%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM083-1 : 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 : n006.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 12:11:43 PM UTC 2026
% Result : Unsatisfiable 8.13s 2.15s
% Output : Refutation 9.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 29
% Syntax : Number of formulae : 114 ( 33 unt; 6 def)
% Number of atoms : 255 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 269 ( 128 ~; 138 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 141 ( 0 sgn 141 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,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(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
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/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f176,negated_conjecture,
subclass(sum_class(x),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitive_class_property1_1) ).
fof(f177,negated_conjecture,
member(u,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitive_class_property1_2) ).
fof(f178,negated_conjecture,
~ subclass(u,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitive_class_property1_3) ).
fof(f179,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(f185,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f198,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,f179]) ).
fof(f201,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f20,f179,f179]) ).
fof(f203,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(f204,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(f269,plain,
subclass(domain_of(intersection(element_relation,cross_product(universal_class,x))),x),
inference(definition_unfolding,[],[f176,f185]) ).
fof(f271,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f276,definition,
sF0 = cross_product(universal_class,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f277,plain,
cross_product(universal_class,x) = sF0,
inference(reorient_equations,[],[f276]) ).
fof(f278,definition,
sF1 = intersection(element_relation,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f279,plain,
intersection(element_relation,sF0) = sF1,
inference(reorient_equations,[],[f278]) ).
fof(f280,definition,
sF2 = domain_of(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f281,plain,
domain_of(sF1) = sF2,
inference(reorient_equations,[],[f280]) ).
fof(f282,plain,
subclass(sF2,x),
inference(definition_folding,[],[f269,f281,f279,f277]) ).
fof(f286,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f290,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[],[f23,f3]) ).
fof(f303,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f304,plain,
! [X0] :
( ~ member(X0,sF0)
| member(X0,sF1)
| ~ member(X0,element_relation) ),
inference(superposition,[],[f23,f279]) ).
fof(f308,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(X1,x)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f198,f277]) ).
fof(f309,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),sF1)
| ~ member(X0,x) ),
inference(resolution,[],[f308,f304]) ).
fof(f323,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f303,f4]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f323,f2]) ).
fof(f333,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f327,f2]) ).
fof(f337,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f340,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),X2)
| ~ subclass(universal_class,X2)
| subclass(X0,X1) ),
inference(resolution,[],[f337,f1]) ).
fof(f363,plain,
! [X0] :
( ~ member(X0,universal_class)
| null_class = intersection(sF1,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF2) ),
inference(superposition,[],[f204,f281]) ).
fof(f373,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f290,f3]) ).
fof(f387,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f373]) ).
fof(f519,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f387,f70]) ).
fof(f521,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f519,f7]) ).
fof(f523,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f521]) ).
fof(f525,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f523,f387]) ).
fof(f535,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f203,f525]) ).
fof(f536,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f535]) ).
fof(f543,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f536,f68]) ).
fof(f559,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f536,f543]) ).
fof(f661,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[],[f302,f286]) ).
fof(f675,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) ),
inference(duplicate_literal_removal,[],[f661]) ).
fof(f680,plain,
! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[],[f675,f2]) ).
fof(f698,plain,
! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f680]) ).
fof(f704,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X1),X0)
| intersection(X0,X1) = X0 ),
inference(resolution,[],[f698,f7]) ).
fof(f715,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| intersection(X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f704,f387]) ).
fof(f718,plain,
! [X0] : intersection(X0,universal_class) = X0,
inference(resolution,[],[f715,f4]) ).
fof(f725,plain,
sF2 = intersection(sF2,x),
inference(resolution,[],[f715,f282]) ).
fof(f742,plain,
! [X0] :
( ~ member(X0,sF2)
| member(X0,x) ),
inference(superposition,[],[f22,f725]) ).
fof(f783,plain,
! [X0,X1] :
( ~ member(X1,X0)
| member(X1,universal_class) ),
inference(superposition,[],[f22,f718]) ).
fof(f893,definition,
( spl3_27
<=> member(not_subclass_element(u,x),universal_class) ),
introduced(definition,[new_symbols(definition,[spl3_27])],[avatar_definition]) ).
fof(f894,plain,
( ~ member(not_subclass_element(u,x),universal_class)
| spl3_27 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f895,plain,
( member(not_subclass_element(u,x),universal_class)
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f903,plain,
( null_class = intersection(sF1,cross_product(unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)),universal_class))
| member(not_subclass_element(u,x),sF2)
| ~ spl3_27 ),
inference(resolution,[],[f895,f363]) ).
fof(f1619,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f201,f198]) ).
fof(f1621,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(forward_subsumption_resolution,[],[f1619,f783]) ).
fof(f1623,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF1)
| ~ member(X1,x) ),
inference(resolution,[],[f1621,f309]) ).
fof(f1628,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF1)
| ~ member(X1,x) ),
inference(forward_subsumption_resolution,[],[f1623,f783]) ).
fof(f1629,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF1)
| ~ member(X0,X1)
| ~ member(X1,x) ),
inference(forward_subsumption_resolution,[],[f1628,f783]) ).
fof(f1936,definition,
( spl3_73
<=> member(not_subclass_element(u,x),sF2) ),
introduced(definition,[new_symbols(definition,[spl3_73])],[avatar_definition]) ).
fof(f1938,plain,
( member(not_subclass_element(u,x),sF2)
| ~ spl3_73 ),
inference(avatar_component_clause,[],[f1936]) ).
fof(f1940,definition,
( spl3_74
<=> null_class = intersection(sF1,cross_product(unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)),universal_class)) ),
introduced(definition,[new_symbols(definition,[spl3_74])],[avatar_definition]) ).
fof(f1942,plain,
( null_class = intersection(sF1,cross_product(unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)),universal_class))
| ~ spl3_74 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f1943,plain,
( spl3_73
| spl3_74
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f903,f893,f1940,f1936]) ).
fof(f1950,plain,
( ~ subclass(universal_class,universal_class)
| subclass(u,x)
| spl3_27 ),
inference(resolution,[],[f894,f340]) ).
fof(f1953,plain,
( subclass(u,x)
| spl3_27 ),
inference(forward_subsumption_resolution,[],[f1950,f271]) ).
fof(f1958,plain,
( $false
| spl3_27 ),
inference(forward_subsumption_resolution,[],[f1953,f178]) ).
fof(f1959,plain,
spl3_27,
inference(avatar_contradiction_clause,[],[f1958]) ).
fof(f1965,plain,
( member(not_subclass_element(u,x),x)
| ~ spl3_73 ),
inference(resolution,[],[f1938,f742]) ).
fof(f1970,plain,
( subclass(u,x)
| ~ spl3_73 ),
inference(resolution,[],[f1965,f3]) ).
fof(f1975,plain,
( $false
| ~ spl3_73 ),
inference(forward_subsumption_resolution,[],[f1970,f178]) ).
fof(f1976,plain,
~ spl3_73,
inference(avatar_contradiction_clause,[],[f1975]) ).
fof(f1980,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,cross_product(unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)),universal_class))
| ~ member(X0,sF1) )
| ~ spl3_74 ),
inference(superposition,[],[f23,f1942]) ).
fof(f1991,plain,
( ! [X0] :
( ~ member(X0,cross_product(unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)),universal_class))
| ~ member(X0,sF1) )
| ~ spl3_74 ),
inference(forward_subsumption_resolution,[],[f1980,f559]) ).
fof(f2000,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF1)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x))) )
| ~ spl3_74 ),
inference(resolution,[],[f1991,f198]) ).
fof(f2005,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)))
| ~ member(X1,X0)
| ~ member(X0,x) )
| ~ spl3_74 ),
inference(resolution,[],[f2000,f1629]) ).
fof(f2007,plain,
( ! [X0,X1] :
( ~ member(X1,unordered_pair(not_subclass_element(u,x),not_subclass_element(u,x)))
| ~ member(X1,X0)
| ~ member(X0,x) )
| ~ spl3_74 ),
inference(forward_subsumption_resolution,[],[f2005,f783]) ).
fof(f2009,plain,
( ! [X0] :
( ~ member(not_subclass_element(u,x),X0)
| ~ member(X0,x)
| ~ member(not_subclass_element(u,x),universal_class) )
| ~ spl3_74 ),
inference(resolution,[],[f2007,f10]) ).
fof(f2021,plain,
( ! [X0] :
( ~ member(not_subclass_element(u,x),X0)
| ~ member(X0,x) )
| ~ spl3_27
| ~ spl3_74 ),
inference(forward_subsumption_resolution,[],[f2009,f895]) ).
fof(f2025,plain,
( ~ member(u,x)
| subclass(u,x)
| ~ spl3_27
| ~ spl3_74 ),
inference(resolution,[],[f2021,f2]) ).
fof(f2040,plain,
( subclass(u,x)
| ~ spl3_27
| ~ spl3_74 ),
inference(forward_subsumption_resolution,[],[f2025,f177]) ).
fof(f2042,plain,
( $false
| ~ spl3_27
| ~ spl3_74 ),
inference(forward_subsumption_resolution,[],[f2040,f178]) ).
fof(f2043,plain,
( ~ spl3_27
| ~ spl3_74 ),
inference(avatar_contradiction_clause,[],[f2042]) ).
cnf(s67,plain,
( ~ spl3_27
| spl3_73
| spl3_74 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s70,plain,
spl3_27,
inference(sat_conversion,[],[f1959]) ).
cnf(s71,plain,
~ spl3_73,
inference(sat_conversion,[],[f1976]) ).
cnf(s74,plain,
( ~ spl3_27
| ~ spl3_74 ),
inference(sat_conversion,[],[f2043]) ).
cnf(s75,plain,
~ spl3_74,
inference(rat,[],[s74,s70]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s67,s75,s71,s70]) ).
fof(f2044,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM083-1 : 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 : n006.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
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 18:50:55 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
% 8.13/2.15 % (3252227)Input is clausal, will run a generic CNF schedule.
% 8.13/2.15 % (3252236)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1242539213:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.13/2.15 % (3252236)Instruction limit reached!
% 8.13/2.15 % (3252236)------------------------------
% 8.13/2.15 % (3252236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252236)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252236)Termination reason: Instruction limit
% 8.13/2.15 % (3252236)Termination phase: Saturation
% 8.13/2.15 % (3252236)Time elapsed: 0.039 s
% 8.13/2.15 % (3252236)Peak memory usage: 89 MB
% 8.13/2.15 % (3252236)Instructions burned: 117 (million)
% 8.13/2.15 % (3252232)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=3194900370:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.13/2.15 % (3252238)dis-21_1_sil=8000:lcm=predicate:random_seed=3322080839: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)
% 8.13/2.15 % (3252233)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2928242969:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.13/2.15 % (3252235)lrs+10_1_sil=8000:sp=occurrence:random_seed=4206351867:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.13/2.15 % (3252237)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=869773862:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.13/2.15 % (3252234)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=965437408:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.13/2.15 % (3252238)Instruction limit reached!
% 8.13/2.15 % (3252238)------------------------------
% 8.13/2.15 % (3252238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252238)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252238)Termination reason: Instruction limit
% 8.13/2.15 % (3252238)Termination phase: Saturation
% 8.13/2.15 % (3252238)Time elapsed: 0.057 s
% 8.13/2.15 % (3252238)Peak memory usage: 89 MB
% 8.13/2.15 % (3252238)Instructions burned: 117 (million)
% 8.13/2.15 % (3252235)Instruction limit reached!
% 8.13/2.15 % (3252235)------------------------------
% 8.13/2.15 % (3252235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252235)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252235)Termination reason: Instruction limit
% 8.13/2.15 % (3252235)Termination phase: Saturation
% 8.13/2.15 % (3252235)Time elapsed: 0.068 s
% 8.13/2.15 % (3252235)Peak memory usage: 89 MB
% 8.13/2.15 % (3252235)Instructions burned: 108 (million)
% 8.13/2.15 % (3252240)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=1508555472:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 8.13/2.15 % (3252240)Refutation not found, incomplete strategy
% 8.13/2.15 % (3252240)------------------------------
% 8.13/2.15 % (3252240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252240)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252240)Termination reason: Refutation not found, incomplete strategy
% 8.13/2.15 % (3252240)Time elapsed: 0.002 s
% 8.13/2.15 % (3252240)Peak memory usage: 88 MB
% 8.13/2.15 % (3252240)Instructions burned: 4 (million)
% 8.13/2.15 % (3252237)Instruction limit reached!
% 8.13/2.15 % (3252237)------------------------------
% 8.13/2.15 % (3252237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252237)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252237)Termination reason: Instruction limit
% 8.13/2.15 % (3252237)Termination phase: Saturation
% 8.13/2.15 % (3252237)Time elapsed: 0.135 s
% 8.13/2.15 % (3252237)Peak memory usage: 90 MB
% 8.13/2.15 % (3252237)Instructions burned: 180 (million)
% 8.13/2.15 % (3252247)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3954932733: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)
% 8.13/2.15 % (3252248)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3250548874:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.13/2.15 % (3252240)------------------------------
% 8.13/2.15 % (3252240)------------------------------
% 8.13/2.15 % (3252250)lrs+10_64_to=lpo:sil=8000:random_seed=299282566:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 8.13/2.15 % (3252247)Instruction limit reached!
% 8.13/2.15 % (3252247)------------------------------
% 8.13/2.15 % (3252247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252247)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252247)Termination reason: Instruction limit
% 8.13/2.15 % (3252247)Termination phase: Saturation
% 8.13/2.15 % (3252247)Time elapsed: 0.090 s
% 8.13/2.15 % (3252247)Peak memory usage: 90 MB
% 8.13/2.15 % (3252247)Instructions burned: 190 (million)
% 8.13/2.15 % (3252248)Refutation not found, incomplete strategy
% 8.13/2.15 % (3252248)------------------------------
% 8.13/2.15 % (3252248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252248)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252248)Termination reason: Refutation not found, incomplete strategy
% 8.13/2.15 % (3252248)Time elapsed: 0.093 s
% 8.13/2.15 % (3252248)Peak memory usage: 89 MB
% 8.13/2.15 % (3252248)Instructions burned: 138 (million)
% 8.13/2.15 % (3252250)Instruction limit reached!
% 8.13/2.15 % (3252250)------------------------------
% 8.13/2.15 % (3252250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252250)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252250)Termination reason: Instruction limit
% 8.13/2.15 % (3252250)Termination phase: Saturation
% 8.13/2.15 % (3252250)Time elapsed: 0.080 s
% 8.13/2.15 % (3252250)Peak memory usage: 90 MB
% 8.13/2.15 % (3252250)Instructions burned: 126 (million)
% 8.13/2.15 % (3252253)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2296594895:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 8.13/2.15 % (3252253)Instruction limit reached!
% 8.13/2.15 % (3252253)------------------------------
% 8.13/2.15 % (3252253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252253)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252253)Termination reason: Instruction limit
% 8.13/2.15 % (3252253)Termination phase: Saturation
% 8.13/2.15 % (3252253)Time elapsed: 0.051 s
% 8.13/2.15 % (3252253)Peak memory usage: 89 MB
% 8.13/2.15 % (3252253)Instructions burned: 195 (million)
% 8.13/2.15 % (3252255)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1142828644:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 8.13/2.15 % (3252256)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=662461397:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 8.13/2.15 % (3252258)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=2781165091:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 8.13/2.15 % (3252255)Instruction limit reached!
% 8.13/2.15 % (3252255)------------------------------
% 8.13/2.15 % (3252255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252255)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252255)Termination reason: Instruction limit
% 8.13/2.15 % (3252255)Termination phase: Saturation
% 8.13/2.15 % (3252255)Time elapsed: 0.114 s
% 8.13/2.15 % (3252255)Peak memory usage: 91 MB
% 8.13/2.15 % (3252255)Instructions burned: 158 (million)
% 8.13/2.15 % (3252248)------------------------------
% 8.13/2.15 % (3252248)------------------------------
% 8.13/2.15 % (3252258)Instruction limit reached!
% 8.13/2.15 % (3252258)------------------------------
% 8.13/2.15 % (3252258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252258)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252258)Termination reason: Instruction limit
% 8.13/2.15 % (3252258)Termination phase: Saturation
% 8.13/2.15 % (3252258)Time elapsed: 0.037 s
% 8.13/2.15 % (3252258)Peak memory usage: 89 MB
% 8.13/2.15 % (3252258)Instructions burned: 108 (million)
% 8.13/2.15 % (3252264)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2194098716:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 8.13/2.15 % (3252262)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=4144058187:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 8.13/2.15 % (3252263)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=15573658:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 8.13/2.15 % (3252262)Instruction limit reached!
% 8.13/2.15 % (3252262)------------------------------
% 8.13/2.15 % (3252262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252262)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252262)Termination reason: Instruction limit
% 8.13/2.15 % (3252262)Termination phase: Saturation
% 8.13/2.15 % (3252262)Time elapsed: 0.073 s
% 8.13/2.15 % (3252262)Peak memory usage: 89 MB
% 8.13/2.15 % (3252262)Instructions burned: 108 (million)
% 8.13/2.15 % (3252263)Instruction limit reached!
% 8.13/2.15 % (3252263)------------------------------
% 8.13/2.15 % (3252263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252263)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252263)Termination reason: Instruction limit
% 8.13/2.15 % (3252263)Termination phase: Saturation
% 8.13/2.15 % (3252263)Time elapsed: 0.140 s
% 8.13/2.15 % (3252263)Peak memory usage: 91 MB
% 8.13/2.15 % (3252263)Instructions burned: 243 (million)
% 8.13/2.15 % (3252232)First to succeed.
% 8.13/2.15 % (3252232)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3252227"
% 8.13/2.15 % (3252268)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1593616659:i=134:sd=2:doe=on:ss=axioms:sgt=14_2990 on theBenchmark for (2990ds/134Mi)
% 8.13/2.15 % (3252269)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=1889818982:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 8.13/2.15 % (3252268)Instruction limit reached!
% 8.13/2.15 % (3252268)------------------------------
% 8.13/2.15 % (3252268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.13/2.15 % (3252268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.13/2.15 % (3252268)CaDiCaL version: 2.1.3
% 8.13/2.15 % (3252268)Termination reason: Instruction limit
% 8.13/2.15 % (3252268)Termination phase: Saturation
% 8.13/2.15 % (3252268)Time elapsed: 0.093 s
% 8.13/2.15 % (3252268)Peak memory usage: 89 MB
% 8.13/2.15 % (3252268)Instructions burned: 135 (million)
% 8.13/2.15 % (3252232)Refutation found. Thanks to Tanya!
% 8.13/2.15 % SZS status Unsatisfiable for theBenchmark
% 8.13/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 9.78/2.35 % (3252232)------------------------------
% 9.78/2.35 % (3252232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.35 % (3252232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.35 % (3252232)CaDiCaL version: 2.1.3
% 9.78/2.35 % (3252232)Termination reason: Refutation
% 9.78/2.35 % (3252232)Time elapsed: 0.860 s
% 9.78/2.35 % (3252232)Peak memory usage: 130 MB
% 9.78/2.35 % (3252232)Instructions burned: 1277 (million)
% 9.78/2.35 % (3252232)------------------------------
% 9.78/2.35 % (3252232)------------------------------
% 9.78/2.35 % (3252227)Success in time 1.301 s
% 9.78/2.35 % Vampire exiting
%------------------------------------------------------------------------------