%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET172-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 2.65s 1.31s
% Output : Refutation 0.18s
% 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/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
intersection(union(x,z),union(y,z)) != union(intersection(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_over_intersection2_1) ).
fof(f135,plain,
intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))) != complement(intersection(complement(intersection(x,y)),complement(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(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(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(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),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(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z))))
| ~ subclass(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))) ),
inference(resolution,[],[f179,f200]) ).
fof(f212,definition,
( spl1_1
<=> subclass(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))))
| spl1_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl1_2
<=> subclass(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f216,plain,
( ~ subclass(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(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(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(intersection(x,y)),complement(z))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f230,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(x),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f231,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(x),complement(z))))
| spl1_3 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f234,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z))))
| spl1_4 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(x,y))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f238,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(x,y)))
| spl1_5 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f241,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(z))
| spl1_6 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f248,definition,
( spl1_8
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f249,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),universal_class)
| spl1_8 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(x),complement(z)))
| spl1_3 ),
inference(resolution,[],[f231,f25]) ).
fof(f253,definition,
( spl1_9
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(x),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f254,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(x),complement(z)))
| ~ 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(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),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(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f270,definition,
( spl1_10
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(intersection(x,y)),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f271,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(intersection(x,y)),complement(z)))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl1_11
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(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(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),universal_class)
| spl1_11 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f276,plain,
( ! [X0] : ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(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(f288,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))))
| spl1_1 ),
inference(resolution,[],[f213,f3]) ).
fof(f289,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(intersection(x,y)),complement(z))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f290,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(intersection(x,y)),complement(z)))
| spl1_1 ),
inference(resolution,[],[f289,f24]) ).
fof(f291,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(z))
| ~ spl1_9 ),
inference(resolution,[],[f254,f22]) ).
fof(f292,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(x))
| ~ spl1_9 ),
inference(resolution,[],[f254,f21]) ).
fof(f293,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z))))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(complement(x),complement(z))))
| spl1_1 ),
inference(resolution,[],[f288,f23]) ).
fof(f294,plain,
( $false
| spl1_6
| ~ spl1_9 ),
inference(resolution,[],[f291,f241]) ).
fof(f296,plain,
( spl1_6
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f297,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(intersection(x,y)))
| spl1_1 ),
inference(resolution,[],[f290,f23]) ).
fof(f298,plain,
( ~ spl1_5
| ~ spl1_6
| spl1_1 ),
inference(avatar_split_clause,[],[f297,f212,f240,f237]) ).
fof(f301,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(x,y))
| spl1_5 ),
inference(resolution,[],[f238,f25]) ).
fof(f303,definition,
( spl1_12
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f304,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(x,y))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f305,plain,
( spl1_12
| ~ spl1_8
| spl1_5 ),
inference(avatar_split_clause,[],[f301,f237,f248,f303]) ).
fof(f306,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),x)
| ~ spl1_9 ),
inference(resolution,[],[f292,f24]) ).
fof(f307,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),y)
| ~ spl1_12 ),
inference(resolution,[],[f304,f22]) ).
fof(f308,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),x)
| ~ spl1_12 ),
inference(resolution,[],[f304,f21]) ).
fof(f309,plain,
( $false
| ~ spl1_9
| ~ spl1_12 ),
inference(resolution,[],[f308,f306]) ).
fof(f310,plain,
( ~ spl1_9
| ~ spl1_12 ),
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f293,f212,f233,f230]) ).
fof(f312,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z)))
| spl1_4 ),
inference(resolution,[],[f234,f25]) ).
fof(f314,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f315,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z)))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( spl1_13
| ~ spl1_8
| spl1_4 ),
inference(avatar_split_clause,[],[f312,f233,f248,f314]) ).
fof(f317,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(z))
| ~ spl1_13 ),
inference(resolution,[],[f315,f22]) ).
fof(f318,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),complement(y))
| ~ spl1_13 ),
inference(resolution,[],[f315,f21]) ).
fof(f320,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(z))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z))))),y)
| ~ spl1_13 ),
inference(resolution,[],[f318,f24]) ).
fof(f321,plain,
( $false
| ~ spl1_12
| ~ spl1_13 ),
inference(resolution,[],[f320,f307]) ).
fof(f322,plain,
( ~ spl1_12
| ~ spl1_13 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f323,plain,
( $false
| spl1_6
| ~ spl1_13 ),
inference(resolution,[],[f241,f317]) ).
fof(f325,plain,
( spl1_6
| ~ spl1_13 ),
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f327,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z))))
| spl1_2 ),
inference(resolution,[],[f216,f3]) ).
fof(f328,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f329,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(intersection(x,y)),complement(z)))
| spl1_2 ),
inference(resolution,[],[f327,f25]) ).
fof(f330,plain,
( spl1_10
| ~ spl1_11
| spl1_2 ),
inference(avatar_split_clause,[],[f329,f215,f273,f270]) ).
fof(f333,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(intersection(complement(y),complement(z))))
| spl1_2 ),
inference(resolution,[],[f328,f22]) ).
fof(f334,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(intersection(complement(x),complement(z))))
| spl1_2 ),
inference(resolution,[],[f328,f21]) ).
fof(f335,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(y),complement(z)))
| spl1_2 ),
inference(resolution,[],[f333,f24]) ).
fof(f336,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(complement(x),complement(z)))
| spl1_2 ),
inference(resolution,[],[f334,f24]) ).
fof(f337,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(z))
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(y))
| spl1_2 ),
inference(resolution,[],[f335,f23]) ).
fof(f339,definition,
( spl1_14
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f340,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(y))
| spl1_14 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f342,definition,
( spl1_15
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f343,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(z))
| spl1_15 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f344,plain,
( ~ spl1_14
| ~ spl1_15
| spl1_2 ),
inference(avatar_split_clause,[],[f337,f215,f342,f339]) ).
fof(f345,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(z))
| ~ spl1_10 ),
inference(resolution,[],[f271,f22]) ).
fof(f346,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(intersection(x,y)))
| ~ spl1_10 ),
inference(resolution,[],[f271,f21]) ).
fof(f348,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),intersection(x,y))
| ~ spl1_10 ),
inference(resolution,[],[f346,f24]) ).
fof(f349,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(z))
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(x))
| spl1_2 ),
inference(resolution,[],[f336,f23]) ).
fof(f351,definition,
( spl1_16
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f352,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),complement(x))
| spl1_16 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( ~ spl1_16
| ~ spl1_15
| spl1_2 ),
inference(avatar_split_clause,[],[f349,f215,f342,f351]) ).
fof(f354,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),y)
| spl1_14 ),
inference(resolution,[],[f340,f25]) ).
fof(f356,definition,
( spl1_17
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),y) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f358,plain,
( spl1_17
| ~ spl1_11
| spl1_14 ),
inference(avatar_split_clause,[],[f354,f339,f273,f356]) ).
fof(f359,plain,
( $false
| ~ spl1_10
| spl1_15 ),
inference(resolution,[],[f343,f345]) ).
fof(f361,plain,
( ~ spl1_10
| spl1_15 ),
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f366,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),x)
| spl1_16 ),
inference(resolution,[],[f352,f25]) ).
fof(f368,definition,
( spl1_19
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),x) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f370,plain,
( spl1_19
| ~ spl1_11
| spl1_16 ),
inference(avatar_split_clause,[],[f366,f351,f273,f368]) ).
fof(f371,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),y)
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(z)))),x)
| ~ spl1_10 ),
inference(resolution,[],[f348,f23]) ).
fof(f374,plain,
( ~ spl1_19
| ~ spl1_17
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f371,f270,f356,f368]) ).
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_6
| ~ spl1_9 ),
inference(sat_conversion,[],[f296]) ).
cnf(s11,plain,
( spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f298]) ).
cnf(s13,plain,
( spl1_5
| ~ spl1_8
| spl1_12 ),
inference(sat_conversion,[],[f305]) ).
cnf(s14,plain,
( ~ spl1_9
| ~ spl1_12 ),
inference(sat_conversion,[],[f310]) ).
cnf(s15,plain,
( spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f311]) ).
cnf(s16,plain,
( spl1_4
| ~ spl1_8
| spl1_13 ),
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( ~ spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f322]) ).
cnf(s18,plain,
( spl1_6
| ~ spl1_13 ),
inference(sat_conversion,[],[f325]) ).
cnf(s20,plain,
( spl1_2
| spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f330]) ).
cnf(s22,plain,
( spl1_2
| ~ spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f344]) ).
cnf(s23,plain,
( spl1_2
| ~ spl1_15
| ~ spl1_16 ),
inference(sat_conversion,[],[f353]) ).
cnf(s24,plain,
( ~ spl1_11
| spl1_14
| spl1_17 ),
inference(sat_conversion,[],[f358]) ).
cnf(s25,plain,
( ~ spl1_10
| spl1_15 ),
inference(sat_conversion,[],[f361]) ).
cnf(s27,plain,
( ~ spl1_11
| spl1_16
| spl1_19 ),
inference(sat_conversion,[],[f370]) ).
cnf(s28,plain,
( ~ spl1_10
| ~ spl1_17
| ~ spl1_19 ),
inference(sat_conversion,[],[f374]) ).
cnf(s29,plain,
( ~ spl1_11
| spl1_2 ),
inference(rat,[],[s28,s24,s27,s22,s23,s25,s20]) ).
cnf(s30,plain,
spl1_2,
inference(rat,[],[s29,s9]) ).
cnf(s31,plain,
( ~ spl1_9
| spl1_1 ),
inference(rat,[],[s11,s13,s10,s14,s7]) ).
cnf(s32,plain,
spl1_1,
inference(rat,[],[s13,s11,s17,s18,s16,s15,s6,s31,s7]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s30,s32]) ).
fof(f375,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET172-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 01:01:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.65/1.31 % (1770368)Input is clausal, will run a generic CNF schedule.
% 2.65/1.31 % (1770376)lrs+10_1_sil=8000:sp=occurrence:random_seed=2048224299:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.31 % (1770376)Refutation not found, incomplete strategy
% 2.65/1.31 % (1770376)------------------------------
% 2.65/1.31 % (1770376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1770376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1770376)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1770376)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.31 % (1770376)Time elapsed: 0.002 s
% 2.65/1.31 % (1770376)Peak memory usage: 88 MB
% 2.65/1.31 % (1770376)Instructions burned: 4 (million)
% 2.65/1.31 % (1770373)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=1006793703:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.31 % (1770379)dis-21_1_sil=8000:lcm=predicate:random_seed=1270741862: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)
% 2.65/1.31 % (1770377)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=874399978:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.31 % (1770378)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3835771887:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.31 % (1770375)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1145039136:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.31 % (1770374)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1387787683:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.31 % (1770379)First to succeed.
% 2.65/1.31 % (1770379)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1770368"
% 2.65/1.31 % (1770377)Instruction limit reached!
% 2.65/1.31 % (1770377)------------------------------
% 2.65/1.31 % (1770377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1770377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1770377)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1770377)Termination reason: Instruction limit
% 2.65/1.31 % (1770377)Termination phase: Saturation
% 2.65/1.31 % (1770377)Time elapsed: 0.069 s
% 2.65/1.31 % (1770377)Peak memory usage: 88 MB
% 2.65/1.31 % (1770377)Instructions burned: 114 (million)
% 2.65/1.31 % (1770376)------------------------------
% 2.65/1.31 % (1770376)------------------------------
% 2.65/1.31 % (1770378)Instruction limit reached!
% 2.65/1.31 % (1770378)------------------------------
% 2.65/1.31 % (1770378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1770378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1770378)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1770378)Termination reason: Instruction limit
% 2.65/1.31 % (1770378)Termination phase: Saturation
% 2.65/1.31 % (1770378)Time elapsed: 0.134 s
% 2.65/1.31 % (1770378)Peak memory usage: 90 MB
% 2.65/1.31 % (1770378)Instructions burned: 180 (million)
% 2.65/1.31 % (1770387)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=2676843959:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.65/1.31 % (1770387)Refutation not found, incomplete strategy
% 2.65/1.31 % (1770387)------------------------------
% 2.65/1.31 % (1770387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1770387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1770387)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1770387)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.31 % (1770387)Time elapsed: 0.003 s
% 2.65/1.31 % (1770387)Peak memory usage: 88 MB
% 2.65/1.31 % (1770387)Instructions burned: 3 (million)
% 2.65/1.31 % (1770388)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=89192202:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.65/1.31 % (1770388)Refutation not found, incomplete strategy
% 2.65/1.31 % (1770388)------------------------------
% 2.65/1.31 % (1770388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1770388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1770388)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1770388)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.31 % (1770388)Time elapsed: 0.005 s
% 2.65/1.31 % (1770388)Peak memory usage: 88 MB
% 2.65/1.31 % (1770388)Instructions burned: 14 (million)
% 2.65/1.31 % (1770379)Refutation found. Thanks to Tanya!
% 2.65/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (1770379)------------------------------
% 0.18/1.51 % (1770379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1770379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1770379)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1770379)Termination reason: Refutation
% 0.18/1.51 % (1770379)Time elapsed: 0.009 s
% 0.18/1.51 % (1770379)Peak memory usage: 89 MB
% 0.18/1.51 % (1770379)Instructions burned: 14 (million)
% 0.18/1.51 % (1770379)------------------------------
% 0.18/1.51 % (1770379)------------------------------
% 0.18/1.51 % (1770368)Success in time 0.441 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------