%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET169-6 : 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 : n002.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 12:40:22 PM UTC 2026
% Result : Unsatisfiable 2.56s 1.29s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 143 ( 17 unt; 18 def)
% Number of atoms : 314 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 308 ( 137 ~; 153 |; 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 : 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(intersection(x,y),intersection(x,z)) != intersection(x,union(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_over_union1_1) ).
fof(f135,plain,
complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))) != intersection(x,complement(intersection(complement(y),complement(z)))),
inference(definition_unfolding,[],[f122,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(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(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(f202,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f209,plain,
( ~ subclass(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))))
| ~ subclass(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))) ),
inference(resolution,[],[f179,f178]) ).
fof(f212,definition,
( spl1_1
<=> subclass(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))))
| spl1_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl1_2
<=> subclass(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f216,plain,
( ~ subclass(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f209,f212,f215]) ).
fof(f219,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))))
| spl1_1 ),
inference(resolution,[],[f213,f3]) ).
fof(f220,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(x,complement(intersection(complement(y),complement(z)))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f225,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),universal_class)
| member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(complement(intersection(x,y)),complement(intersection(x,z))))
| spl1_1 ),
inference(resolution,[],[f25,f219]) ).
fof(f227,definition,
( spl1_3
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(complement(intersection(x,y)),complement(intersection(x,z)))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f228,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(complement(intersection(x,y)),complement(intersection(x,z))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,definition,
( spl1_4
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f231,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f225,f212,f230,f227]) ).
fof(f233,plain,
( ! [X0] : ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),X0)
| spl1_4 ),
inference(resolution,[],[f231,f202]) ).
fof(f234,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f233,f220]) ).
fof(f245,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f246,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(intersection(x,z)))
| ~ spl1_3 ),
inference(resolution,[],[f228,f22]) ).
fof(f247,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(intersection(x,y)))
| ~ spl1_3 ),
inference(resolution,[],[f228,f21]) ).
fof(f248,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(x,z))
| ~ spl1_3 ),
inference(resolution,[],[f246,f24]) ).
fof(f249,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(x,y))
| ~ spl1_3 ),
inference(resolution,[],[f247,f24]) ).
fof(f255,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),z)
| ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),x)
| ~ spl1_3 ),
inference(resolution,[],[f23,f248]) ).
fof(f256,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),y)
| ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),x)
| ~ spl1_3 ),
inference(resolution,[],[f23,f249]) ).
fof(f258,definition,
( spl1_5
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),x) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f259,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),x)
| spl1_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,definition,
( spl1_6
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),y) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f263,plain,
( ~ spl1_5
| ~ spl1_6
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f256,f227,f261,f258]) ).
fof(f265,definition,
( spl1_7
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),z) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f267,plain,
( ~ spl1_5
| ~ spl1_7
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f255,f227,f265,f258]) ).
fof(f269,definition,
( spl1_8
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f270,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(y))
| spl1_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,definition,
( spl1_9
<=> member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f273,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(z))
| spl1_9 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),universal_class)
| member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),z)
| spl1_9 ),
inference(resolution,[],[f273,f25]) ).
fof(f277,plain,
( spl1_7
| ~ spl1_4
| spl1_9 ),
inference(avatar_split_clause,[],[f275,f272,f230,f265]) ).
fof(f279,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f282,definition,
( spl1_10
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),x) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f283,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),x)
| spl1_10 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,definition,
( spl1_11
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z)))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f286,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z))))
| spl1_11 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f292,definition,
( spl1_12
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,y))) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f293,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,y)))
| spl1_12 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,z))) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f296,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,z)))
| spl1_13 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f311,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,y))
| spl1_12 ),
inference(resolution,[],[f293,f25]) ).
fof(f313,definition,
( spl1_14
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f314,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,y))
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,definition,
( spl1_15
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f317,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),universal_class)
| spl1_15 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( spl1_14
| ~ spl1_15
| spl1_12 ),
inference(avatar_split_clause,[],[f311,f292,f316,f313]) ).
fof(f319,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),X0)
| spl1_15 ),
inference(resolution,[],[f317,f202]) ).
fof(f320,plain,
( $false
| spl1_2
| spl1_15 ),
inference(resolution,[],[f319,f279]) ).
fof(f328,plain,
( spl1_2
| spl1_15 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f330,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(x,complement(intersection(complement(y),complement(z)))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f332,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),x)
| spl1_1 ),
inference(resolution,[],[f330,f21]) ).
fof(f333,plain,
( $false
| spl1_1
| spl1_5 ),
inference(resolution,[],[f332,f259]) ).
fof(f334,plain,
( spl1_1
| spl1_5 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f335,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,complement(intersection(complement(y),complement(z)))))
| spl1_2 ),
inference(resolution,[],[f216,f3]) ).
fof(f336,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f337,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),y)
| ~ spl1_14 ),
inference(resolution,[],[f314,f22]) ).
fof(f338,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),x)
| ~ spl1_14 ),
inference(resolution,[],[f314,f21]) ).
fof(f339,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(complement(y),complement(z))))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),x)
| spl1_2 ),
inference(resolution,[],[f335,f23]) ).
fof(f340,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(complement(intersection(x,y)),complement(intersection(x,z))))
| spl1_2 ),
inference(resolution,[],[f336,f24]) ).
fof(f341,plain,
( $false
| spl1_10
| ~ spl1_14 ),
inference(resolution,[],[f338,f283]) ).
fof(f342,plain,
( spl1_10
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f343,plain,
( ~ spl1_10
| ~ spl1_11
| spl1_2 ),
inference(avatar_split_clause,[],[f339,f215,f285,f282]) ).
fof(f344,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z)))
| spl1_11 ),
inference(resolution,[],[f286,f25]) ).
fof(f346,definition,
( spl1_16
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f347,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(complement(y),complement(z)))
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f348,plain,
( spl1_16
| ~ spl1_15
| spl1_11 ),
inference(avatar_split_clause,[],[f344,f285,f316,f346]) ).
fof(f349,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(z))
| ~ spl1_16 ),
inference(resolution,[],[f347,f22]) ).
fof(f350,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(y))
| ~ spl1_16 ),
inference(resolution,[],[f347,f21]) ).
fof(f351,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,z)))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),complement(intersection(x,y)))
| spl1_2 ),
inference(resolution,[],[f340,f23]) ).
fof(f352,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),z)
| ~ spl1_16 ),
inference(resolution,[],[f349,f24]) ).
fof(f353,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),y)
| ~ spl1_16 ),
inference(resolution,[],[f350,f24]) ).
fof(f354,plain,
( $false
| ~ spl1_14
| ~ spl1_16 ),
inference(resolution,[],[f353,f337]) ).
fof(f355,plain,
( ~ spl1_14
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f356,plain,
( ~ spl1_12
| ~ spl1_13
| spl1_2 ),
inference(avatar_split_clause,[],[f351,f215,f295,f292]) ).
fof(f357,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,z))
| spl1_13 ),
inference(resolution,[],[f296,f25]) ).
fof(f359,definition,
( spl1_17
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,z)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f360,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),intersection(x,z))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f361,plain,
( spl1_17
| ~ spl1_15
| spl1_13 ),
inference(avatar_split_clause,[],[f357,f295,f316,f359]) ).
fof(f362,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),z)
| ~ spl1_17 ),
inference(resolution,[],[f360,f22]) ).
fof(f363,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,y)),complement(intersection(x,z)))),intersection(x,complement(intersection(complement(y),complement(z))))),x)
| ~ spl1_17 ),
inference(resolution,[],[f360,f21]) ).
fof(f364,plain,
( $false
| ~ spl1_16
| ~ spl1_17 ),
inference(resolution,[],[f362,f352]) ).
fof(f365,plain,
( ~ spl1_16
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f366,plain,
( $false
| spl1_10
| ~ spl1_17 ),
inference(resolution,[],[f363,f283]) ).
fof(f367,plain,
( spl1_10
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f369,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(x,complement(intersection(complement(y),complement(z)))))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f371,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(intersection(complement(y),complement(z))))
| spl1_1 ),
inference(resolution,[],[f369,f22]) ).
fof(f374,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),intersection(complement(y),complement(z)))
| spl1_1 ),
inference(resolution,[],[f371,f24]) ).
fof(f375,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(z))
| ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),complement(y))
| spl1_1 ),
inference(resolution,[],[f374,f23]) ).
fof(f376,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_1 ),
inference(avatar_split_clause,[],[f375,f212,f272,f269]) ).
fof(f384,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),universal_class)
| member(not_subclass_element(intersection(x,complement(intersection(complement(y),complement(z)))),complement(intersection(complement(intersection(x,y)),complement(intersection(x,z))))),y)
| spl1_8 ),
inference(resolution,[],[f270,f25]) ).
fof(f386,plain,
( spl1_6
| ~ spl1_4
| spl1_8 ),
inference(avatar_split_clause,[],[f384,f269,f230,f261]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f218]) ).
cnf(s3,plain,
( spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f232]) ).
cnf(s6,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s7,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s8,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_7 ),
inference(sat_conversion,[],[f267]) ).
cnf(s10,plain,
( ~ spl1_4
| spl1_7
| spl1_9 ),
inference(sat_conversion,[],[f277]) ).
cnf(s16,plain,
( spl1_12
| spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f318]) ).
cnf(s17,plain,
( spl1_2
| spl1_15 ),
inference(sat_conversion,[],[f328]) ).
cnf(s18,plain,
( spl1_1
| spl1_5 ),
inference(sat_conversion,[],[f334]) ).
cnf(s19,plain,
( spl1_10
| ~ spl1_14 ),
inference(sat_conversion,[],[f342]) ).
cnf(s20,plain,
( spl1_2
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f343]) ).
cnf(s21,plain,
( spl1_11
| ~ spl1_15
| spl1_16 ),
inference(sat_conversion,[],[f348]) ).
cnf(s22,plain,
( ~ spl1_14
| ~ spl1_16 ),
inference(sat_conversion,[],[f355]) ).
cnf(s23,plain,
( spl1_2
| ~ spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f356]) ).
cnf(s24,plain,
( spl1_13
| ~ spl1_15
| spl1_17 ),
inference(sat_conversion,[],[f361]) ).
cnf(s25,plain,
( ~ spl1_16
| ~ spl1_17 ),
inference(sat_conversion,[],[f365]) ).
cnf(s26,plain,
( spl1_10
| ~ spl1_17 ),
inference(sat_conversion,[],[f367]) ).
cnf(s27,plain,
( spl1_1
| ~ spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f376]) ).
cnf(s28,plain,
( ~ spl1_4
| spl1_6
| spl1_8 ),
inference(sat_conversion,[],[f386]) ).
cnf(s29,plain,
spl1_1,
inference(rat,[],[s27,s28,s10,s7,s8,s3,s6,s18]) ).
cnf(s30,plain,
~ spl1_2,
inference(rat,[],[s2,s29]) ).
cnf(s31,plain,
spl1_15,
inference(rat,[],[s17,s30]) ).
cnf(s32,plain,
spl1_10,
inference(rat,[],[s23,s16,s24,s19,s26,s30,s31]) ).
cnf(s33,plain,
~ spl1_11,
inference(rat,[],[s20,s30,s32]) ).
cnf(s34,plain,
spl1_16,
inference(rat,[],[s21,s31,s33]) ).
cnf(s35,plain,
~ spl1_17,
inference(rat,[],[s25,s34]) ).
cnf(s36,plain,
~ spl1_14,
inference(rat,[],[s22,s34]) ).
cnf(s37,plain,
spl1_13,
inference(rat,[],[s24,s31,s35]) ).
cnf(s38,plain,
spl1_12,
inference(rat,[],[s16,s31,s36]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s23,s30,s37,s38]) ).
fof(f387,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET169-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n002.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 01:01:22 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.56/1.29 % (4062101)Input is clausal, will run a generic CNF schedule.
% 2.56/1.29 % (4062110)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4220559845:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.56/1.29 % (4062107)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3559835151:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.56/1.29 % (4062110)Instruction limit reached!
% 2.56/1.29 % (4062110)------------------------------
% 2.56/1.29 % (4062110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.29 % (4062110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.29 % (4062110)CaDiCaL version: 2.1.3
% 2.56/1.29 % (4062110)Termination reason: Instruction limit
% 2.56/1.29 % (4062110)Termination phase: Saturation
% 2.56/1.29 % (4062110)Time elapsed: 0.038 s
% 2.56/1.29 % (4062110)Peak memory usage: 89 MB
% 2.56/1.29 % (4062110)Instructions burned: 114 (million)
% 2.56/1.29 % (4062106)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=1174515040:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.56/1.29 % (4062111)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1568361672:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.56/1.29 % (4062108)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4180409738:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.56/1.29 % (4062109)lrs+10_1_sil=8000:sp=occurrence:random_seed=4143775911:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.56/1.29 % (4062109)Refutation not found, incomplete strategy
% 2.56/1.29 % (4062109)------------------------------
% 2.56/1.29 % (4062109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.29 % (4062109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.29 % (4062109)CaDiCaL version: 2.1.3
% 2.56/1.29 % (4062109)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.29 % (4062109)Time elapsed: 0.004 s
% 2.56/1.29 % (4062109)Peak memory usage: 88 MB
% 2.56/1.29 % (4062109)Instructions burned: 4 (million)
% 2.56/1.29 % (4062112)dis-21_1_sil=8000:lcm=predicate:random_seed=448249173: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)
% 2.56/1.29 % (4062112)First to succeed.
% 2.56/1.29 % (4062112)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4062101"
% 2.56/1.29 % (4062115)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=1518550103:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.56/1.29 % (4062115)Refutation not found, incomplete strategy
% 2.56/1.29 % (4062115)------------------------------
% 2.56/1.29 % (4062115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.29 % (4062115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.29 % (4062115)CaDiCaL version: 2.1.3
% 2.56/1.29 % (4062115)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.29 % (4062115)Time elapsed: 0.001 s
% 2.56/1.29 % (4062115)Peak memory usage: 88 MB
% 2.56/1.29 % (4062115)Instructions burned: 3 (million)
% 2.56/1.29 % (4062111)Instruction limit reached!
% 2.56/1.29 % (4062111)------------------------------
% 2.56/1.29 % (4062111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.29 % (4062111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.29 % (4062111)CaDiCaL version: 2.1.3
% 2.56/1.29 % (4062111)Termination reason: Instruction limit
% 2.56/1.29 % (4062111)Termination phase: Saturation
% 2.56/1.29 % (4062111)Time elapsed: 0.136 s
% 2.56/1.29 % (4062111)Peak memory usage: 90 MB
% 2.56/1.29 % (4062111)Instructions burned: 181 (million)
% 2.56/1.29 % (4062115)------------------------------
% 2.56/1.29 % (4062115)------------------------------
% 2.56/1.29 % (4062109)------------------------------
% 2.56/1.29 % (4062109)------------------------------
% 2.56/1.29 % (4062112)Refutation found. Thanks to Tanya!
% 2.56/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.49 % (4062112)------------------------------
% 3.58/1.49 % (4062112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (4062112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (4062112)CaDiCaL version: 2.1.3
% 3.58/1.49 % (4062112)Termination reason: Refutation
% 3.58/1.49 % (4062112)Time elapsed: 0.009 s
% 3.58/1.49 % (4062112)Peak memory usage: 89 MB
% 3.58/1.49 % (4062112)Instructions burned: 14 (million)
% 3.58/1.49 % (4062112)------------------------------
% 3.58/1.49 % (4062112)------------------------------
% 3.58/1.49 % (4062101)Success in time 0.427 s
% 3.58/1.49 % Vampire exiting
%------------------------------------------------------------------------------