%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET179-6 : 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 : n004.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 12:40:25 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.77s
% Output : Refutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 122 ( 14 unt; 16 def)
% Number of atoms : 268 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 265 ( 119 ~; 130 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 16 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(complement(x),intersection(y,z))) != union(intersection(x,z),intersection(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_distribution_property1_1) ).
fof(f136,plain,
complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))) != complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),
inference(definition_unfolding,[],[f122,f26,f26]) ).
fof(f180,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f181,plain,
~ sQ0_eqProxy(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),
inference(equality_proxy_replacement,[],[f136,f180]) ).
fof(f182,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f180]) ).
fof(f207,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f215,plain,
( ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))))
| ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))) ),
inference(resolution,[],[f182,f181]) ).
fof(f218,definition,
( spl1_1
<=> subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f219,plain,
( ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))))
| spl1_1 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,definition,
( spl1_2
<=> subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f222,plain,
( ~ subclass(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f215,f218,f221]) ).
fof(f225,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))))
| spl1_1 ),
inference(resolution,[],[f219,f3]) ).
fof(f226,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f219,f2]) ).
fof(f229,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f25,f225]) ).
fof(f231,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f232,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f235,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f229,f218,f234,f231]) ).
fof(f237,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),X0)
| spl1_4 ),
inference(resolution,[],[f235,f207]) ).
fof(f238,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f237,f226]) ).
fof(f245,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f246,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(complement(x),intersection(y,z))))
| ~ spl1_3 ),
inference(resolution,[],[f232,f22]) ).
fof(f247,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(x,z)))
| ~ spl1_3 ),
inference(resolution,[],[f232,f21]) ).
fof(f248,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(x,z))
| ~ spl1_3 ),
inference(resolution,[],[f247,f24]) ).
fof(f249,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(complement(x),intersection(y,z)))
| ~ spl1_3 ),
inference(resolution,[],[f246,f24]) ).
fof(f255,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(y,z))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(x))
| ~ spl1_3 ),
inference(resolution,[],[f23,f249]) ).
fof(f256,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),z)
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),x)
| ~ spl1_3 ),
inference(resolution,[],[f23,f248]) ).
fof(f258,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),x) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f261,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),z) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f262,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),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,f231,f261,f258]) ).
fof(f265,definition,
( spl1_7
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f266,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(x))
| spl1_7 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,definition,
( spl1_8
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(y,z)) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f270,plain,
( ~ spl1_7
| ~ spl1_8
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f255,f231,f268,f265]) ).
fof(f272,definition,
( spl1_9
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(x,z))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f273,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(x,z)))
| spl1_9 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,definition,
( spl1_10
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(y,z))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f276,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(y,z)))
| spl1_10 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(y,z))
| spl1_10 ),
inference(resolution,[],[f276,f25]) ).
fof(f279,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(y,z))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f280,plain,
( spl1_8
| ~ spl1_4
| spl1_10 ),
inference(avatar_split_clause,[],[f278,f275,f234,f268]) ).
fof(f281,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_2 ),
inference(resolution,[],[f222,f3]) ).
fof(f282,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))))
| spl1_2 ),
inference(resolution,[],[f222,f2]) ).
fof(f283,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| spl1_2 ),
inference(resolution,[],[f281,f25]) ).
fof(f285,definition,
( spl1_11
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(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_11])],[avatar_definition]) ).
fof(f286,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,definition,
( spl1_12
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f289,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| spl1_12 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( spl1_11
| ~ spl1_12
| spl1_2 ),
inference(avatar_split_clause,[],[f283,f221,f288,f285]) ).
fof(f292,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))
| spl1_2 ),
inference(resolution,[],[f282,f24]) ).
fof(f293,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),X0)
| spl1_12 ),
inference(resolution,[],[f289,f207]) ).
fof(f294,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(x),intersection(y,z))))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(x,z)))
| spl1_2 ),
inference(resolution,[],[f292,f23]) ).
fof(f296,definition,
( spl1_13
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(x,z))) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f297,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(x,z)))
| spl1_13 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f299,definition,
( spl1_14
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(x),intersection(y,z)))) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f300,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(complement(x),intersection(y,z))))
| spl1_14 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f301,plain,
( ~ spl1_13
| ~ spl1_14
| spl1_2 ),
inference(avatar_split_clause,[],[f294,f221,f299,f296]) ).
fof(f315,plain,
( $false
| spl1_2
| spl1_12 ),
inference(resolution,[],[f293,f282]) ).
fof(f323,plain,
( spl1_2
| spl1_12 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f324,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(y,z)))
| ~ spl1_11 ),
inference(resolution,[],[f286,f22]) ).
fof(f325,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),complement(intersection(x,z)))
| ~ spl1_11 ),
inference(resolution,[],[f286,f21]) ).
fof(f326,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),x)
| spl1_7 ),
inference(resolution,[],[f266,f25]) ).
fof(f328,plain,
( spl1_5
| ~ spl1_4
| spl1_7 ),
inference(avatar_split_clause,[],[f326,f265,f234,f258]) ).
fof(f343,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),z)
| ~ spl1_8 ),
inference(resolution,[],[f279,f22]) ).
fof(f346,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(y,z))
| ~ spl1_11 ),
inference(resolution,[],[f324,f24]) ).
fof(f350,definition,
( spl1_16
<=> member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(x),intersection(y,z))) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f351,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(x),intersection(y,z)))
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f353,plain,
( $false
| ~ spl1_11
| spl1_13 ),
inference(resolution,[],[f297,f325]) ).
fof(f355,plain,
( ~ spl1_11
| spl1_13 ),
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f359,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),universal_class)
| member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(complement(x),intersection(y,z)))
| spl1_14 ),
inference(resolution,[],[f300,f25]) ).
fof(f360,plain,
( spl1_16
| ~ spl1_12
| spl1_14 ),
inference(avatar_split_clause,[],[f359,f299,f288,f350]) ).
fof(f376,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z))))),intersection(y,z))
| ~ spl1_16 ),
inference(resolution,[],[f351,f22]) ).
fof(f379,plain,
( $false
| ~ spl1_11
| ~ spl1_16 ),
inference(resolution,[],[f376,f346]) ).
fof(f382,plain,
( ~ spl1_11
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f379]) ).
fof(f384,plain,
( member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))))
| spl1_1 ),
inference(resolution,[],[f219,f2]) ).
fof(f385,plain,
( $false
| spl1_6
| ~ spl1_8 ),
inference(resolution,[],[f262,f343]) ).
fof(f386,plain,
( spl1_6
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f387,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),intersection(complement(intersection(x,z)),complement(intersection(y,z))))
| spl1_1 ),
inference(resolution,[],[f384,f24]) ).
fof(f392,plain,
( ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(y,z)))
| ~ member(not_subclass_element(complement(intersection(complement(intersection(x,z)),complement(intersection(y,z)))),complement(intersection(complement(intersection(x,z)),complement(intersection(complement(x),intersection(y,z)))))),complement(intersection(x,z)))
| spl1_1 ),
inference(resolution,[],[f387,f23]) ).
fof(f393,plain,
( ~ spl1_9
| ~ spl1_10
| spl1_1 ),
inference(avatar_split_clause,[],[f392,f218,f275,f272]) ).
fof(f399,plain,
( $false
| ~ spl1_3
| spl1_9 ),
inference(resolution,[],[f273,f247]) ).
fof(f401,plain,
( ~ spl1_3
| spl1_9 ),
inference(avatar_contradiction_clause,[],[f399]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
( spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f236]) ).
cnf(s4,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
( ~ spl1_3
| ~ spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f270]) ).
cnf(s8,plain,
( ~ spl1_4
| spl1_8
| spl1_10 ),
inference(sat_conversion,[],[f280]) ).
cnf(s9,plain,
( spl1_2
| spl1_11
| ~ spl1_12 ),
inference(sat_conversion,[],[f290]) ).
cnf(s10,plain,
( spl1_2
| ~ spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f301]) ).
cnf(s14,plain,
( spl1_2
| spl1_12 ),
inference(sat_conversion,[],[f323]) ).
cnf(s15,plain,
( ~ spl1_4
| spl1_5
| spl1_7 ),
inference(sat_conversion,[],[f328]) ).
cnf(s19,plain,
( ~ spl1_11
| spl1_13 ),
inference(sat_conversion,[],[f355]) ).
cnf(s21,plain,
( ~ spl1_12
| spl1_14
| spl1_16 ),
inference(sat_conversion,[],[f360]) ).
cnf(s25,plain,
( ~ spl1_11
| ~ spl1_16 ),
inference(sat_conversion,[],[f382]) ).
cnf(s26,plain,
( spl1_6
| ~ spl1_8 ),
inference(sat_conversion,[],[f386]) ).
cnf(s29,plain,
( spl1_1
| ~ spl1_9
| ~ spl1_10 ),
inference(sat_conversion,[],[f393]) ).
cnf(s30,plain,
( ~ spl1_3
| spl1_9 ),
inference(sat_conversion,[],[f401]) ).
cnf(s32,plain,
( spl1_1
| ~ spl1_4 ),
inference(rat,[],[s15,s5,s6,s26,s8,s29,s30,s3]) ).
cnf(s33,plain,
spl1_1,
inference(rat,[],[s32,s4]) ).
cnf(s34,plain,
~ spl1_2,
inference(rat,[],[s2,s33]) ).
cnf(s35,plain,
spl1_12,
inference(rat,[],[s14,s34]) ).
cnf(s36,plain,
spl1_11,
inference(rat,[],[s9,s34,s35]) ).
cnf(s37,plain,
~ spl1_16,
inference(rat,[],[s25,s36]) ).
cnf(s39,plain,
spl1_13,
inference(rat,[],[s19,s36]) ).
cnf(s40,plain,
spl1_14,
inference(rat,[],[s21,s35,s37]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s10,s34,s40,s39]) ).
fof(f406,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET179-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n004.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 28 01:01:37 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 1.66/1.77 % (4047711)Input is clausal, will run a generic CNF schedule.
% 1.66/1.77 % (4047720)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=2937259711:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.66/1.77 % (4047721)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4044602695:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.66/1.77 % (4047724)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=626184425:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.66/1.77 % (4047723)lrs+10_1_sil=8000:sp=occurrence:random_seed=614893266:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.66/1.77 % (4047726)dis-21_1_sil=8000:lcm=predicate:random_seed=2913299555: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)
% 1.66/1.77 % (4047722)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=843475483:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.66/1.77 % (4047725)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3691941033:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.66/1.77 % (4047723)Refutation not found, incomplete strategy
% 1.66/1.77 % (4047723)------------------------------
% 1.66/1.77 % (4047723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.77 % (4047723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.77 % (4047723)CaDiCaL version: 2.1.3
% 1.66/1.77 % (4047723)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.77 % (4047723)Time elapsed: 0.003 s
% 1.66/1.77 % (4047723)Peak memory usage: 88 MB
% 1.66/1.77 % (4047723)Instructions burned: 1 (million)
% 1.66/1.77 % (4047726)First to succeed.
% 1.66/1.77 % (4047726)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4047711"
% 1.66/1.77 % (4047724)Instruction limit reached!
% 1.66/1.77 % (4047724)------------------------------
% 1.66/1.77 % (4047724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.77 % (4047724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.77 % (4047724)CaDiCaL version: 2.1.3
% 1.66/1.77 % (4047724)Termination reason: Instruction limit
% 1.66/1.77 % (4047724)Termination phase: Saturation
% 1.66/1.77 % (4047724)Time elapsed: 0.110 s
% 1.66/1.77 % (4047724)Peak memory usage: 89 MB
% 1.66/1.77 % (4047724)Instructions burned: 115 (million)
% 1.66/1.77 % (4047725)Instruction limit reached!
% 1.66/1.77 % (4047725)------------------------------
% 1.66/1.77 % (4047725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.77 % (4047725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.77 % (4047725)CaDiCaL version: 2.1.3
% 1.66/1.77 % (4047725)Termination reason: Instruction limit
% 1.66/1.77 % (4047725)Termination phase: Saturation
% 1.66/1.77 % (4047725)Time elapsed: 0.213 s
% 1.66/1.77 % (4047725)Peak memory usage: 90 MB
% 1.66/1.77 % (4047725)Instructions burned: 180 (million)
% 1.66/1.77 % (4047734)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=2442486535:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 1.66/1.77 % (4047734)Refutation not found, incomplete strategy
% 1.66/1.77 % (4047734)------------------------------
% 1.66/1.77 % (4047734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.77 % (4047734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.77 % (4047734)CaDiCaL version: 2.1.3
% 1.66/1.77 % (4047734)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.77 % (4047734)Time elapsed: 0.005 s
% 1.66/1.77 % (4047734)Peak memory usage: 88 MB
% 1.66/1.77 % (4047734)Instructions burned: 3 (million)
% 1.66/1.77 % (4047723)------------------------------
% 1.66/1.77 % (4047723)------------------------------
% 1.66/1.77 % (4047735)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3073604125:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 1.66/1.77 % (4047735)Refutation not found, incomplete strategy
% 1.66/1.77 % (4047735)------------------------------
% 1.66/1.77 % (4047735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.77 % (4047735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.77 % (4047735)CaDiCaL version: 2.1.3
% 1.66/1.77 % (4047735)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.77 % (4047735)Time elapsed: 0.011 s
% 1.66/1.77 % (4047735)Peak memory usage: 88 MB
% 1.66/1.77 % (4047735)Instructions burned: 14 (million)
% 1.66/1.77 % (4047726)Refutation found. Thanks to Tanya!
% 1.66/1.77 % SZS status Unsatisfiable for theBenchmark
% 1.66/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 5.77/1.98 % (4047726)------------------------------
% 5.77/1.98 % (4047726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.98 % (4047726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.98 % (4047726)CaDiCaL version: 2.1.3
% 5.77/1.98 % (4047726)Termination reason: Refutation
% 5.77/1.98 % (4047726)Time elapsed: 0.016 s
% 5.77/1.98 % (4047726)Peak memory usage: 89 MB
% 5.77/1.98 % (4047726)Instructions burned: 15 (million)
% 5.77/1.98 % (4047726)------------------------------
% 5.77/1.98 % (4047726)------------------------------
% 5.77/1.98 % (4047711)Success in time 0.709 s
% 5.77/1.99 % Vampire exiting
%------------------------------------------------------------------------------