%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET171-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:40:23 PM UTC 2026
% Result : Unsatisfiable 1.94s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 138 ( 10 unt; 18 def)
% Number of atoms : 311 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 309 ( 136 ~; 155 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
intersection(union(x,y),union(x,z)) != union(x,intersection(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_over_intersection1_1) ).
fof(f135,plain,
intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))) != complement(intersection(complement(x),complement(intersection(y,z)))),
inference(definition_unfolding,[],[f122,f26,f26,f26]) ).
fof(f177,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f178,plain,
~ sQ0_eqProxy(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),
inference(equality_proxy_replacement,[],[f135,f177]) ).
fof(f179,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f177]) ).
fof(f199,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f177]) ).
fof(f200,plain,
~ sQ0_eqProxy(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),
inference(resolution,[],[f199,f178]) ).
fof(f202,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f210,plain,
( ~ subclass(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z)))))
| ~ subclass(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))) ),
inference(resolution,[],[f179,f200]) ).
fof(f212,definition,
( spl1_1
<=> subclass(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))))
| spl1_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl1_2
<=> subclass(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f216,plain,
( ~ subclass(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f217,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f210,f215,f212]) ).
fof(f220,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f230,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f231,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(y))))
| spl1_3 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f234,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(z))))
| spl1_4 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f238,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(x))
| spl1_5 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(y,z))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f241,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(y,z)))
| spl1_6 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f245,definition,
( spl1_7
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(y,z)) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f246,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(y,z))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl1_8
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f249,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),universal_class)
| spl1_8 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(y)))
| spl1_3 ),
inference(resolution,[],[f231,f25]) ).
fof(f253,definition,
( spl1_9
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f254,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(y)))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( spl1_9
| ~ spl1_8
| spl1_3 ),
inference(avatar_split_clause,[],[f251,f230,f248,f253]) ).
fof(f256,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),X0)
| spl1_8 ),
inference(resolution,[],[f249,f202]) ).
fof(f257,plain,
( $false
| spl1_1
| spl1_8 ),
inference(resolution,[],[f256,f220]) ).
fof(f265,plain,
( spl1_1
| spl1_8 ),
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f267,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f270,definition,
( spl1_10
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(x),complement(intersection(y,z)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f271,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(x),complement(intersection(y,z))))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl1_11
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f274,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),universal_class)
| spl1_11 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f276,plain,
( ! [X0] : ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),X0)
| spl1_11 ),
inference(resolution,[],[f274,f202]) ).
fof(f279,plain,
( $false
| spl1_2
| spl1_11 ),
inference(resolution,[],[f276,f267]) ).
fof(f287,plain,
( spl1_2
| spl1_11 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f290,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),z)
| ~ spl1_7 ),
inference(resolution,[],[f246,f22]) ).
fof(f291,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),y)
| ~ spl1_7 ),
inference(resolution,[],[f246,f21]) ).
fof(f295,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(y))
| ~ spl1_9 ),
inference(resolution,[],[f254,f22]) ).
fof(f296,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(x))
| ~ spl1_9 ),
inference(resolution,[],[f254,f21]) ).
fof(f297,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),y)
| ~ spl1_9 ),
inference(resolution,[],[f295,f24]) ).
fof(f298,plain,
( $false
| ~ spl1_7
| ~ spl1_9 ),
inference(resolution,[],[f297,f291]) ).
fof(f299,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f300,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(intersection(complement(x),complement(intersection(y,z)))))
| spl1_2 ),
inference(resolution,[],[f216,f3]) ).
fof(f301,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f303,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(x),complement(intersection(y,z))))
| spl1_2 ),
inference(resolution,[],[f300,f25]) ).
fof(f304,plain,
( spl1_10
| ~ spl1_11
| spl1_2 ),
inference(avatar_split_clause,[],[f303,f215,f273,f270]) ).
fof(f316,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(intersection(complement(x),complement(z))))
| spl1_2 ),
inference(resolution,[],[f301,f22]) ).
fof(f317,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(intersection(complement(x),complement(y))))
| spl1_2 ),
inference(resolution,[],[f301,f21]) ).
fof(f319,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(x),complement(z)))
| spl1_2 ),
inference(resolution,[],[f316,f24]) ).
fof(f320,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(complement(x),complement(y)))
| spl1_2 ),
inference(resolution,[],[f317,f24]) ).
fof(f321,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(z))
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(x))
| spl1_2 ),
inference(resolution,[],[f319,f23]) ).
fof(f323,definition,
( spl1_12
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f324,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(x))
| spl1_12 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f326,definition,
( spl1_13
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f327,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(z))
| spl1_13 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f328,plain,
( ~ spl1_12
| ~ spl1_13
| spl1_2 ),
inference(avatar_split_clause,[],[f321,f215,f326,f323]) ).
fof(f329,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(intersection(y,z)))
| ~ spl1_10 ),
inference(resolution,[],[f271,f22]) ).
fof(f330,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(x))
| ~ spl1_10 ),
inference(resolution,[],[f271,f21]) ).
fof(f332,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),intersection(y,z))
| ~ spl1_10 ),
inference(resolution,[],[f329,f24]) ).
fof(f333,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(y))
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(x))
| spl1_2 ),
inference(resolution,[],[f320,f23]) ).
fof(f335,definition,
( spl1_14
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f336,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),complement(y))
| spl1_14 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( ~ spl1_12
| ~ spl1_14
| spl1_2 ),
inference(avatar_split_clause,[],[f333,f215,f335,f323]) ).
fof(f338,plain,
( $false
| ~ spl1_10
| spl1_12 ),
inference(resolution,[],[f324,f330]) ).
fof(f340,plain,
( ~ spl1_10
| spl1_12 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f345,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),z)
| spl1_13 ),
inference(resolution,[],[f327,f25]) ).
fof(f347,definition,
( spl1_16
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),z) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f349,plain,
( spl1_16
| ~ spl1_11
| spl1_13 ),
inference(avatar_split_clause,[],[f345,f326,f273,f347]) ).
fof(f350,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),y)
| spl1_14 ),
inference(resolution,[],[f336,f25]) ).
fof(f352,definition,
( spl1_17
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),y) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f354,plain,
( spl1_17
| ~ spl1_11
| spl1_14 ),
inference(avatar_split_clause,[],[f350,f335,f273,f352]) ).
fof(f355,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),z)
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))),complement(intersection(complement(x),complement(intersection(y,z))))),y)
| ~ spl1_10 ),
inference(resolution,[],[f332,f23]) ).
fof(f358,plain,
( ~ spl1_17
| ~ spl1_16
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f355,f270,f347,f352]) ).
fof(f359,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z)))))
| spl1_1 ),
inference(resolution,[],[f213,f3]) ).
fof(f360,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f361,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(intersection(y,z))))
| spl1_1 ),
inference(resolution,[],[f360,f24]) ).
fof(f362,plain,
( $false
| spl1_5
| ~ spl1_9 ),
inference(resolution,[],[f238,f296]) ).
fof(f364,plain,
( spl1_5
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f369,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(z))))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(complement(x),complement(y))))
| spl1_1 ),
inference(resolution,[],[f359,f23]) ).
fof(f370,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f369,f212,f233,f230]) ).
fof(f371,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(z)))
| spl1_4 ),
inference(resolution,[],[f234,f25]) ).
fof(f373,definition,
( spl1_19
<=> member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f374,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(complement(x),complement(z)))
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( spl1_19
| ~ spl1_8
| spl1_4 ),
inference(avatar_split_clause,[],[f371,f233,f248,f373]) ).
fof(f376,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(z))
| ~ spl1_19 ),
inference(resolution,[],[f374,f22]) ).
fof(f377,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(x))
| ~ spl1_19 ),
inference(resolution,[],[f374,f21]) ).
fof(f378,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(intersection(y,z)))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),complement(x))
| spl1_1 ),
inference(resolution,[],[f361,f23]) ).
fof(f379,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),z)
| ~ spl1_19 ),
inference(resolution,[],[f376,f24]) ).
fof(f380,plain,
( $false
| spl1_5
| ~ spl1_19 ),
inference(resolution,[],[f377,f238]) ).
fof(f382,plain,
( spl1_5
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f383,plain,
( ~ spl1_5
| ~ spl1_6
| spl1_1 ),
inference(avatar_split_clause,[],[f378,f212,f240,f237]) ).
fof(f384,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(z))))),intersection(y,z))
| spl1_6 ),
inference(resolution,[],[f241,f25]) ).
fof(f385,plain,
( spl1_7
| ~ spl1_8
| spl1_6 ),
inference(avatar_split_clause,[],[f384,f240,f248,f245]) ).
fof(f388,plain,
( $false
| ~ spl1_7
| ~ spl1_19 ),
inference(resolution,[],[f379,f290]) ).
fof(f389,plain,
( ~ spl1_7
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f388]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s6,plain,
( spl1_3
| ~ spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f255]) ).
cnf(s7,plain,
( spl1_1
| spl1_8 ),
inference(sat_conversion,[],[f265]) ).
cnf(s9,plain,
( spl1_2
| spl1_11 ),
inference(sat_conversion,[],[f287]) ).
cnf(s10,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(sat_conversion,[],[f299]) ).
cnf(s11,plain,
( spl1_2
| spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f304]) ).
cnf(s14,plain,
( spl1_2
| ~ spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f328]) ).
cnf(s15,plain,
( spl1_2
| ~ spl1_12
| ~ spl1_14 ),
inference(sat_conversion,[],[f337]) ).
cnf(s16,plain,
( ~ spl1_10
| spl1_12 ),
inference(sat_conversion,[],[f340]) ).
cnf(s18,plain,
( ~ spl1_11
| spl1_13
| spl1_16 ),
inference(sat_conversion,[],[f349]) ).
cnf(s19,plain,
( ~ spl1_11
| spl1_14
| spl1_17 ),
inference(sat_conversion,[],[f354]) ).
cnf(s20,plain,
( ~ spl1_10
| ~ spl1_16
| ~ spl1_17 ),
inference(sat_conversion,[],[f358]) ).
cnf(s21,plain,
( spl1_5
| ~ spl1_9 ),
inference(sat_conversion,[],[f364]) ).
cnf(s23,plain,
( spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f370]) ).
cnf(s24,plain,
( spl1_4
| ~ spl1_8
| spl1_19 ),
inference(sat_conversion,[],[f375]) ).
cnf(s25,plain,
( spl1_5
| ~ spl1_19 ),
inference(sat_conversion,[],[f382]) ).
cnf(s26,plain,
( spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f383]) ).
cnf(s27,plain,
( spl1_6
| spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f385]) ).
cnf(s28,plain,
( ~ spl1_7
| ~ spl1_19 ),
inference(sat_conversion,[],[f389]) ).
cnf(s29,plain,
( ~ spl1_11
| spl1_2 ),
inference(rat,[],[s20,s18,s19,s14,s15,s16,s11]) ).
cnf(s30,plain,
spl1_2,
inference(rat,[],[s29,s9]) ).
cnf(s31,plain,
( ~ spl1_9
| spl1_1 ),
inference(rat,[],[s27,s26,s10,s21,s7]) ).
cnf(s32,plain,
spl1_1,
inference(rat,[],[s26,s27,s25,s28,s24,s23,s6,s31,s7]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s30,s32]) ).
fof(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET171-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 01:05:33 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.94/1.31 % (3161407)Input is clausal, will run a generic CNF schedule.
% 1.94/1.31 % (3161412)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1040424500:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.94/1.31 % (3161416)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=663413841:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.94/1.31 % (3161417)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4068615707:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.94/1.31 % (3161414)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2593068234:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.94/1.31 % (3161415)lrs+10_1_sil=8000:sp=occurrence:random_seed=831311973:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.94/1.31 % (3161418)dis-21_1_sil=8000:lcm=predicate:random_seed=3353663658:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.94/1.31 % (3161413)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=247913301:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.94/1.31 % (3161415)Refutation not found, incomplete strategy
% 1.94/1.31 % (3161415)------------------------------
% 1.94/1.31 % (3161415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.94/1.31 % (3161415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.94/1.31 % (3161415)CaDiCaL version: 2.1.3
% 1.94/1.31 % (3161415)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.31 % (3161415)Time elapsed: 0.004 s
% 1.94/1.31 % (3161415)Peak memory usage: 88 MB
% 1.94/1.31 % (3161415)Instructions burned: 4 (million)
% 1.94/1.31 % (3161418)First to succeed.
% 1.94/1.31 % (3161418)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3161407"
% 1.94/1.31 % (3161416)Instruction limit reached!
% 1.94/1.31 % (3161416)------------------------------
% 1.94/1.31 % (3161416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.94/1.31 % (3161416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.94/1.31 % (3161416)CaDiCaL version: 2.1.3
% 1.94/1.31 % (3161416)Termination reason: Instruction limit
% 1.94/1.31 % (3161416)Termination phase: Saturation
% 1.94/1.31 % (3161416)Time elapsed: 0.070 s
% 1.94/1.31 % (3161416)Peak memory usage: 89 MB
% 1.94/1.31 % (3161416)Instructions burned: 115 (million)
% 1.94/1.31 % (3161417)Instruction limit reached!
% 1.94/1.31 % (3161417)------------------------------
% 1.94/1.31 % (3161417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.94/1.31 % (3161417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.94/1.31 % (3161417)CaDiCaL version: 2.1.3
% 1.94/1.31 % (3161417)Termination reason: Instruction limit
% 1.94/1.31 % (3161417)Termination phase: Saturation
% 1.94/1.31 % (3161417)Time elapsed: 0.135 s
% 1.94/1.31 % (3161417)Peak memory usage: 90 MB
% 1.94/1.31 % (3161417)Instructions burned: 180 (million)
% 1.94/1.31 % (3161415)------------------------------
% 1.94/1.31 % (3161415)------------------------------
% 1.94/1.31 % (3161426)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=981623072:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.94/1.31 % (3161426)Refutation not found, incomplete strategy
% 1.94/1.31 % (3161426)------------------------------
% 1.94/1.31 % (3161426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.94/1.31 % (3161426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.94/1.31 % (3161426)CaDiCaL version: 2.1.3
% 1.94/1.31 % (3161426)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.31 % (3161426)Time elapsed: 0.003 s
% 1.94/1.31 % (3161426)Peak memory usage: 88 MB
% 1.94/1.31 % (3161426)Instructions burned: 3 (million)
% 1.94/1.31 % (3161418)Refutation found. Thanks to Tanya!
% 1.94/1.31 % SZS status Unsatisfiable for theBenchmark
% 1.94/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (3161418)------------------------------
% 0.17/1.40 % (3161418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (3161418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (3161418)CaDiCaL version: 2.1.3
% 0.17/1.40 % (3161418)Termination reason: Refutation
% 0.17/1.40 % (3161418)Time elapsed: 0.009 s
% 0.17/1.40 % (3161418)Peak memory usage: 89 MB
% 0.17/1.40 % (3161418)Instructions burned: 14 (million)
% 0.17/1.40 % (3161418)------------------------------
% 0.17/1.40 % (3161418)------------------------------
% 0.17/1.40 % (3161407)Success in time 0.438 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------