275,plain,
! [X1] :
( ~ being_limit_ordinal(sK14)
| ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(consistent_polarity_flipping,[],[f218]) ).
fof(f279,definition,
( spl16_1
<=> ! [X1] :
( ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f280,plain,
( ! [X1] :
( sK14 != set_union2(X1,singleton(X1))
| ordinal(X1) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,definition,
( spl16_2
<=> being_limit_ordinal(sK14) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f283,plain,
( being_limit_ordinal(sK14)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f284,plain,
( ~ being_limit_ordinal(sK14)
| spl16_2 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,plain,
( spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f275,f282,f279]) ).
fof(f287,definition,
( spl16_3
<=> ordinal(sK15) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f289,plain,
( ~ ordinal(sK15)
| spl16_3 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f290,plain,
( spl16_1
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f274,f287,f279]) ).
fof(f292,definition,
( spl16_4
<=> sK14 = set_union2(sK15,singleton(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f294,plain,
( sK14 = set_union2(sK15,singleton(sK15))
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,plain,
( spl16_1
| spl16_4 ),
inference(avatar_split_clause,[],[f273,f292,f279]) ).
fof(f296,plain,
( spl16_2
| spl16_4 ),
inference(avatar_split_clause,[],[f272,f292,f282]) ).
fof(f297,plain,
( spl16_2
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f271,f287,f282]) ).
fof(f332,plain,
( in(sK15,sK14)
| ~ spl16_4 ),
inference(superposition,[],[f210,f294]) ).
fof(f386,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ordinal(X1)
| ordinal_subset(X0,X1)
| X0 = X1
| ordinal(X0) ),
inference(resolution,[],[f256,f125]) ).
fof(f419,plain,
( ordinal(sK15)
| ordinal(sK14)
| in(set_union2(sK15,singleton(sK15)),sK14)
| being_limit_ordinal(sK14)
| ~ spl16_4 ),
inference(resolution,[],[f269,f332]) ).
fof(f420,plain,
( ordinal(sK14)
| in(set_union2(sK15,singleton(sK15)),sK14)
| being_limit_ordinal(sK14)
| spl16_3
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f419,f289]) ).
fof(f422,plain,
( in(set_union2(sK15,singleton(sK15)),sK14)
| being_limit_ordinal(sK14)
| spl16_3
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f420,f270]) ).
fof(f423,plain,
( in(set_union2(sK15,singleton(sK15)),sK14)
| spl16_2
| spl16_3
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f422,f284]) ).
fof(f424,plain,
( in(sK14,sK14)
| spl16_2
| spl16_3
| ~ spl16_4 ),
inference(forward_demodulation,[],[f423,f294]) ).
fof(f462,plain,
( ~ in(sK14,sK14)
| spl16_2
| spl16_3
| ~ spl16_4 ),
inference(resolution,[],[f424,f112]) ).
fof(f466,plain,
( $false
| spl16_2
| spl16_3
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f462,f424]) ).
fof(f467,plain,
( spl16_2
| spl16_3
| ~ spl16_4 ),
inference(avatar_contradiction_clause,[],[f466]) ).
fof(f477,plain,
( ~ in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ordinal(sK14)
| ~ spl16_2 ),
inference(resolution,[],[f283,f266]) ).
fof(f478,plain,
( in(sK13(sK14),sK14)
| ordinal(sK14)
| ~ spl16_2 ),
inference(resolution,[],[f283,f267]) ).
fof(f479,plain,
( in(sK13(sK14),sK14)
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f478,f270]) ).
fof(f480,plain,
( ~ in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f477,f270]) ).
fof(f482,plain,
( ordinal(sK14)
| ~ ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ordinal(sK13(sK14))
| ~ spl16_2 ),
inference(resolution,[],[f479,f262]) ).
fof(f487,plain,
( ~ ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ordinal(sK13(sK14))
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f482,f270]) ).
fof(f489,definition,
( spl16_11
<=> ordinal(sK13(sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
fof(f490,plain,
( ~ ordinal(sK13(sK14))
| spl16_11 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f491,plain,
( ordinal(sK13(sK14))
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f493,definition,
( spl16_12
<=> ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
fof(f495,plain,
( ~ ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| spl16_12 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f496,plain,
( spl16_11
| ~ spl16_12
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f487,f282,f493,f489]) ).
fof(f568,plain,
! [X0,X1] :
( ordinal(X0)
| ordinal_subset(X1,X0)
| X0 = X1
| ordinal(X1)
| ordinal(X0)
| epsilon_transitive(X1)
| in(X1,X0) ),
inference(resolution,[],[f386,f260]) ).
fof(f570,plain,
! [X0,X1] :
( ordinal(X0)
| ordinal_subset(X1,X0)
| X0 = X1
| ordinal(X1)
| epsilon_transitive(X1)
| in(X1,X0) ),
inference(duplicate_literal_removal,[],[f568]) ).
fof(f572,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal(X0)
| X0 = X1
| ordinal(X1)
| in(X1,X0) ),
inference(forward_subsumption_resolution,[],[f570,f219]) ).
fof(f822,plain,
( ordinal(sK14)
| sK14 = set_union2(sK13(sK14),singleton(sK13(sK14)))
| ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| spl16_12 ),
inference(resolution,[],[f572,f495]) ).
fof(f831,plain,
( sK14 = set_union2(sK13(sK14),singleton(sK13(sK14)))
| ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| spl16_12 ),
inference(forward_subsumption_resolution,[],[f822,f270]) ).
fof(f837,plain,
( sK14 = set_union2(sK13(sK14),singleton(sK13(sK14)))
| ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ spl16_2
| spl16_12 ),
inference(forward_subsumption_resolution,[],[f831,f480]) ).
fof(f845,definition,
( spl16_26
<=> ordinal(set_union2(sK13(sK14),singleton(sK13(sK14)))) ),
introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition]) ).
fof(f847,plain,
( ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f849,definition,
( spl16_27
<=> sK14 = set_union2(sK13(sK14),singleton(sK13(sK14))) ),
introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition]) ).
fof(f851,plain,
( sK14 = set_union2(sK13(sK14),singleton(sK13(sK14)))
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f852,plain,
( spl16_26
| spl16_27
| ~ spl16_2
| spl16_12 ),
inference(avatar_split_clause,[],[f837,f493,f282,f849,f845]) ).
fof(f945,plain,
( sK14 != sK14
| ordinal(sK13(sK14))
| ~ spl16_1
| ~ spl16_27 ),
inference(superposition,[],[f280,f851]) ).
fof(f960,plain,
( ordinal(sK13(sK14))
| ~ spl16_1
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f945]) ).
fof(f970,plain,
( spl16_11
| ~ spl16_1
| ~ spl16_27 ),
inference(avatar_split_clause,[],[f960,f849,f279,f489]) ).
fof(f979,plain,
( ordinal(sK14)
| ~ being_limit_ordinal(sK14)
| ~ spl16_11 ),
inference(resolution,[],[f491,f268]) ).
fof(f991,plain,
( ~ being_limit_ordinal(sK14)
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f979,f270]) ).
fof(f992,plain,
( $false
| ~ spl16_2
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f991,f283]) ).
fof(f993,plain,
( ~ spl16_2
| ~ spl16_11 ),
inference(avatar_contradiction_clause,[],[f992]) ).
fof(f998,plain,
( ordinal(sK13(sK14))
| ~ spl16_26 ),
inference(resolution,[],[f847,f237]) ).
fof(f1010,plain,
( $false
| spl16_11
| ~ spl16_26 ),
inference(forward_subsumption_resolution,[],[f998,f490]) ).
fof(f1011,plain,
( spl16_11
| ~ spl16_26 ),
inference(avatar_contradiction_clause,[],[f1010]) ).
cnf(s1,plain,
( spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f285]) ).
cnf(s2,plain,
( spl16_1
| ~ spl16_3 ),
inference(sat_conversion,[],[f290]) ).
cnf(s3,plain,
( spl16_1
| spl16_4 ),
inference(sat_conversion,[],[f295]) ).
cnf(s4,plain,
( spl16_2
| spl16_4 ),
inference(sat_conversion,[],[f296]) ).
cnf(s5,plain,
( spl16_2
| ~ spl16_3 ),
inference(sat_conversion,[],[f297]) ).
cnf(s8,plain,
( spl16_2
| spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f467]) ).
cnf(s10,plain,
( ~ spl16_2
| spl16_11
| ~ spl16_12 ),
inference(sat_conversion,[],[f496]) ).
cnf(s26,plain,
( ~ spl16_2
| spl16_12
| spl16_26
| spl16_27 ),
inference(sat_conversion,[],[f852]) ).
cnf(s30,plain,
( ~ spl16_1
| spl16_11
| ~ spl16_27 ),
inference(sat_conversion,[],[f970]) ).
cnf(s37,plain,
( ~ spl16_2
| ~ spl16_11 ),
inference(sat_conversion,[],[f993]) ).
cnf(s39,plain,
( spl16_11
| ~ spl16_26 ),
inference(sat_conversion,[],[f1011]) ).
cnf(s41,plain,
spl16_1,
inference(rat,[],[s8,s1,s2,s3]) ).
cnf(s42,plain,
spl16_2,
inference(rat,[],[s8,s4,s5]) ).
cnf(s43,plain,
~ spl16_11,
inference(rat,[],[s37,s42]) ).
cnf(s44,plain,
~ spl16_12,
inference(rat,[],[s10,s43,s42]) ).
cnf(s45,plain,
~ spl16_26,
inference(rat,[],[s39,s43]) ).
cnf(s46,plain,
~ spl16_27,
inference(rat,[],[s30,s41,s43]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s26,s46,s42,s45,s44]) ).
fof(f1012,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU238+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 28 04:16:19 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 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
% 0.18/0.50 % (4017316)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (4017321)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2765512354_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % TRYING [1]
% 0.18/0.50 % TRYING [2]
% 0.18/0.50 % TRYING [3]
% 0.18/0.50 % TRYING [4]
% 0.18/0.50 % (4017322)% WARNING: option uhcvi not known.
% 0.18/0.50 % TRYING [5]
% 0.18/0.50 % (4017323)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=599338529:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (4017322)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3564624068:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (4017324)dis+10_1_sil=32000:sp=arity:random_seed=1557060666:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (4017325)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2396051409:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % (4017326)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=476267914:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (4017327)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1061427861:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % (4017322) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4017316-4017322"...
% 0.18/0.50 % (4017322)...printing done.
% 0.18/0.50 % (4017322)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (4017322)------------------------------
% 0.18/0.50 % (4017322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (4017322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (4017322)CaDiCaL version: 2.1.3
% 0.18/0.50 % (4017322)Termination reason: Refutation
% 0.18/0.50 % (4017322)Time elapsed: 0.020 s
% 0.18/0.50 % (4017322)Peak memory usage: 13 MB
% 0.18/0.50 % (4017322)Instructions burned: 25 (million)
% 0.18/0.50 % (4017316)Success in time 0.053 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------