%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET161-6 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:40:21 PM UTC 2026
% Result : Unsatisfiable 2.66s 1.35s
% Output : Refutation 3.56s
% 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/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,
union(x,union(y,z)) != union(y,union(x,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity_outside_union_1) ).
fof(f134,plain,
complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))) != complement(intersection(complement(y),complement(complement(intersection(complement(x),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(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),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(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| ~ subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))) ),
inference(resolution,[],[f177,f176]) ).
fof(f209,definition,
( spl1_1
<=> subclass(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f210,plain,
( ~ subclass(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_1 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,definition,
( spl1_2
<=> subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),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(y),complement(complement(intersection(complement(x),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_1 ),
inference(resolution,[],[f210,f3]) ).
fof(f217,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))))
| spl1_1 ),
inference(resolution,[],[f210,f2]) ).
fof(f220,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))
| spl1_1 ),
inference(resolution,[],[f25,f216]) ).
fof(f222,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),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_3])],[avatar_definition]) ).
fof(f223,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(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(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(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(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(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(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(y),complement(z)))))
| ~ spl1_3 ),
inference(resolution,[],[f223,f22]) ).
fof(f238,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| ~ spl1_3 ),
inference(resolution,[],[f223,f21]) ).
fof(f240,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(y),complement(z))))
| ~ spl1_3 ),
inference(resolution,[],[f237,f24]) ).
fof(f241,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z)))
| ~ spl1_3 ),
inference(resolution,[],[f240,f25]) ).
fof(f243,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f244,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(z)))
| ~ 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(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))))
| spl1_2 ),
inference(resolution,[],[f213,f3]) ).
fof(f247,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))))
| spl1_2 ),
inference(resolution,[],[f213,f2]) ).
fof(f249,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))
| spl1_2 ),
inference(resolution,[],[f246,f25]) ).
fof(f251,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f252,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,definition,
( spl1_7
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f255,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),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(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),X0)
| spl1_7 ),
inference(resolution,[],[f255,f199]) ).
fof(f260,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(x),complement(complement(intersection(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(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(complement(intersection(complement(x),complement(z)))))
| ~ spl1_6 ),
inference(resolution,[],[f252,f22]) ).
fof(f282,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(y))
| ~ spl1_6 ),
inference(resolution,[],[f252,f21]) ).
fof(f284,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(x),complement(z))))
| ~ spl1_6 ),
inference(resolution,[],[f281,f24]) ).
fof(f285,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(x),complement(z)))
| ~ spl1_6 ),
inference(resolution,[],[f284,f25]) ).
fof(f287,definition,
( spl1_8
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(x),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f288,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(x),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(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(z))
| ~ spl1_8 ),
inference(resolution,[],[f288,f22]) ).
fof(f291,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(x))
| ~ spl1_8 ),
inference(resolution,[],[f288,f21]) ).
fof(f297,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),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(y),complement(complement(intersection(complement(x),complement(z))))))),complement(x))
| spl1_2 ),
inference(resolution,[],[f23,f260]) ).
fof(f299,definition,
( spl1_9
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f300,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(x))
| spl1_9 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,definition,
( spl1_10
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(complement(intersection(complement(y),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f303,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(complement(intersection(complement(y),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,
( $false
| ~ spl1_8
| spl1_9 ),
inference(resolution,[],[f300,f291]) ).
fof(f307,plain,
( ~ spl1_8
| spl1_9 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f312,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(y),complement(z))))
| spl1_10 ),
inference(resolution,[],[f303,f25]) ).
fof(f314,definition,
( spl1_12
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(y),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f315,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(intersection(complement(y),complement(z))))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( spl1_12
| ~ spl1_7
| spl1_10 ),
inference(avatar_split_clause,[],[f312,f302,f254,f314]) ).
fof(f317,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),intersection(complement(y),complement(z)))
| ~ spl1_12 ),
inference(resolution,[],[f315,f24]) ).
fof(f318,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(y))
| ~ spl1_12 ),
inference(resolution,[],[f317,f23]) ).
fof(f320,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f321,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(y))
| spl1_13 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f323,definition,
( spl1_14
<=> member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f324,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z)))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))),complement(z))
| spl1_14 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( ~ spl1_13
| ~ spl1_14
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f318,f314,f323,f320]) ).
fof(f326,plain,
( $false
| ~ spl1_6
| spl1_13 ),
inference(resolution,[],[f321,f282]) ).
fof(f328,plain,
( ~ spl1_6
| spl1_13 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f333,plain,
( $false
| ~ spl1_8
| spl1_14 ),
inference(resolution,[],[f324,f290]) ).
fof(f335,plain,
( ~ spl1_8
| spl1_14 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f341,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))))
| spl1_1 ),
inference(resolution,[],[f210,f2]) ).
fof(f344,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(y),complement(complement(intersection(complement(x),complement(z))))))
| spl1_1 ),
inference(resolution,[],[f341,f24]) ).
fof(f348,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| ~ spl1_5 ),
inference(resolution,[],[f244,f22]) ).
fof(f349,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| ~ spl1_5 ),
inference(resolution,[],[f244,f21]) ).
fof(f350,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(z)))))
| ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| spl1_1 ),
inference(resolution,[],[f344,f23]) ).
fof(f352,definition,
( spl1_17
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f353,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(y))
| spl1_17 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f355,definition,
( spl1_18
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f356,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(complement(intersection(complement(x),complement(z)))))
| spl1_18 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
( ~ spl1_17
| ~ spl1_18
| spl1_1 ),
inference(avatar_split_clause,[],[f350,f209,f355,f352]) ).
fof(f366,plain,
( $false
| ~ spl1_5
| spl1_17 ),
inference(resolution,[],[f349,f353]) ).
fof(f368,plain,
( ~ spl1_5
| spl1_17 ),
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f369,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(z))))
| spl1_18 ),
inference(resolution,[],[f356,f25]) ).
fof(f371,definition,
( spl1_20
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f372,plain,
( member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(intersection(complement(x),complement(z))))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f373,plain,
( spl1_20
| ~ spl1_4
| spl1_18 ),
inference(avatar_split_clause,[],[f369,f355,f225,f371]) ).
fof(f376,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),intersection(complement(x),complement(z)))
| ~ spl1_20 ),
inference(resolution,[],[f372,f24]) ).
fof(f377,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| ~ spl1_20 ),
inference(resolution,[],[f376,f23]) ).
fof(f379,definition,
( spl1_21
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f380,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(x))
| spl1_21 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f382,definition,
( spl1_22
<=> member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f383,plain,
( ~ member(not_subclass_element(complement(intersection(complement(y),complement(complement(intersection(complement(x),complement(z)))))),complement(intersection(complement(x),complement(complement(intersection(complement(y),complement(z))))))),complement(z))
| spl1_22 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( ~ spl1_21
| ~ spl1_22
| ~ spl1_20 ),
inference(avatar_split_clause,[],[f377,f371,f382,f379]) ).
fof(f385,plain,
( $false
| ~ spl1_3
| spl1_21 ),
inference(resolution,[],[f380,f238]) ).
fof(f387,plain,
( ~ spl1_3
| spl1_21 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f392,plain,
( $false
| ~ spl1_5
| spl1_22 ),
inference(resolution,[],[f383,f348]) ).
fof(f394,plain,
( ~ spl1_5
| spl1_22 ),
inference(avatar_contradiction_clause,[],[f392]) ).
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_8
| spl1_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s15,plain,
( ~ spl1_7
| spl1_10
| spl1_12 ),
inference(sat_conversion,[],[f316]) ).
cnf(s16,plain,
( ~ spl1_12
| ~ spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f325]) ).
cnf(s17,plain,
( ~ spl1_6
| spl1_13 ),
inference(sat_conversion,[],[f328]) ).
cnf(s19,plain,
( ~ spl1_8
| spl1_14 ),
inference(sat_conversion,[],[f335]) ).
cnf(s22,plain,
( spl1_1
| ~ spl1_17
| ~ spl1_18 ),
inference(sat_conversion,[],[f357]) ).
cnf(s24,plain,
( ~ spl1_5
| spl1_17 ),
inference(sat_conversion,[],[f368]) ).
cnf(s25,plain,
( ~ spl1_4
| spl1_18
| spl1_20 ),
inference(sat_conversion,[],[f373]) ).
cnf(s27,plain,
( ~ spl1_20
| ~ spl1_21
| ~ spl1_22 ),
inference(sat_conversion,[],[f384]) ).
cnf(s28,plain,
( ~ spl1_3
| spl1_21 ),
inference(sat_conversion,[],[f387]) ).
cnf(s30,plain,
( ~ spl1_5
| spl1_22 ),
inference(sat_conversion,[],[f394]) ).
cnf(s32,plain,
( spl1_1
| ~ spl1_4 ),
inference(rat,[],[s25,s22,s27,s24,s30,s5,s28,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_9,
inference(rat,[],[s13,s38]) ).
cnf(s41,plain,
~ spl1_12,
inference(rat,[],[s16,s37,s39]) ).
cnf(s42,plain,
~ spl1_10,
inference(rat,[],[s12,s34,s40]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s15,s35,s41,s42]) ).
fof(f399,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET161-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 00:58:35 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
% 2.66/1.35 % (3934789)Input is clausal, will run a generic CNF schedule.
% 2.66/1.35 % (3934814)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1997362176:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.66/1.35 % (3934810)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2572704199:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.66/1.35 % (3934813)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2100513037:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.66/1.35 % (3934809)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=2958460399:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.66/1.35 % (3934815)dis-21_1_sil=8000:lcm=predicate:random_seed=4135660306: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)
% 2.66/1.35 % (3934811)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2703376724:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.66/1.35 % (3934815)First to succeed.
% 2.66/1.35 % (3934815)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3934789"
% 2.66/1.35 % (3934812)lrs+10_1_sil=8000:sp=occurrence:random_seed=1426593402:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.66/1.35 % (3934812)Refutation not found, incomplete strategy
% 2.66/1.35 % (3934812)------------------------------
% 2.66/1.35 % (3934812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3934812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3934812)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3934812)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.35 % (3934812)Time elapsed: 0.004 s
% 2.66/1.35 % (3934812)Peak memory usage: 88 MB
% 2.66/1.35 % (3934812)Instructions burned: 4 (million)
% 2.66/1.35 % (3934814)Instruction limit reached!
% 2.66/1.35 % (3934814)------------------------------
% 2.66/1.35 % (3934814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3934814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3934814)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3934814)Termination reason: Instruction limit
% 2.66/1.35 % (3934814)Termination phase: Saturation
% 2.66/1.35 % (3934814)Time elapsed: 0.073 s
% 2.66/1.35 % (3934814)Peak memory usage: 91 MB
% 2.66/1.35 % (3934814)Instructions burned: 182 (million)
% 2.66/1.35 % (3934813)Instruction limit reached!
% 2.66/1.35 % (3934813)------------------------------
% 2.66/1.35 % (3934813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3934813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3934813)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3934813)Termination reason: Instruction limit
% 2.66/1.35 % (3934813)Termination phase: Saturation
% 2.66/1.35 % (3934813)Time elapsed: 0.069 s
% 2.66/1.35 % (3934813)Peak memory usage: 89 MB
% 2.66/1.35 % (3934813)Instructions burned: 115 (million)
% 2.66/1.35 % (3934824)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=3008426890:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.66/1.35 % (3934824)Refutation not found, incomplete strategy
% 2.66/1.35 % (3934824)------------------------------
% 2.66/1.35 % (3934824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3934824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3934824)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3934824)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.35 % (3934824)Time elapsed: 0.001 s
% 2.66/1.35 % (3934824)Peak memory usage: 88 MB
% 2.66/1.35 % (3934824)Instructions burned: 2 (million)
% 2.66/1.35 % (3934825)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2057332325:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 2.66/1.35 % (3934825)Refutation not found, incomplete strategy
% 2.66/1.35 % (3934825)------------------------------
% 2.66/1.35 % (3934825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3934825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3934825)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3934825)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.35 % (3934825)Time elapsed: 0.004 s
% 2.66/1.35 % (3934825)Peak memory usage: 88 MB
% 2.66/1.35 % (3934825)Instructions burned: 4 (million)
% 2.66/1.35 % (3934812)------------------------------
% 2.66/1.35 % (3934812)------------------------------
% 2.66/1.35 % (3934815)Refutation found. Thanks to Tanya!
% 2.66/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.66/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.55 % (3934815)------------------------------
% 3.56/1.55 % (3934815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.55 % (3934815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.55 % (3934815)CaDiCaL version: 2.1.3
% 3.56/1.55 % (3934815)Termination reason: Refutation
% 3.56/1.55 % (3934815)Time elapsed: 0.009 s
% 3.56/1.55 % (3934815)Peak memory usage: 89 MB
% 3.56/1.55 % (3934815)Instructions burned: 14 (million)
% 3.56/1.55 % (3934815)------------------------------
% 3.56/1.55 % (3934815)------------------------------
% 3.56/1.55 % (3934789)Success in time 0.403 s
% 3.56/1.55 % Vampire exiting
%------------------------------------------------------------------------------