%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET535-6 : 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 : n020.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 12:41:07 PM UTC 2026
% Result : Unsatisfiable 11.17s 2.46s
% Output : Refutation 11.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 36
% Syntax : Number of formulae : 115 ( 53 unt; 12 def)
% Number of atoms : 236 ( 56 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 231 ( 110 ~; 119 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 16 con; 0-3 aty)
% Number of variables : 126 ( 0 sgn 126 !; 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
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(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(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/sandbox/benchmark/theBenchmark.p',element_relation3) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
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(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
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(f71,axiom,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
fof(f122,negated_conjecture,
member(y,image(xf,singleton(x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_application_property3_1) ).
fof(f123,negated_conjecture,
~ subclass(y,apply(xf,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_application_property3_2) ).
fof(f124,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f125,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f126,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f125,f28]) ).
fof(f127,plain,
! [X0,X1] : apply(X0,X1) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f71,f124,f126,f12]) ).
fof(f128,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(f139,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,f128]) ).
fof(f142,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,f128,f128]) ).
fof(f144,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(f145,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(f186,plain,
member(y,domain_of(domain_of(flip(cross_product(intersection(xf,cross_product(unordered_pair(x,x),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f122,f126,f12]) ).
fof(f187,plain,
~ subclass(y,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(xf,cross_product(unordered_pair(x,x),universal_class)),universal_class)))))))),
inference(definition_unfolding,[],[f123,f127]) ).
fof(f192,definition,
sF0 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f193,plain,
unordered_pair(x,x) = sF0,
inference(reorient_equations,[],[f192]) ).
fof(f194,definition,
sF1 = cross_product(sF0,universal_class),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f195,plain,
cross_product(sF0,universal_class) = sF1,
inference(reorient_equations,[],[f194]) ).
fof(f196,definition,
sF2 = intersection(xf,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f197,plain,
intersection(xf,sF1) = sF2,
inference(reorient_equations,[],[f196]) ).
fof(f198,definition,
sF3 = cross_product(sF2,universal_class),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f199,plain,
cross_product(sF2,universal_class) = sF3,
inference(reorient_equations,[],[f198]) ).
fof(f200,definition,
sF4 = flip(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f201,plain,
flip(sF3) = sF4,
inference(reorient_equations,[],[f200]) ).
fof(f202,definition,
sF5 = domain_of(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f203,plain,
domain_of(sF4) = sF5,
inference(reorient_equations,[],[f202]) ).
fof(f204,definition,
sF6 = domain_of(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f205,plain,
domain_of(sF5) = sF6,
inference(reorient_equations,[],[f204]) ).
fof(f206,plain,
member(y,sF6),
inference(definition_folding,[],[f186,f205,f203,f201,f199,f197,f195,f193]) ).
fof(f207,definition,
sF7 = cross_product(universal_class,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f208,plain,
cross_product(universal_class,sF6) = sF7,
inference(reorient_equations,[],[f207]) ).
fof(f209,definition,
sF8 = intersection(element_relation,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f210,plain,
intersection(element_relation,sF7) = sF8,
inference(reorient_equations,[],[f209]) ).
fof(f211,definition,
sF9 = domain_of(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f212,plain,
domain_of(sF8) = sF9,
inference(reorient_equations,[],[f211]) ).
fof(f213,plain,
~ subclass(y,sF9),
inference(definition_folding,[],[f187,f212,f210,f208,f205,f203,f201,f199,f197,f195,f193]) ).
fof(f216,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f263,plain,
! [X0] :
( ~ member(X0,sF7)
| member(X0,sF8)
| ~ member(X0,element_relation) ),
inference(superposition,[],[f23,f210]) ).
fof(f295,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X0,X1),X2)
| member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0) ),
inference(resolution,[],[f1,f23]) ).
fof(f296,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f297,plain,
! [X0] :
( ~ subclass(sF6,X0)
| member(y,X0) ),
inference(resolution,[],[f1,f206]) ).
fof(f300,plain,
member(y,universal_class),
inference(resolution,[],[f297,f4]) ).
fof(f319,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF7)
| ~ member(X1,sF6)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f139,f208]) ).
fof(f323,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))),sF8)
| ~ member(X0,sF6) ),
inference(resolution,[],[f319,f263]) ).
fof(f393,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,domain_of(X0)),universal_class)
| null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
| subclass(X1,domain_of(X0)) ),
inference(resolution,[],[f145,f3]) ).
fof(f511,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f295,f4]) ).
fof(f522,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f511,f2]) ).
fof(f536,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f522,f2]) ).
fof(f543,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f536]) ).
fof(f763,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF9),universal_class)
| null_class = intersection(sF8,cross_product(unordered_pair(not_subclass_element(X0,sF9),not_subclass_element(X0,sF9)),universal_class))
| subclass(X0,sF9) ),
inference(superposition,[],[f393,f212]) ).
fof(f769,plain,
! [X0] :
( subclass(X0,sF9)
| null_class = intersection(sF8,cross_product(unordered_pair(not_subclass_element(X0,sF9),not_subclass_element(X0,sF9)),universal_class)) ),
inference(forward_subsumption_resolution,[],[f763,f543]) ).
fof(f773,plain,
null_class = intersection(sF8,cross_product(unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9)),universal_class)),
inference(resolution,[],[f769,f213]) ).
fof(f777,plain,
! [X0] :
( ~ member(X0,cross_product(unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9)),universal_class))
| member(X0,null_class)
| ~ member(X0,sF8) ),
inference(superposition,[],[f23,f773]) ).
fof(f788,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF8)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9))) ),
inference(resolution,[],[f777,f139]) ).
fof(f864,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f216,f3]) ).
fof(f893,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f864]) ).
fof(f1126,definition,
( spl10_47
<=> member(not_subclass_element(y,sF9),universal_class) ),
introduced(definition,[new_symbols(definition,[spl10_47])],[avatar_definition]) ).
fof(f1128,plain,
( ~ member(not_subclass_element(y,sF9),universal_class)
| spl10_47 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1737,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f893,f70]) ).
fof(f2680,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f1737,f7]) ).
fof(f2681,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f2680]) ).
fof(f2845,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f2681,f893]) ).
fof(f2869,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f144,f2845]) ).
fof(f2872,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f2869]) ).
fof(f2893,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f2872,f68]) ).
fof(f2901,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f2872,f2893]) ).
fof(f4517,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)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f142,f139]) ).
fof(f4526,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF8)
| ~ member(X1,sF6) ),
inference(resolution,[],[f4517,f323]) ).
fof(f4540,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF8)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X0,X1)
| ~ member(X1,sF6) ),
inference(duplicate_literal_removal,[],[f4526]) ).
fof(f4549,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| ~ member(X1,X0)
| ~ member(X0,sF6)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),null_class)
| ~ member(X0,universal_class)
| ~ member(X1,unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9))) ),
inference(resolution,[],[f4540,f788]) ).
fof(f4566,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| ~ member(X1,X0)
| ~ member(X0,sF6)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),null_class)
| ~ member(X1,unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9))) ),
inference(duplicate_literal_removal,[],[f4549]) ).
fof(f4574,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ member(X0,sF6)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),null_class)
| ~ member(X1,unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9))) ),
inference(forward_subsumption_resolution,[],[f4566,f511]) ).
fof(f4580,plain,
! [X0,X1] :
( ~ member(X1,unordered_pair(not_subclass_element(y,sF9),not_subclass_element(y,sF9)))
| ~ member(X1,X0)
| ~ member(X0,sF6)
| ~ member(X0,universal_class) ),
inference(forward_subsumption_resolution,[],[f4574,f2901]) ).
fof(f4661,plain,
! [X0] :
( ~ member(not_subclass_element(y,sF9),X0)
| ~ member(X0,sF6)
| ~ member(X0,universal_class)
| ~ member(not_subclass_element(y,sF9),universal_class) ),
inference(resolution,[],[f4580,f9]) ).
fof(f4682,definition,
( spl10_193
<=> ! [X0] :
( ~ member(not_subclass_element(y,sF9),X0)
| ~ member(X0,universal_class)
| ~ member(X0,sF6) ) ),
introduced(definition,[new_symbols(definition,[spl10_193])],[avatar_definition]) ).
fof(f4683,plain,
( ! [X0] :
( ~ member(not_subclass_element(y,sF9),X0)
| ~ member(X0,universal_class)
| ~ member(X0,sF6) )
| ~ spl10_193 ),
inference(avatar_component_clause,[],[f4682]) ).
fof(f4686,plain,
( ~ spl10_47
| spl10_193 ),
inference(avatar_split_clause,[],[f4661,f4682,f1126]) ).
fof(f4688,plain,
( ~ subclass(y,universal_class)
| subclass(y,sF9)
| spl10_47 ),
inference(resolution,[],[f1128,f296]) ).
fof(f4689,plain,
( subclass(y,sF9)
| spl10_47 ),
inference(forward_subsumption_resolution,[],[f4688,f4]) ).
fof(f4692,plain,
( $false
| spl10_47 ),
inference(forward_subsumption_resolution,[],[f4689,f213]) ).
fof(f4693,plain,
spl10_47,
inference(avatar_contradiction_clause,[],[f4692]) ).
fof(f4747,plain,
( ~ member(y,universal_class)
| ~ member(y,sF6)
| subclass(y,sF9)
| ~ spl10_193 ),
inference(resolution,[],[f4683,f2]) ).
fof(f4763,plain,
( ~ member(y,sF6)
| subclass(y,sF9)
| ~ spl10_193 ),
inference(forward_subsumption_resolution,[],[f4747,f300]) ).
fof(f4769,plain,
( subclass(y,sF9)
| ~ spl10_193 ),
inference(forward_subsumption_resolution,[],[f4763,f206]) ).
fof(f4770,plain,
( $false
| ~ spl10_193 ),
inference(forward_subsumption_resolution,[],[f4769,f213]) ).
fof(f4771,plain,
~ spl10_193,
inference(avatar_contradiction_clause,[],[f4770]) ).
cnf(s201,plain,
( ~ spl10_47
| spl10_193 ),
inference(sat_conversion,[],[f4686]) ).
cnf(s203,plain,
spl10_47,
inference(sat_conversion,[],[f4693]) ).
cnf(s212,plain,
~ spl10_193,
inference(sat_conversion,[],[f4771]) ).
cnf(s213,plain,
$false,
inference(rat,[],[s201,s212,s203]) ).
fof(f4772,plain,
$false,
inference(avatar_sat_refutation,[],[s213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET535-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:07:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 11.17/2.44 % (3962974)Input is clausal, will run a generic CNF schedule.
% 11.17/2.44 % (3962980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1271839125:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 11.17/2.44 % (3962984)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=865481831:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 11.17/2.44 % (3962981)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2282640684:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 11.17/2.44 % (3962982)lrs+10_1_sil=8000:sp=occurrence:random_seed=3950284022:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 11.17/2.44 % (3962983)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3632777722:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 11.17/2.44 % (3962985)dis-21_1_sil=8000:lcm=predicate:random_seed=3581691740: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)
% 11.17/2.44 % (3962979)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=4272661137:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 11.17/2.44 % (3962985)Instruction limit reached!
% 11.17/2.44 % (3962985)------------------------------
% 11.17/2.44 % (3962985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.44 % (3962985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.44 % (3962985)CaDiCaL version: 2.1.3
% 11.17/2.44 % (3962985)Termination reason: Instruction limit
% 11.17/2.44 % (3962985)Termination phase: Saturation
% 11.17/2.44 % (3962985)Time elapsed: 0.059 s
% 11.17/2.44 % (3962985)Peak memory usage: 88 MB
% 11.17/2.44 % (3962985)Instructions burned: 117 (million)
% 11.17/2.44 % (3962983)Instruction limit reached!
% 11.17/2.44 % (3962983)------------------------------
% 11.17/2.44 % (3962983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.44 % (3962983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.44 % (3962983)CaDiCaL version: 2.1.3
% 11.17/2.44 % (3962983)Termination reason: Instruction limit
% 11.17/2.44 % (3962983)Termination phase: Saturation
% 11.17/2.44 % (3962983)Time elapsed: 0.067 s
% 11.17/2.44 % (3962983)Peak memory usage: 89 MB
% 11.17/2.44 % (3962983)Instructions burned: 116 (million)
% 11.17/2.44 % (3962982)Instruction limit reached!
% 11.17/2.44 % (3962982)------------------------------
% 11.17/2.44 % (3962982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.44 % (3962982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.44 % (3962982)CaDiCaL version: 2.1.3
% 11.17/2.44 % (3962982)Termination reason: Instruction limit
% 11.17/2.44 % (3962982)Termination phase: Saturation
% 11.17/2.44 % (3962982)Time elapsed: 0.070 s
% 11.17/2.44 % (3962982)Peak memory usage: 89 MB
% 11.17/2.44 % (3962982)Instructions burned: 108 (million)
% 11.17/2.44 % (3962984)Instruction limit reached!
% 11.17/2.44 % (3962984)------------------------------
% 11.17/2.44 % (3962984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.44 % (3962984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.44 % (3962984)CaDiCaL version: 2.1.3
% 11.17/2.44 % (3962984)Termination reason: Instruction limit
% 11.17/2.44 % (3962984)Termination phase: Saturation
% 11.17/2.44 % (3962984)Time elapsed: 0.135 s
% 11.17/2.44 % (3962984)Peak memory usage: 90 MB
% 11.17/2.44 % (3962984)Instructions burned: 180 (million)
% 11.17/2.44 % (3962993)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=1957216791:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 11.17/2.44 % (3962993)Refutation not found, incomplete strategy
% 11.17/2.44 % (3962993)------------------------------
% 11.17/2.44 % (3962993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.44 % (3962993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.44 % (3962993)CaDiCaL version: 2.1.3
% 11.17/2.44 % (3962993)Termination reason: Refutation not found, incomplete strategy
% 11.17/2.44 % (3962993)Time elapsed: 0.005 s
% 11.17/2.44 % (3962993)Peak memory usage: 88 MB
% 11.17/2.44 % (3962993)Instructions burned: 5 (million)
% 11.17/2.44 % (3962994)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3580176096: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)
% 11.17/2.46 % (3962995)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1711969480:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 11.17/2.46 % (3962995)Refutation not found, incomplete strategy
% 11.17/2.46 % (3962995)------------------------------
% 11.17/2.46 % (3962995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3962995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3962995)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3962995)Termination reason: Refutation not found, incomplete strategy
% 11.17/2.46 % (3962995)Time elapsed: 0.003 s
% 11.17/2.46 % (3962995)Peak memory usage: 87 MB
% 11.17/2.46 % (3962995)Instructions burned: 4 (million)
% 11.17/2.46 % (3962996)lrs+10_64_to=lpo:sil=8000:random_seed=477304136:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 11.17/2.46 % (3962994)Instruction limit reached!
% 11.17/2.46 % (3962994)------------------------------
% 11.17/2.46 % (3962994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3962994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3962994)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3962994)Termination reason: Instruction limit
% 11.17/2.46 % (3962994)Termination phase: Saturation
% 11.17/2.46 % (3962994)Time elapsed: 0.102 s
% 11.17/2.46 % (3962994)Peak memory usage: 90 MB
% 11.17/2.46 % (3962994)Instructions burned: 189 (million)
% 11.17/2.46 % (3962996)Instruction limit reached!
% 11.17/2.46 % (3962996)------------------------------
% 11.17/2.46 % (3962996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3962996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3962996)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3962996)Termination reason: Instruction limit
% 11.17/2.46 % (3962996)Termination phase: Saturation
% 11.17/2.46 % (3962996)Time elapsed: 0.076 s
% 11.17/2.46 % (3962996)Peak memory usage: 90 MB
% 11.17/2.46 % (3962996)Instructions burned: 126 (million)
% 11.17/2.46 % (3962993)------------------------------
% 11.17/2.46 % (3962993)------------------------------
% 11.17/2.46 % (3962995)------------------------------
% 11.17/2.46 % (3962995)------------------------------
% 11.17/2.46 % (3963001)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4226386288:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 11.17/2.46 % (3963002)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=982551029:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 11.17/2.46 % (3963003)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3040919836:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 11.17/2.46 % (3963001)Instruction limit reached!
% 11.17/2.46 % (3963001)------------------------------
% 11.17/2.46 % (3963001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963001)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963001)Termination reason: Instruction limit
% 11.17/2.46 % (3963001)Termination phase: Saturation
% 11.17/2.46 % (3963001)Time elapsed: 0.128 s
% 11.17/2.46 % (3963001)Peak memory usage: 90 MB
% 11.17/2.46 % (3963001)Instructions burned: 194 (million)
% 11.17/2.46 % (3963004)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=1207372618:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 11.17/2.46 % (3963002)Instruction limit reached!
% 11.17/2.46 % (3963002)------------------------------
% 11.17/2.46 % (3963002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963002)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963002)Termination reason: Instruction limit
% 11.17/2.46 % (3963002)Termination phase: Saturation
% 11.17/2.46 % (3963002)Time elapsed: 0.106 s
% 11.17/2.46 % (3963002)Peak memory usage: 91 MB
% 11.17/2.46 % (3963002)Instructions burned: 157 (million)
% 11.17/2.46 % (3963004)Instruction limit reached!
% 11.17/2.46 % (3963004)------------------------------
% 11.17/2.46 % (3963004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963004)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963004)Termination reason: Instruction limit
% 11.17/2.46 % (3963004)Termination phase: Saturation
% 11.17/2.46 % (3963004)Time elapsed: 0.050 s
% 11.17/2.46 % (3963004)Peak memory usage: 93 MB
% 11.17/2.46 % (3963004)Instructions burned: 106 (million)
% 11.17/2.46 % (3963008)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1015747271:i=107_2991 on theBenchmark for (2991ds/107Mi)
% 11.17/2.46 % (3963010)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=411695374:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 11.17/2.46 % (3963008)Instruction limit reached!
% 11.17/2.46 % (3963008)------------------------------
% 11.17/2.46 % (3963008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963008)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963008)Termination reason: Instruction limit
% 11.17/2.46 % (3963008)Termination phase: Saturation
% 11.17/2.46 % (3963008)Time elapsed: 0.073 s
% 11.17/2.46 % (3963008)Peak memory usage: 89 MB
% 11.17/2.46 % (3963008)Instructions burned: 108 (million)
% 11.17/2.46 % (3963011)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3812462871:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 11.17/2.46 % (3963010)Instruction limit reached!
% 11.17/2.46 % (3963010)------------------------------
% 11.17/2.46 % (3963010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963010)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963010)Termination reason: Instruction limit
% 11.17/2.46 % (3963010)Termination phase: Saturation
% 11.17/2.46 % (3963010)Time elapsed: 0.167 s
% 11.17/2.46 % (3963010)Peak memory usage: 90 MB
% 11.17/2.46 % (3963010)Instructions burned: 243 (million)
% 11.17/2.46 % (3963015)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=373743928:i=134:sd=2:doe=on:ss=axioms:sgt=14_2989 on theBenchmark for (2989ds/134Mi)
% 11.17/2.46 % (3963015)Instruction limit reached!
% 11.17/2.46 % (3963015)------------------------------
% 11.17/2.46 % (3963015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963015)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963015)Termination reason: Instruction limit
% 11.17/2.46 % (3963015)Termination phase: Saturation
% 11.17/2.46 % (3963015)Time elapsed: 0.100 s
% 11.17/2.46 % (3963015)Peak memory usage: 90 MB
% 11.17/2.46 % (3963015)Instructions burned: 134 (million)
% 11.17/2.46 % (3963016)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=1080946850:i=499:bd=all_2988 on theBenchmark for (2988ds/499Mi)
% 11.17/2.46 % (3962979)First to succeed.
% 11.17/2.46 % (3962979)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3962974"
% 11.17/2.46 % (3963018)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=614337475:i=191:fgj=on:bd=all_2987 on theBenchmark for (2987ds/191Mi)
% 11.17/2.46 % (3963018)Instruction limit reached!
% 11.17/2.46 % (3963018)------------------------------
% 11.17/2.46 % (3963018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963018)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963018)Termination reason: Instruction limit
% 11.17/2.46 % (3963018)Termination phase: Saturation
% 11.17/2.46 % (3963018)Time elapsed: 0.110 s
% 11.17/2.46 % (3963018)Peak memory usage: 89 MB
% 11.17/2.46 % (3963018)Instructions burned: 191 (million)
% 11.17/2.46 % (3963016)Instruction limit reached!
% 11.17/2.46 % (3963016)------------------------------
% 11.17/2.46 % (3963016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.17/2.46 % (3963016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.17/2.46 % (3963016)CaDiCaL version: 2.1.3
% 11.17/2.46 % (3963016)Termination reason: Instruction limit
% 11.17/2.46 % (3963016)Termination phase: Saturation
% 11.17/2.46 % (3963016)Time elapsed: 0.287 s
% 11.17/2.46 % (3963016)Peak memory usage: 95 MB
% 11.17/2.46 % (3963016)Instructions burned: 499 (million)
% 11.17/2.46 % (3962979)Refutation found. Thanks to Tanya!
% 11.17/2.46 % SZS status Unsatisfiable for theBenchmark
% 11.17/2.46 % SZS output start Proof for theBenchmark
% See solution above
% 11.96/2.66 % (3962979)------------------------------
% 11.96/2.66 % (3962979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.66 % (3962979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.66 % (3962979)CaDiCaL version: 2.1.3
% 11.96/2.66 % (3962979)Termination reason: Refutation
% 11.96/2.66 % (3962979)Time elapsed: 1.176 s
% 11.96/2.66 % (3962979)Peak memory usage: 136 MB
% 11.96/2.66 % (3962979)Instructions burned: 1785 (million)
% 11.96/2.66 % (3962979)------------------------------
% 11.96/2.66 % (3962979)------------------------------
% 11.96/2.66 % (3962974)Success in time 1.613 s
% 11.96/2.66 % Vampire exiting
%------------------------------------------------------------------------------