%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET170-6 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:40:23 PM UTC 2026
% Result : Unsatisfiable 3.11s 1.32s
% Output : Refutation 3.75s
% 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 : 309 ( 138 ~; 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,z),intersection(y,z)) != intersection(union(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_over_union2_1) ).
fof(f135,plain,
complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))) != intersection(complement(intersection(complement(x),complement(y))),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,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),
inference(equality_proxy_replacement,[],[f135,f177]) ).
fof(f179,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f177]) ).
fof(f202,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f209,plain,
( ~ subclass(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)) ),
inference(resolution,[],[f179,f178]) ).
fof(f212,definition,
( spl1_1
<=> subclass(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f213,plain,
( ~ subclass(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl1_2
<=> subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f216,plain,
( ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),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(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f213,f3]) ).
fof(f220,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(complement(x),complement(y))),z))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f225,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| spl1_1 ),
inference(resolution,[],[f25,f219]) ).
fof(f227,definition,
( spl1_3
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(y,z)))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f228,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,definition,
( spl1_4
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f231,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,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(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,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(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(y,z)))
| ~ spl1_3 ),
inference(resolution,[],[f228,f22]) ).
fof(f247,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(x,z)))
| ~ spl1_3 ),
inference(resolution,[],[f228,f21]) ).
fof(f248,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(y,z))
| ~ spl1_3 ),
inference(resolution,[],[f246,f24]) ).
fof(f249,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(x,z))
| ~ spl1_3 ),
inference(resolution,[],[f247,f24]) ).
fof(f255,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),z)
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),y)
| ~ spl1_3 ),
inference(resolution,[],[f23,f248]) ).
fof(f256,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),z)
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),x)
| ~ spl1_3 ),
inference(resolution,[],[f23,f249]) ).
fof(f258,definition,
( spl1_5
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),x) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f261,definition,
( spl1_6
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),z) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f262,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),z)
| spl1_6 ),
inference(avatar_component_clause,[],[f261]) ).
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(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),y) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f267,plain,
( ~ spl1_7
| ~ spl1_6
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f255,f227,f261,f265]) ).
fof(f269,definition,
( spl1_8
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f270,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(x))
| spl1_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,definition,
( spl1_9
<=> member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f273,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(y))
| spl1_9 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),y)
| 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,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f282,definition,
( spl1_10
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(complement(x),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f283,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(complement(x),complement(y))))
| spl1_10 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,definition,
( spl1_11
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),z) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f286,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),z)
| spl1_11 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f305,definition,
( spl1_12
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f306,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(complement(x),complement(y)))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f308,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f309,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),universal_class)
| spl1_13 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),X0)
| spl1_13 ),
inference(resolution,[],[f309,f202]) ).
fof(f314,definition,
( spl1_14
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(x,z))) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f315,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(x,z)))
| spl1_14 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,definition,
( spl1_15
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(y,z))) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f318,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(y,z)))
| spl1_15 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f320,plain,
( $false
| spl1_2
| spl1_13 ),
inference(resolution,[],[f311,f279]) ).
fof(f328,plain,
( spl1_2
| spl1_13 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f329,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(x,z))
| spl1_14 ),
inference(resolution,[],[f315,f25]) ).
fof(f331,definition,
( spl1_16
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(x,z)) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f332,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(x,z))
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( spl1_16
| ~ spl1_13
| spl1_14 ),
inference(avatar_split_clause,[],[f329,f314,f308,f331]) ).
fof(f335,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(complement(x),complement(y))),z))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f336,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),z)
| spl1_1 ),
inference(resolution,[],[f335,f22]) ).
fof(f338,plain,
( $false
| spl1_1
| spl1_6 ),
inference(resolution,[],[f336,f262]) ).
fof(f339,plain,
( spl1_1
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f340,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(complement(intersection(complement(x),complement(y))),z))
| spl1_2 ),
inference(resolution,[],[f216,f3]) ).
fof(f341,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_2 ),
inference(resolution,[],[f216,f2]) ).
fof(f342,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),z)
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(complement(x),complement(y))))
| spl1_2 ),
inference(resolution,[],[f340,f23]) ).
fof(f345,definition,
( spl1_17
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(y,z)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f346,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(y,z))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f348,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| spl1_2 ),
inference(resolution,[],[f341,f24]) ).
fof(f349,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),z)
| ~ spl1_16 ),
inference(resolution,[],[f332,f22]) ).
fof(f350,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),x)
| ~ spl1_16 ),
inference(resolution,[],[f332,f21]) ).
fof(f351,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(y,z)))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(intersection(x,z)))
| spl1_2 ),
inference(resolution,[],[f348,f23]) ).
fof(f352,plain,
( ~ spl1_14
| ~ spl1_15
| spl1_2 ),
inference(avatar_split_clause,[],[f351,f215,f317,f314]) ).
fof(f353,plain,
( $false
| spl1_11
| ~ spl1_16 ),
inference(resolution,[],[f349,f286]) ).
fof(f354,plain,
( spl1_11
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f355,plain,
( ~ spl1_10
| ~ spl1_11
| spl1_2 ),
inference(avatar_split_clause,[],[f342,f215,f285,f282]) ).
fof(f356,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(complement(x),complement(y)))
| spl1_10 ),
inference(resolution,[],[f283,f25]) ).
fof(f357,plain,
( spl1_12
| ~ spl1_13
| spl1_10 ),
inference(avatar_split_clause,[],[f356,f282,f308,f305]) ).
fof(f359,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(y))
| ~ spl1_12 ),
inference(resolution,[],[f306,f22]) ).
fof(f360,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),complement(x))
| ~ spl1_12 ),
inference(resolution,[],[f306,f21]) ).
fof(f361,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),y)
| ~ spl1_12 ),
inference(resolution,[],[f359,f24]) ).
fof(f362,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),x)
| ~ spl1_12 ),
inference(resolution,[],[f360,f24]) ).
fof(f363,plain,
( $false
| ~ spl1_12
| ~ spl1_16 ),
inference(resolution,[],[f362,f350]) ).
fof(f364,plain,
( ~ spl1_12
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f365,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),intersection(y,z))
| spl1_15 ),
inference(resolution,[],[f318,f25]) ).
fof(f366,plain,
( spl1_17
| ~ spl1_13
| spl1_15 ),
inference(avatar_split_clause,[],[f365,f317,f308,f345]) ).
fof(f367,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),z)
| ~ spl1_17 ),
inference(resolution,[],[f346,f22]) ).
fof(f368,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),intersection(complement(intersection(complement(x),complement(y))),z)),y)
| ~ spl1_17 ),
inference(resolution,[],[f346,f21]) ).
fof(f369,plain,
( $false
| ~ spl1_12
| ~ spl1_17 ),
inference(resolution,[],[f368,f361]) ).
fof(f370,plain,
( ~ spl1_12
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f371,plain,
( $false
| spl1_11
| ~ spl1_17 ),
inference(resolution,[],[f286,f367]) ).
fof(f372,plain,
( spl1_11
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f374,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(complement(x),complement(y))),z))
| spl1_1 ),
inference(resolution,[],[f213,f2]) ).
fof(f376,plain,
( member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(x),complement(y))))
| spl1_1 ),
inference(resolution,[],[f374,f21]) ).
fof(f378,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(x),complement(y)))
| spl1_1 ),
inference(resolution,[],[f376,f24]) ).
fof(f381,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(y))
| ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(x))
| spl1_1 ),
inference(resolution,[],[f378,f23]) ).
fof(f382,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_1 ),
inference(avatar_split_clause,[],[f381,f212,f272,f269]) ).
fof(f383,plain,
( ~ member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(intersection(complement(intersection(complement(x),complement(y))),z),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),x)
| spl1_8 ),
inference(resolution,[],[f270,f25]) ).
fof(f385,plain,
( spl1_5
| ~ spl1_4
| spl1_8 ),
inference(avatar_split_clause,[],[f383,f269,f230,f258]) ).
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_6
| ~ spl1_7 ),
inference(sat_conversion,[],[f267]) ).
cnf(s10,plain,
( ~ spl1_4
| spl1_7
| spl1_9 ),
inference(sat_conversion,[],[f277]) ).
cnf(s17,plain,
( spl1_2
| spl1_13 ),
inference(sat_conversion,[],[f328]) ).
cnf(s18,plain,
( ~ spl1_13
| spl1_14
| spl1_16 ),
inference(sat_conversion,[],[f333]) ).
cnf(s19,plain,
( spl1_1
| spl1_6 ),
inference(sat_conversion,[],[f339]) ).
cnf(s21,plain,
( spl1_2
| ~ spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f352]) ).
cnf(s22,plain,
( spl1_11
| ~ spl1_16 ),
inference(sat_conversion,[],[f354]) ).
cnf(s23,plain,
( spl1_2
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f355]) ).
cnf(s24,plain,
( spl1_10
| spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f357]) ).
cnf(s25,plain,
( ~ spl1_12
| ~ spl1_16 ),
inference(sat_conversion,[],[f364]) ).
cnf(s26,plain,
( ~ spl1_13
| spl1_15
| spl1_17 ),
inference(sat_conversion,[],[f366]) ).
cnf(s27,plain,
( ~ spl1_12
| ~ spl1_17 ),
inference(sat_conversion,[],[f370]) ).
cnf(s28,plain,
( spl1_11
| ~ spl1_17 ),
inference(sat_conversion,[],[f372]) ).
cnf(s29,plain,
( spl1_1
| ~ spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f382]) ).
cnf(s30,plain,
( ~ spl1_4
| spl1_5
| spl1_8 ),
inference(sat_conversion,[],[f385]) ).
cnf(s31,plain,
spl1_1,
inference(rat,[],[s29,s30,s10,s7,s8,s3,s6,s19]) ).
cnf(s32,plain,
~ spl1_2,
inference(rat,[],[s2,s31]) ).
cnf(s33,plain,
spl1_13,
inference(rat,[],[s17,s32]) ).
cnf(s34,plain,
~ spl1_12,
inference(rat,[],[s21,s18,s26,s25,s27,s32,s33]) ).
cnf(s35,plain,
spl1_10,
inference(rat,[],[s24,s33,s34]) ).
cnf(s36,plain,
~ spl1_11,
inference(rat,[],[s23,s32,s35]) ).
cnf(s37,plain,
~ spl1_17,
inference(rat,[],[s28,s36]) ).
cnf(s38,plain,
~ spl1_16,
inference(rat,[],[s22,s36]) ).
cnf(s39,plain,
spl1_15,
inference(rat,[],[s26,s33,s37]) ).
cnf(s40,plain,
spl1_14,
inference(rat,[],[s18,s33,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s21,s32,s39,s40]) ).
fof(f386,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET170-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 01:04:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.11/1.32 % (4123173)Input is clausal, will run a generic CNF schedule.
% 3.11/1.32 % (4123182)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3788495832:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.11/1.32 % (4123178)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=2233983748:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.11/1.32 % (4123181)lrs+10_1_sil=8000:sp=occurrence:random_seed=28028817:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.11/1.32 % (4123179)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3444530585:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.11/1.32 % (4123180)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2662758768:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.11/1.32 % (4123181)Refutation not found, incomplete strategy
% 3.11/1.32 % (4123181)------------------------------
% 3.11/1.32 % (4123181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (4123181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (4123181)CaDiCaL version: 2.1.3
% 3.11/1.32 % (4123181)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.32 % (4123181)Time elapsed: 0.004 s
% 3.11/1.32 % (4123181)Peak memory usage: 88 MB
% 3.11/1.32 % (4123181)Instructions burned: 4 (million)
% 3.11/1.32 % (4123182)Instruction limit reached!
% 3.11/1.32 % (4123182)------------------------------
% 3.11/1.32 % (4123182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (4123182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (4123182)CaDiCaL version: 2.1.3
% 3.11/1.32 % (4123182)Termination reason: Instruction limit
% 3.11/1.32 % (4123182)Termination phase: Saturation
% 3.11/1.32 % (4123182)Time elapsed: 0.039 s
% 3.11/1.32 % (4123182)Peak memory usage: 89 MB
% 3.11/1.32 % (4123182)Instructions burned: 115 (million)
% 3.11/1.32 % (4123183)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=641554848:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.11/1.32 % (4123184)dis-21_1_sil=8000:lcm=predicate:random_seed=2149189272: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)
% 3.11/1.32 % (4123184)First to succeed.
% 3.11/1.32 % (4123184)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4123173"
% 3.11/1.32 % (4123190)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=1382227044:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.11/1.32 % (4123190)Refutation not found, incomplete strategy
% 3.11/1.32 % (4123190)------------------------------
% 3.11/1.32 % (4123190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (4123190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (4123190)CaDiCaL version: 2.1.3
% 3.11/1.32 % (4123190)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.32 % (4123190)Time elapsed: 0.002 s
% 3.11/1.32 % (4123190)Peak memory usage: 88 MB
% 3.11/1.32 % (4123190)Instructions burned: 3 (million)
% 3.11/1.32 % (4123183)Instruction limit reached!
% 3.11/1.32 % (4123183)------------------------------
% 3.11/1.32 % (4123183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (4123183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (4123183)CaDiCaL version: 2.1.3
% 3.11/1.32 % (4123183)Termination reason: Instruction limit
% 3.11/1.32 % (4123183)Termination phase: Saturation
% 3.11/1.32 % (4123183)Time elapsed: 0.136 s
% 3.11/1.32 % (4123183)Peak memory usage: 90 MB
% 3.11/1.32 % (4123183)Instructions burned: 180 (million)
% 3.11/1.32 % (4123181)------------------------------
% 3.11/1.32 % (4123181)------------------------------
% 3.11/1.32 % (4123184)Refutation found. Thanks to Tanya!
% 3.11/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.11/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.42 % (4123184)------------------------------
% 3.75/1.42 % (4123184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.42 % (4123184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.42 % (4123184)CaDiCaL version: 2.1.3
% 3.75/1.42 % (4123184)Termination reason: Refutation
% 3.75/1.42 % (4123184)Time elapsed: 0.009 s
% 3.75/1.42 % (4123184)Peak memory usage: 89 MB
% 3.75/1.42 % (4123184)Instructions burned: 14 (million)
% 3.75/1.42 % (4123184)------------------------------
% 3.75/1.42 % (4123184)------------------------------
% 3.75/1.42 % (4123173)Success in time 0.457 s
% 3.75/1.42 % Vampire exiting
%------------------------------------------------------------------------------