%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET159-6 : 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 : n019.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 12:40:20 PM UTC 2026
% Result : Unsatisfiable 2.60s 1.29s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 144 ( 17 unt; 19 def)
% Number of atoms : 314 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 310 ( 140 ~; 151 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 23 ( 21 usr; 19 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 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,
union(union(x,y),z) != union(x,union(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_union_1) ).
fof(f134,plain,
complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))) != complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),
inference(definition_unfolding,[],[f122,f26,f26,f26,f26]) ).
fof(f175,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f176,plain,
~ sQ0_eqProxy(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),
inference(equality_proxy_replacement,[],[f134,f175]) ).
fof(f177,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f175]) ).
fof(f199,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f206,plain,
( ~ subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))))
| ~ subclass(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))) ),
inference(resolution,[],[f177,f176]) ).
fof(f209,definition,
( spl1_1
<=> subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f210,plain,
( ~ subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))))
| spl1_1 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,definition,
( spl1_2
<=> subclass(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_2 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f206,f209,f212]) ).
fof(f216,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))))
| spl1_1 ),
inference(resolution,[],[f210,f3]) ).
fof(f217,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_1 ),
inference(resolution,[],[f210,f2]) ).
fof(f220,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))
| spl1_1 ),
inference(resolution,[],[f25,f216]) ).
fof(f222,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f223,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f226,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f227,plain,
( spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f220,f209,f225,f222]) ).
fof(f228,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),X0)
| spl1_4 ),
inference(resolution,[],[f226,f199]) ).
fof(f229,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f228,f217]) ).
fof(f236,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f237,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(z))
| ~ spl1_3 ),
inference(resolution,[],[f223,f22]) ).
fof(f238,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(complement(intersection(complement(x),complement(y)))))
| ~ spl1_3 ),
inference(resolution,[],[f223,f21]) ).
fof(f240,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(x),complement(y))))
| ~ spl1_3 ),
inference(resolution,[],[f238,f24]) ).
fof(f241,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(x),complement(y)))
| ~ spl1_3 ),
inference(resolution,[],[f240,f25]) ).
fof(f243,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f244,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(x),complement(y)))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( spl1_5
| ~ spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f241,f222,f225,f243]) ).
fof(f246,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_2 ),
inference(resolution,[],[f213,f3]) ).
fof(f247,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))))
| spl1_2 ),
inference(resolution,[],[f213,f2]) ).
fof(f249,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))
| spl1_2 ),
inference(resolution,[],[f246,f25]) ).
fof(f251,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f252,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,definition,
( spl1_7
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f255,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| spl1_7 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( spl1_6
| ~ spl1_7
| spl1_2 ),
inference(avatar_split_clause,[],[f249,f212,f254,f251]) ).
fof(f259,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),X0)
| spl1_7 ),
inference(resolution,[],[f255,f199]) ).
fof(f260,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))
| spl1_2 ),
inference(resolution,[],[f247,f24]) ).
fof(f273,plain,
( $false
| spl1_2
| spl1_7 ),
inference(resolution,[],[f259,f247]) ).
fof(f280,plain,
( spl1_2
| spl1_7 ),
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f281,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(y),complement(z)))))
| ~ spl1_6 ),
inference(resolution,[],[f252,f22]) ).
fof(f282,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| ~ spl1_6 ),
inference(resolution,[],[f252,f21]) ).
fof(f284,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(y),complement(z))))
| ~ spl1_6 ),
inference(resolution,[],[f281,f24]) ).
fof(f285,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z)))
| ~ spl1_6 ),
inference(resolution,[],[f284,f25]) ).
fof(f287,definition,
( spl1_8
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f288,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z)))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f289,plain,
( spl1_8
| ~ spl1_7
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f285,f251,f254,f287]) ).
fof(f290,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| ~ spl1_8 ),
inference(resolution,[],[f288,f22]) ).
fof(f291,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| ~ spl1_8 ),
inference(resolution,[],[f288,f21]) ).
fof(f297,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(y)))))
| spl1_2 ),
inference(resolution,[],[f23,f260]) ).
fof(f299,definition,
( spl1_9
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(y))))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f300,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(y)))))
| spl1_9 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,definition,
( spl1_10
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f303,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| spl1_10 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f304,plain,
( ~ spl1_9
| ~ spl1_10
| spl1_2 ),
inference(avatar_split_clause,[],[f297,f212,f302,f299]) ).
fof(f305,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(y))))
| spl1_9 ),
inference(resolution,[],[f300,f25]) ).
fof(f307,definition,
( spl1_11
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f308,plain,
( member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(y))))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f309,plain,
( spl1_11
| ~ spl1_7
| spl1_9 ),
inference(avatar_split_clause,[],[f305,f299,f254,f307]) ).
fof(f310,plain,
( $false
| ~ spl1_8
| spl1_10 ),
inference(resolution,[],[f303,f290]) ).
fof(f312,plain,
( ~ spl1_8
| spl1_10 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f317,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(y)))
| ~ spl1_11 ),
inference(resolution,[],[f308,f24]) ).
fof(f319,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| ~ spl1_11 ),
inference(resolution,[],[f317,f23]) ).
fof(f321,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f322,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| spl1_13 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f324,definition,
( spl1_14
<=> member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f325,plain,
( ~ member(not_subclass_element(complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| spl1_14 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( ~ spl1_13
| ~ spl1_14
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f319,f307,f324,f321]) ).
fof(f327,plain,
( $false
| ~ spl1_6
| spl1_13 ),
inference(resolution,[],[f322,f282]) ).
fof(f329,plain,
( ~ spl1_6
| spl1_13 ),
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f334,plain,
( $false
| ~ spl1_8
| spl1_14 ),
inference(resolution,[],[f325,f291]) ).
fof(f336,plain,
( ~ spl1_8
| spl1_14 ),
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f342,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_1 ),
inference(resolution,[],[f210,f2]) ).
fof(f346,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))
| spl1_1 ),
inference(resolution,[],[f342,f24]) ).
fof(f347,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(y))
| ~ spl1_5 ),
inference(resolution,[],[f244,f22]) ).
fof(f348,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(x))
| ~ spl1_5 ),
inference(resolution,[],[f244,f21]) ).
fof(f352,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(complement(intersection(complement(y),complement(z)))))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(x))
| spl1_1 ),
inference(resolution,[],[f346,f23]) ).
fof(f354,definition,
( spl1_17
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f355,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(x))
| spl1_17 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f357,definition,
( spl1_18
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(complement(intersection(complement(y),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f358,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(complement(intersection(complement(y),complement(z)))))
| spl1_18 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( ~ spl1_17
| ~ spl1_18
| spl1_1 ),
inference(avatar_split_clause,[],[f352,f209,f357,f354]) ).
fof(f366,plain,
( $false
| ~ spl1_5
| spl1_17 ),
inference(resolution,[],[f348,f355]) ).
fof(f368,plain,
( ~ spl1_5
| spl1_17 ),
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f371,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(y),complement(z))))
| spl1_18 ),
inference(resolution,[],[f358,f25]) ).
fof(f373,definition,
( spl1_20
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(y),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f374,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(intersection(complement(y),complement(z))))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( spl1_20
| ~ spl1_4
| spl1_18 ),
inference(avatar_split_clause,[],[f371,f357,f225,f373]) ).
fof(f377,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),intersection(complement(y),complement(z)))
| ~ spl1_20 ),
inference(resolution,[],[f374,f24]) ).
fof(f378,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(y))
| ~ spl1_20 ),
inference(resolution,[],[f377,f23]) ).
fof(f380,definition,
( spl1_21
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f381,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(y))
| spl1_21 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f383,definition,
( spl1_22
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f384,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(complement(intersection(complement(x),complement(y)))),complement(z)))),complement(z))
| spl1_22 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f385,plain,
( ~ spl1_21
| ~ spl1_22
| ~ spl1_20 ),
inference(avatar_split_clause,[],[f378,f373,f383,f380]) ).
fof(f386,plain,
( $false
| ~ spl1_5
| spl1_21 ),
inference(resolution,[],[f381,f347]) ).
fof(f388,plain,
( ~ spl1_5
| spl1_21 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f393,plain,
( $false
| ~ spl1_3
| spl1_22 ),
inference(resolution,[],[f384,f237]) ).
fof(f395,plain,
( ~ spl1_3
| spl1_22 ),
inference(avatar_contradiction_clause,[],[f393]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f215]) ).
cnf(s3,plain,
( spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f227]) ).
cnf(s4,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f236]) ).
cnf(s5,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f245]) ).
cnf(s6,plain,
( spl1_2
| spl1_6
| ~ spl1_7 ),
inference(sat_conversion,[],[f256]) ).
cnf(s10,plain,
( spl1_2
| spl1_7 ),
inference(sat_conversion,[],[f280]) ).
cnf(s11,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f289]) ).
cnf(s12,plain,
( spl1_2
| ~ spl1_9
| ~ spl1_10 ),
inference(sat_conversion,[],[f304]) ).
cnf(s13,plain,
( ~ spl1_7
| spl1_9
| spl1_11 ),
inference(sat_conversion,[],[f309]) ).
cnf(s14,plain,
( ~ spl1_8
| spl1_10 ),
inference(sat_conversion,[],[f312]) ).
cnf(s16,plain,
( ~ spl1_11
| ~ spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f326]) ).
cnf(s17,plain,
( ~ spl1_6
| spl1_13 ),
inference(sat_conversion,[],[f329]) ).
cnf(s19,plain,
( ~ spl1_8
| spl1_14 ),
inference(sat_conversion,[],[f336]) ).
cnf(s22,plain,
( spl1_1
| ~ spl1_17
| ~ spl1_18 ),
inference(sat_conversion,[],[f359]) ).
cnf(s24,plain,
( ~ spl1_5
| spl1_17 ),
inference(sat_conversion,[],[f368]) ).
cnf(s26,plain,
( ~ spl1_4
| spl1_18
| spl1_20 ),
inference(sat_conversion,[],[f375]) ).
cnf(s27,plain,
( ~ spl1_20
| ~ spl1_21
| ~ spl1_22 ),
inference(sat_conversion,[],[f385]) ).
cnf(s28,plain,
( ~ spl1_5
| spl1_21 ),
inference(sat_conversion,[],[f388]) ).
cnf(s30,plain,
( ~ spl1_3
| spl1_22 ),
inference(sat_conversion,[],[f395]) ).
cnf(s32,plain,
( spl1_1
| ~ spl1_4 ),
inference(rat,[],[s26,s22,s27,s24,s28,s5,s30,s3]) ).
cnf(s33,plain,
spl1_1,
inference(rat,[],[s32,s4]) ).
cnf(s34,plain,
~ spl1_2,
inference(rat,[],[s2,s33]) ).
cnf(s35,plain,
spl1_7,
inference(rat,[],[s10,s34]) ).
cnf(s36,plain,
spl1_6,
inference(rat,[],[s6,s35,s34]) ).
cnf(s37,plain,
spl1_13,
inference(rat,[],[s17,s36]) ).
cnf(s38,plain,
spl1_8,
inference(rat,[],[s11,s35,s36]) ).
cnf(s39,plain,
spl1_14,
inference(rat,[],[s19,s38]) ).
cnf(s40,plain,
spl1_10,
inference(rat,[],[s14,s38]) ).
cnf(s41,plain,
~ spl1_11,
inference(rat,[],[s16,s37,s39]) ).
cnf(s42,plain,
~ spl1_9,
inference(rat,[],[s12,s34,s40]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s13,s35,s41,s42]) ).
fof(f400,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET159-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 00:57:49 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 2.60/1.29 % (3563867)Input is clausal, will run a generic CNF schedule.
% 2.60/1.29 % (3563872)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=241231454:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.60/1.29 % (3563877)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1131010644:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.60/1.29 % (3563873)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=925141103:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.60/1.29 % (3563875)lrs+10_1_sil=8000:sp=occurrence:random_seed=3256754210:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.60/1.29 % (3563876)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1895143022:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.60/1.29 % (3563874)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=120539344:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.60/1.29 % (3563875)Refutation not found, incomplete strategy
% 2.60/1.29 % (3563875)------------------------------
% 2.60/1.29 % (3563875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.29 % (3563875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.29 % (3563875)CaDiCaL version: 2.1.3
% 2.60/1.29 % (3563875)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.29 % (3563875)Time elapsed: 0.004 s
% 2.60/1.29 % (3563875)Peak memory usage: 88 MB
% 2.60/1.29 % (3563875)Instructions burned: 4 (million)
% 2.60/1.29 % (3563878)dis-21_1_sil=8000:lcm=predicate:random_seed=1546834596: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)
% 2.60/1.29 % (3563878)First to succeed.
% 2.60/1.29 % (3563878)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3563867"
% 2.60/1.29 % (3563876)Instruction limit reached!
% 2.60/1.29 % (3563876)------------------------------
% 2.60/1.29 % (3563876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.29 % (3563876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.29 % (3563876)CaDiCaL version: 2.1.3
% 2.60/1.29 % (3563876)Termination reason: Instruction limit
% 2.60/1.29 % (3563876)Termination phase: Saturation
% 2.60/1.29 % (3563876)Time elapsed: 0.069 s
% 2.60/1.29 % (3563876)Peak memory usage: 89 MB
% 2.60/1.29 % (3563876)Instructions burned: 114 (million)
% 2.60/1.29 % (3563877)Instruction limit reached!
% 2.60/1.29 % (3563877)------------------------------
% 2.60/1.29 % (3563877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.29 % (3563877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.29 % (3563877)CaDiCaL version: 2.1.3
% 2.60/1.29 % (3563877)Termination reason: Instruction limit
% 2.60/1.29 % (3563877)Termination phase: Saturation
% 2.60/1.29 % (3563877)Time elapsed: 0.133 s
% 2.60/1.29 % (3563877)Peak memory usage: 91 MB
% 2.60/1.29 % (3563877)Instructions burned: 180 (million)
% 2.60/1.29 % (3563886)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=2143080964:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.60/1.29 % (3563886)Refutation not found, incomplete strategy
% 2.60/1.29 % (3563886)------------------------------
% 2.60/1.29 % (3563886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.29 % (3563886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.29 % (3563886)CaDiCaL version: 2.1.3
% 2.60/1.29 % (3563886)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.29 % (3563886)Time elapsed: 0.002 s
% 2.60/1.29 % (3563886)Peak memory usage: 88 MB
% 2.60/1.29 % (3563886)Instructions burned: 2 (million)
% 2.60/1.29 % (3563875)------------------------------
% 2.60/1.29 % (3563875)------------------------------
% 2.60/1.29 % (3563887)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1645634725: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)
% 2.60/1.29 % (3563887)Refutation not found, incomplete strategy
% 2.60/1.29 % (3563887)------------------------------
% 2.60/1.29 % (3563887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.29 % (3563887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.29 % (3563887)CaDiCaL version: 2.1.3
% 2.60/1.29 % (3563887)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.29 % (3563887)Time elapsed: 0.003 s
% 2.60/1.29 % (3563887)Peak memory usage: 88 MB
% 2.60/1.29 % (3563887)Instructions burned: 4 (million)
% 2.60/1.29 % (3563878)Refutation found. Thanks to Tanya!
% 2.60/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.60/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.49 % (3563878)------------------------------
% 3.58/1.49 % (3563878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (3563878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (3563878)CaDiCaL version: 2.1.3
% 3.58/1.49 % (3563878)Termination reason: Refutation
% 3.58/1.49 % (3563878)Time elapsed: 0.010 s
% 3.58/1.49 % (3563878)Peak memory usage: 89 MB
% 3.58/1.49 % (3563878)Instructions burned: 14 (million)
% 3.58/1.49 % (3563878)------------------------------
% 3.58/1.49 % (3563878)------------------------------
% 3.58/1.49 % (3563867)Success in time 0.43 s
% 3.58/1.49 % Vampire exiting
%------------------------------------------------------------------------------