%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET268-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:40:39 PM UTC 2026
% Result : Unsatisfiable 6.88s 1.97s
% Output : Refutation 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 31
% Syntax : Number of formulae : 130 ( 34 unt; 11 def)
% Number of atoms : 279 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 265 ( 116 ~; 142 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f31,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| restrict(X1,singleton(X0),universal_class) = null_class
| member(X0,domain_of(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| member(X0,domain_of(X1)) ),
inference(reorient_equations,[],[f31]) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
~ subclass(intersection(x,cross_product(universal_class,universal_class)),cross_product(domain_of(x),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property1_1) ).
fof(f127,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f127]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f127]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f127]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f127]) ).
fof(f143,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f144,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f32,f28,f12]) ).
fof(f189,definition,
sF0 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f190,plain,
cross_product(universal_class,universal_class) = sF0,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF1 = intersection(x,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f192,plain,
intersection(x,sF0) = sF1,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF2 = domain_of(x),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f194,plain,
domain_of(x) = sF2,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF3 = cross_product(sF2,universal_class),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f196,plain,
cross_product(sF2,universal_class) = sF3,
inference(reorient_equations,[],[f195]) ).
fof(f197,plain,
~ subclass(sF1,sF3),
inference(definition_folding,[],[f122,f196,f194,f192,f190]) ).
fof(f200,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f201,plain,
! [X0] :
( ~ member(X0,sF1)
| member(X0,x) ),
inference(superposition,[],[f21,f192]) ).
fof(f203,plain,
! [X0] :
( ~ member(X0,sF1)
| member(X0,sF0) ),
inference(superposition,[],[f22,f192]) ).
fof(f204,plain,
! [X0] :
( member(not_subclass_element(sF1,X0),x)
| subclass(sF1,X0) ),
inference(resolution,[],[f201,f2]) ).
fof(f205,plain,
( subclass(sF1,x)
| subclass(sF1,x) ),
inference(resolution,[],[f204,f3]) ).
fof(f206,plain,
subclass(sF1,x),
inference(duplicate_literal_removal,[],[f205]) ).
fof(f207,plain,
! [X0] :
( member(not_subclass_element(sF1,X0),sF0)
| subclass(sF1,X0) ),
inference(resolution,[],[f203,f2]) ).
fof(f208,plain,
( subclass(sF1,sF0)
| subclass(sF1,sF0) ),
inference(resolution,[],[f207,f3]) ).
fof(f209,plain,
subclass(sF1,sF0),
inference(duplicate_literal_removal,[],[f208]) ).
fof(f222,plain,
! [X0] :
( ~ member(X0,sF0)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(superposition,[],[f139,f190]) ).
fof(f224,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f242,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF3)
| ~ member(X1,universal_class)
| ~ member(X0,sF2) ),
inference(superposition,[],[f138,f196]) ).
fof(f246,plain,
! [X0] :
( subclass(sF1,X0)
| not_subclass_element(sF1,X0) = unordered_pair(unordered_pair(first(not_subclass_element(sF1,X0)),first(not_subclass_element(sF1,X0))),unordered_pair(first(not_subclass_element(sF1,X0)),unordered_pair(second(not_subclass_element(sF1,X0)),second(not_subclass_element(sF1,X0))))) ),
inference(resolution,[],[f222,f207]) ).
fof(f249,plain,
not_subclass_element(sF1,sF3) = unordered_pair(unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))),unordered_pair(first(not_subclass_element(sF1,sF3)),unordered_pair(second(not_subclass_element(sF1,sF3)),second(not_subclass_element(sF1,sF3))))),
inference(resolution,[],[f246,f197]) ).
fof(f250,plain,
( member(not_subclass_element(sF1,sF3),sF3)
| ~ member(second(not_subclass_element(sF1,sF3)),universal_class)
| ~ member(first(not_subclass_element(sF1,sF3)),sF2) ),
inference(superposition,[],[f242,f249]) ).
fof(f252,plain,
! [X0,X1] :
( ~ member(not_subclass_element(sF1,sF3),cross_product(X0,X1))
| member(second(not_subclass_element(sF1,sF3)),X1) ),
inference(superposition,[],[f137,f249]) ).
fof(f253,plain,
! [X0,X1] :
( ~ member(not_subclass_element(sF1,sF3),cross_product(X0,X1))
| member(first(not_subclass_element(sF1,sF3)),X0) ),
inference(superposition,[],[f136,f249]) ).
fof(f255,definition,
( spl4_1
<=> member(first(not_subclass_element(sF1,sF3)),sF2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f257,plain,
( ~ member(first(not_subclass_element(sF1,sF3)),sF2)
| spl4_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl4_2
<=> member(second(not_subclass_element(sF1,sF3)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f260,plain,
( member(second(not_subclass_element(sF1,sF3)),universal_class)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ member(second(not_subclass_element(sF1,sF3)),universal_class)
| spl4_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,definition,
( spl4_3
<=> member(not_subclass_element(sF1,sF3),sF3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f265,plain,
( member(not_subclass_element(sF1,sF3),sF3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f250,f263,f259,f255]) ).
fof(f269,plain,
( ~ member(not_subclass_element(sF1,sF3),sF0)
| member(first(not_subclass_element(sF1,sF3)),universal_class) ),
inference(superposition,[],[f253,f190]) ).
fof(f271,definition,
( spl4_4
<=> member(first(not_subclass_element(sF1,sF3)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f273,plain,
( member(first(not_subclass_element(sF1,sF3)),universal_class)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f275,definition,
( spl4_5
<=> member(not_subclass_element(sF1,sF3),sF0) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f276,plain,
( member(not_subclass_element(sF1,sF3),sF0)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f277,plain,
( ~ member(not_subclass_element(sF1,sF3),sF0)
| spl4_5 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,plain,
( spl4_4
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f269,f275,f271]) ).
fof(f285,plain,
( ~ member(not_subclass_element(sF1,sF3),sF0)
| member(second(not_subclass_element(sF1,sF3)),universal_class) ),
inference(superposition,[],[f252,f190]) ).
fof(f296,plain,
( ~ subclass(sF1,sF0)
| subclass(sF1,sF3)
| spl4_5 ),
inference(resolution,[],[f277,f224]) ).
fof(f297,plain,
( subclass(sF1,sF3)
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f296,f209]) ).
fof(f300,plain,
( $false
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f297,f197]) ).
fof(f301,plain,
spl4_5,
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f302,plain,
( member(second(not_subclass_element(sF1,sF3)),universal_class)
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f285,f276]) ).
fof(f303,plain,
( $false
| spl4_2
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f302,f261]) ).
fof(f304,plain,
( spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f309,definition,
( spl4_6
<=> member(not_subclass_element(sF1,sF3),x) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f310,plain,
( member(not_subclass_element(sF1,sF3),x)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f311,plain,
( ~ member(not_subclass_element(sF1,sF3),x)
| spl4_6 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f318,plain,
( ~ subclass(sF1,x)
| subclass(sF1,sF3)
| spl4_6 ),
inference(resolution,[],[f311,f224]) ).
fof(f319,plain,
( subclass(sF1,sF3)
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f318,f206]) ).
fof(f322,plain,
( $false
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f319,f197]) ).
fof(f323,plain,
spl4_6,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f356,plain,
! [X0] :
( ~ member(X0,universal_class)
| null_class = intersection(x,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF2) ),
inference(superposition,[],[f144,f194]) ).
fof(f360,plain,
( null_class = intersection(x,cross_product(unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))),universal_class))
| member(first(not_subclass_element(sF1,sF3)),sF2)
| ~ spl4_4 ),
inference(resolution,[],[f356,f273]) ).
fof(f507,definition,
( spl4_29
<=> member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3)))) ),
introduced(definition,[new_symbols(definition,[spl4_29])],[avatar_definition]) ).
fof(f508,plain,
( member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| ~ spl4_29 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f509,plain,
( ~ member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| spl4_29 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f604,plain,
( subclass(sF1,sF3)
| ~ spl4_3 ),
inference(resolution,[],[f265,f3]) ).
fof(f607,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f604,f197]) ).
fof(f608,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f609,plain,
( null_class = intersection(x,cross_product(unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))),universal_class))
| spl4_1
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f360,f257]) ).
fof(f618,plain,
( ! [X0] :
( ~ member(X0,cross_product(unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))),universal_class))
| member(X0,null_class)
| ~ member(X0,x) )
| spl4_1
| ~ spl4_4 ),
inference(superposition,[],[f23,f609]) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3)))) )
| spl4_1
| ~ spl4_4 ),
inference(resolution,[],[f618,f138]) ).
fof(f657,plain,
( ~ member(not_subclass_element(sF1,sF3),x)
| member(not_subclass_element(sF1,sF3),null_class)
| ~ member(second(not_subclass_element(sF1,sF3)),universal_class)
| ~ member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| spl4_1
| ~ spl4_4 ),
inference(superposition,[],[f653,f249]) ).
fof(f878,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f200,f3]) ).
fof(f898,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f878]) ).
fof(f1250,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f898,f70]) ).
fof(f1757,plain,
( member(not_subclass_element(sF1,sF3),null_class)
| ~ member(second(not_subclass_element(sF1,sF3)),universal_class)
| ~ member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| spl4_1
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f657,f310]) ).
fof(f1762,plain,
( member(not_subclass_element(sF1,sF3),null_class)
| ~ member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1757,f260]) ).
fof(f2128,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0
| null_class = X0 ),
inference(resolution,[],[f7,f1250]) ).
fof(f2132,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f2128]) ).
fof(f2135,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f2132,f898]) ).
fof(f2151,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f143,f2135]) ).
fof(f2153,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f2151]) ).
fof(f2168,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f2153,f68]) ).
fof(f2184,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f2153,f2168]) ).
fof(f3501,plain,
( ~ member(first(not_subclass_element(sF1,sF3)),universal_class)
| spl4_29 ),
inference(resolution,[],[f9,f509]) ).
fof(f3526,plain,
( $false
| ~ spl4_4
| spl4_29 ),
inference(forward_subsumption_resolution,[],[f3501,f273]) ).
fof(f3527,plain,
( ~ spl4_4
| spl4_29 ),
inference(avatar_contradiction_clause,[],[f3526]) ).
fof(f3538,plain,
( ~ member(first(not_subclass_element(sF1,sF3)),unordered_pair(first(not_subclass_element(sF1,sF3)),first(not_subclass_element(sF1,sF3))))
| spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1762,f2184]) ).
fof(f3548,plain,
( $false
| spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_29 ),
inference(forward_subsumption_resolution,[],[f3538,f508]) ).
fof(f3549,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_29 ),
inference(avatar_contradiction_clause,[],[f3548]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f266]) ).
cnf(s2,plain,
( spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f278]) ).
cnf(s6,plain,
spl4_5,
inference(sat_conversion,[],[f301]) ).
cnf(s7,plain,
( spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f304]) ).
cnf(s10,plain,
spl4_6,
inference(sat_conversion,[],[f323]) ).
cnf(s39,plain,
~ spl4_3,
inference(sat_conversion,[],[f608]) ).
cnf(s149,plain,
( ~ spl4_4
| spl4_29 ),
inference(sat_conversion,[],[f3527]) ).
cnf(s155,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_29 ),
inference(sat_conversion,[],[f3549]) ).
cnf(s174,plain,
spl4_2,
inference(rat,[],[s7,s6]) ).
cnf(s176,plain,
spl4_4,
inference(rat,[],[s2,s6]) ).
cnf(s177,plain,
spl4_29,
inference(rat,[],[s149,s176]) ).
cnf(s178,plain,
spl4_1,
inference(rat,[],[s155,s177,s10,s174,s176]) ).
cnf(s179,plain,
$false,
inference(rat,[],[s1,s39,s174,s178]) ).
fof(f3562,plain,
$false,
inference(avatar_sat_refutation,[],[s179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET268-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 01:15:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/1.97 % (1341050)Input is clausal, will run a generic CNF schedule.
% 6.88/1.97 % (1341058)lrs+10_1_sil=8000:sp=occurrence:random_seed=330186688:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.88/1.97 % (1341058)Refutation not found, incomplete strategy
% 6.88/1.97 % (1341058)------------------------------
% 6.88/1.97 % (1341058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341058)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341058)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.97 % (1341058)Time elapsed: 0.001 s
% 6.88/1.97 % (1341058)Peak memory usage: 88 MB
% 6.88/1.97 % (1341058)Instructions burned: 1 (million)
% 6.88/1.97 % (1341055)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=1893906491:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.88/1.97 % (1341057)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2675672006:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.88/1.97 % (1341056)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2463227654:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.88/1.97 % (1341059)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1678549974:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.88/1.97 % (1341061)dis-21_1_sil=8000:lcm=predicate:random_seed=2213712034: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)
% 6.88/1.97 % (1341059)Refutation not found, incomplete strategy
% 6.88/1.97 % (1341059)------------------------------
% 6.88/1.97 % (1341059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341059)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341059)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.97 % (1341059)Time elapsed: 0.004 s
% 6.88/1.97 % (1341059)Peak memory usage: 88 MB
% 6.88/1.97 % (1341059)Instructions burned: 4 (million)
% 6.88/1.97 % (1341060)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4110719574:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.88/1.97 % (1341061)Instruction limit reached!
% 6.88/1.97 % (1341061)------------------------------
% 6.88/1.97 % (1341061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341061)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341061)Termination reason: Instruction limit
% 6.88/1.97 % (1341061)Termination phase: Saturation
% 6.88/1.97 % (1341061)Time elapsed: 0.070 s
% 6.88/1.97 % (1341061)Peak memory usage: 89 MB
% 6.88/1.97 % (1341061)Instructions burned: 118 (million)
% 6.88/1.97 % (1341058)------------------------------
% 6.88/1.97 % (1341058)------------------------------
% 6.88/1.97 % (1341060)Instruction limit reached!
% 6.88/1.97 % (1341060)------------------------------
% 6.88/1.97 % (1341060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341060)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341060)Termination reason: Instruction limit
% 6.88/1.97 % (1341060)Termination phase: Saturation
% 6.88/1.97 % (1341060)Time elapsed: 0.131 s
% 6.88/1.97 % (1341060)Peak memory usage: 90 MB
% 6.88/1.97 % (1341060)Instructions burned: 180 (million)
% 6.88/1.97 % (1341070)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=476844078:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.88/1.97 % (1341069)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=84544440:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.88/1.97 % (1341069)Refutation not found, incomplete strategy
% 6.88/1.97 % (1341069)------------------------------
% 6.88/1.97 % (1341069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341069)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341069)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.97 % (1341069)Time elapsed: 0.003 s
% 6.88/1.97 % (1341069)Peak memory usage: 88 MB
% 6.88/1.97 % (1341069)Instructions burned: 3 (million)
% 6.88/1.97 % (1341070)Refutation not found, incomplete strategy
% 6.88/1.97 % (1341070)------------------------------
% 6.88/1.97 % (1341070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341070)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341070)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.97 % (1341070)Time elapsed: 0.006 s
% 6.88/1.97 % (1341070)Peak memory usage: 89 MB
% 6.88/1.97 % (1341070)Instructions burned: 20 (million)
% 6.88/1.97 % (1341059)------------------------------
% 6.88/1.97 % (1341059)------------------------------
% 6.88/1.97 % (1341071)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1629689479:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.88/1.97 % (1341070)------------------------------
% 6.88/1.97 % (1341070)------------------------------
% 6.88/1.97 % (1341071)Instruction limit reached!
% 6.88/1.97 % (1341071)------------------------------
% 6.88/1.97 % (1341071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341071)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341071)Termination reason: Instruction limit
% 6.88/1.97 % (1341071)Termination phase: Saturation
% 6.88/1.97 % (1341071)Time elapsed: 0.118 s
% 6.88/1.97 % (1341071)Peak memory usage: 88 MB
% 6.88/1.97 % (1341071)Instructions burned: 220 (million)
% 6.88/1.97 % (1341074)lrs+10_64_to=lpo:sil=8000:random_seed=1954316126:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.88/1.97 % (1341069)------------------------------
% 6.88/1.97 % (1341069)------------------------------
% 6.88/1.97 % (1341074)Instruction limit reached!
% 6.88/1.97 % (1341074)------------------------------
% 6.88/1.97 % (1341074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341074)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341074)Termination reason: Instruction limit
% 6.88/1.97 % (1341074)Termination phase: Saturation
% 6.88/1.97 % (1341074)Time elapsed: 0.080 s
% 6.88/1.97 % (1341074)Peak memory usage: 89 MB
% 6.88/1.97 % (1341074)Instructions burned: 126 (million)
% 6.88/1.97 % (1341076)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1253301106:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.88/1.97 % (1341077)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=983705156:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.88/1.97 % (1341079)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1777883801:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.88/1.97 % (1341076)Instruction limit reached!
% 6.88/1.97 % (1341076)------------------------------
% 6.88/1.97 % (1341076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341076)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341076)Termination reason: Instruction limit
% 6.88/1.97 % (1341076)Termination phase: Saturation
% 6.88/1.97 % (1341076)Time elapsed: 0.117 s
% 6.88/1.97 % (1341076)Peak memory usage: 89 MB
% 6.88/1.97 % (1341076)Instructions burned: 195 (million)
% 6.88/1.97 % (1341080)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=224748804:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.88/1.97 % (1341077)Instruction limit reached!
% 6.88/1.97 % (1341077)------------------------------
% 6.88/1.97 % (1341077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341077)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341077)Termination reason: Instruction limit
% 6.88/1.97 % (1341077)Termination phase: Saturation
% 6.88/1.97 % (1341077)Time elapsed: 0.108 s
% 6.88/1.97 % (1341077)Peak memory usage: 91 MB
% 6.88/1.97 % (1341077)Instructions burned: 159 (million)
% 6.88/1.97 % (1341080)Instruction limit reached!
% 6.88/1.97 % (1341080)------------------------------
% 6.88/1.97 % (1341080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341080)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341080)Termination reason: Instruction limit
% 6.88/1.97 % (1341080)Termination phase: Saturation
% 6.88/1.97 % (1341080)Time elapsed: 0.053 s
% 6.88/1.97 % (1341080)Peak memory usage: 89 MB
% 6.88/1.97 % (1341080)Instructions burned: 107 (million)
% 6.88/1.97 % (1341055)First to succeed.
% 6.88/1.97 % (1341055)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1341050"
% 6.88/1.97 % (1341084)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1968458274:i=107_2991 on theBenchmark for (2991ds/107Mi)
% 6.88/1.97 % (1341086)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3594478266:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 6.88/1.97 % (1341087)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2155029301:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 6.88/1.97 % (1341084)Instruction limit reached!
% 6.88/1.97 % (1341084)------------------------------
% 6.88/1.97 % (1341084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/1.97 % (1341084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.97 % (1341084)CaDiCaL version: 2.1.3
% 6.88/1.97 % (1341084)Termination reason: Instruction limit
% 6.88/1.97 % (1341084)Termination phase: Saturation
% 6.88/1.97 % (1341084)Time elapsed: 0.074 s
% 6.88/1.97 % (1341084)Peak memory usage: 89 MB
% 6.88/1.97 % (1341084)Instructions burned: 108 (million)
% 6.88/1.97 % (1341055)Refutation found. Thanks to Tanya!
% 6.88/1.97 % SZS status Unsatisfiable for theBenchmark
% 6.88/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.53/2.17 % (1341055)------------------------------
% 8.53/2.17 % (1341055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/2.17 % (1341055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/2.17 % (1341055)CaDiCaL version: 2.1.3
% 8.53/2.17 % (1341055)Termination reason: Refutation
% 8.53/2.17 % (1341055)Time elapsed: 0.789 s
% 8.53/2.17 % (1341055)Peak memory usage: 134 MB
% 8.53/2.17 % (1341055)Instructions burned: 1526 (million)
% 8.53/2.17 % (1341055)------------------------------
% 8.53/2.17 % (1341055)------------------------------
% 8.53/2.17 % (1341050)Success in time 1.123 s
% 8.53/2.17 % Vampire exiting
%------------------------------------------------------------------------------