%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET288-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:40:42 PM UTC 2026
% Result : Unsatisfiable 9.37s 2.18s
% Output : Refutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 29
% Syntax : Number of formulae : 100 ( 32 unt; 5 def)
% Number of atoms : 268 ( 37 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 330 ( 162 ~; 167 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 162 ( 0 sgn 162 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,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(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(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
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(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
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(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(f122,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_property9_1) ).
fof(f123,negated_conjecture,
domain_of(intersection(complement(y),x)) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_property9_2) ).
fof(f124,plain,
null_class = domain_of(intersection(complement(y),x)),
inference(reorient_equations,[],[f123]) ).
fof(f125,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_property9_3) ).
fof(f130,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(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f130]) ).
fof(f140,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,f130]) ).
fof(f141,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,f130]) ).
fof(f142,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f130]) ).
fof(f146,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(f147,plain,
! [X0,X1] :
( null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class)
| member(X0,domain_of(X1)) ),
inference(definition_unfolding,[],[f32,f28,f12]) ).
fof(f192,definition,
sF0 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f193,plain,
cross_product(universal_class,universal_class) = sF0,
inference(reorient_equations,[],[f192]) ).
fof(f194,plain,
subclass(x,sF0),
inference(definition_folding,[],[f122,f193]) ).
fof(f195,definition,
sF1 = complement(y),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f196,plain,
complement(y) = sF1,
inference(reorient_equations,[],[f195]) ).
fof(f197,definition,
sF2 = intersection(sF1,x),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f198,plain,
intersection(sF1,x) = sF2,
inference(reorient_equations,[],[f197]) ).
fof(f199,definition,
sF3 = domain_of(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f200,plain,
domain_of(sF2) = sF3,
inference(reorient_equations,[],[f199]) ).
fof(f201,plain,
null_class = sF3,
inference(definition_folding,[],[f124,f200,f198,f196]) ).
fof(f222,plain,
null_class = domain_of(sF2),
inference(forward_demodulation,[],[f200,f201]) ).
fof(f226,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f232,plain,
! [X0] :
( member(X0,sF1)
| ~ member(X0,universal_class)
| member(X0,y) ),
inference(superposition,[],[f25,f196]) ).
fof(f280,plain,
! [X0] :
( member(X0,sF2)
| ~ member(X0,x)
| ~ member(X0,sF1) ),
inference(superposition,[],[f23,f198]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(unordered_pair(X2,X2),universal_class))
| member(X0,null_class)
| ~ member(X0,X1)
| ~ member(X2,universal_class)
| member(X2,domain_of(X1)) ),
inference(superposition,[],[f23,f147]) ).
fof(f297,definition,
( spl4_6
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f298,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f330,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f226,f3]) ).
fof(f339,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f330]) ).
fof(f621,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f339,f70]) ).
fof(f625,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f621,f7]) ).
fof(f627,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f625]) ).
fof(f629,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f627,f339]) ).
fof(f641,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f146,f629]) ).
fof(f642,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f641]) ).
fof(f673,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f68,f642]) ).
fof(f690,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_demodulation,[],[f642,f673]) ).
fof(f913,plain,
spl4_6,
inference(avatar_split_clause,[],[f690,f297]) ).
fof(f1185,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ member(X3,universal_class)
| member(X3,domain_of(X2))
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X3,X3)) ),
inference(resolution,[],[f285,f141]) ).
fof(f1188,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ member(X3,universal_class)
| member(X3,domain_of(X2))
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X3,X3)) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1185,f298]) ).
fof(f1335,plain,
( ! [X2,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))),sF1)
| ~ member(X2,universal_class)
| member(X2,domain_of(sF2))
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X2,X2)) )
| ~ spl4_6 ),
inference(resolution,[],[f280,f1188]) ).
fof(f1336,plain,
( ! [X2,X0,X1] :
( member(X2,null_class)
| ~ 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))),sF1)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X2,X2)) )
| ~ spl4_6 ),
inference(forward_demodulation,[],[f1335,f222]) ).
fof(f1345,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X2,X2)) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1336,f298]) ).
fof(f1385,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X2,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),y) )
| ~ spl4_6 ),
inference(resolution,[],[f1345,f232]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),y)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(X2,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f1385,f11]) ).
fof(f2065,plain,
( ! [X2,X3,X0,X1] :
( ~ member(first(X0),unordered_pair(X1,X1))
| ~ member(X1,universal_class)
| ~ member(second(X0),universal_class)
| member(X0,y)
| ~ member(X0,x)
| ~ member(X0,cross_product(X2,X3)) )
| ~ spl4_6 ),
inference(superposition,[],[f1388,f142]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( ~ member(first(X0),universal_class)
| ~ member(second(X0),universal_class)
| member(X0,y)
| ~ member(X0,x)
| ~ member(X0,cross_product(X1,X2))
| ~ member(first(X0),universal_class) )
| ~ spl4_6 ),
inference(resolution,[],[f2065,f10]) ).
fof(f2079,plain,
( ! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(second(X0),universal_class)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f2077]) ).
fof(f2088,plain,
( ! [X0] :
( ~ member(second(X0),universal_class)
| ~ member(X0,sF0)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class) )
| ~ spl4_6 ),
inference(superposition,[],[f2079,f193]) ).
fof(f2089,plain,
( ! [X0,X1] :
( ~ member(X0,sF0)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class)
| ~ member(second(X0),X1)
| ~ subclass(X1,universal_class) )
| ~ spl4_6 ),
inference(resolution,[],[f2088,f1]) ).
fof(f2090,plain,
( ! [X0,X1] :
( ~ member(second(X0),X1)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class)
| ~ member(X0,sF0) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f2089,f4]) ).
fof(f2179,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(first(X0),X1)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f139,f142]) ).
fof(f2193,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| member(first(X0),X1)
| ~ member(X0,sF0) ),
inference(superposition,[],[f2179,f193]) ).
fof(f2203,plain,
! [X0] :
( ~ member(X0,sF0)
| member(first(X0),universal_class)
| ~ member(X0,sF0) ),
inference(superposition,[],[f2193,f193]) ).
fof(f2204,plain,
! [X0] :
( member(first(X0),universal_class)
| ~ member(X0,sF0) ),
inference(duplicate_literal_removal,[],[f2203]) ).
fof(f2208,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(second(X0),X2)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f140,f142]) ).
fof(f2222,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X2,X1))
| member(second(X0),X1)
| ~ member(X0,sF0) ),
inference(superposition,[],[f2208,f193]) ).
fof(f2232,plain,
! [X0] :
( ~ member(X0,sF0)
| member(second(X0),universal_class)
| ~ member(X0,sF0) ),
inference(superposition,[],[f2222,f193]) ).
fof(f2233,plain,
! [X0] :
( member(second(X0),universal_class)
| ~ member(X0,sF0) ),
inference(duplicate_literal_removal,[],[f2232]) ).
fof(f2239,plain,
( ! [X0] :
( ~ member(X0,sF0)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class)
| ~ member(X0,sF0) )
| ~ spl4_6 ),
inference(resolution,[],[f2233,f2090]) ).
fof(f2240,plain,
( ! [X0] :
( ~ member(X0,sF0)
| member(X0,y)
| ~ member(X0,x)
| ~ member(first(X0),universal_class) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f2239]) ).
fof(f2244,plain,
( ! [X0] :
( member(X0,y)
| ~ member(X0,sF0)
| ~ member(X0,x) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f2240,f2204]) ).
fof(f2254,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,y),sF0)
| ~ member(not_subclass_element(X0,y),x)
| subclass(X0,y) )
| ~ spl4_6 ),
inference(resolution,[],[f2244,f3]) ).
fof(f2274,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,y),x)
| subclass(X0,y)
| ~ member(not_subclass_element(X0,y),X1)
| ~ subclass(X1,sF0) )
| ~ spl4_6 ),
inference(resolution,[],[f2254,f1]) ).
fof(f2331,plain,
( ! [X0] :
( subclass(x,y)
| ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,sF0)
| subclass(x,y) )
| ~ spl4_6 ),
inference(resolution,[],[f2274,f2]) ).
fof(f2338,plain,
( ! [X0] :
( subclass(x,y)
| ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,sF0) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f2331]) ).
fof(f2339,plain,
( ! [X0] :
( ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,sF0) )
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f2338,f125]) ).
fof(f2340,plain,
( ~ subclass(x,sF0)
| subclass(x,y)
| ~ spl4_6 ),
inference(resolution,[],[f2339,f2]) ).
fof(f2438,plain,
( subclass(x,y)
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f2340,f194]) ).
fof(f2440,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f2438,f125]) ).
fof(f2441,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f2440]) ).
cnf(s21,plain,
spl4_6,
inference(sat_conversion,[],[f913]) ).
cnf(s88,plain,
~ spl4_6,
inference(sat_conversion,[],[f2441]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s21,s88]) ).
fof(f2442,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET288-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 01:20:27 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 9.37/2.18 % (1102512)Input is clausal, will run a generic CNF schedule.
% 9.37/2.18 % (1102518)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=645533597:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.37/2.18 % (1102519)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3039100028:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.37/2.18 % (1102522)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=43335518:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.37/2.18 % (1102520)lrs+10_1_sil=8000:sp=occurrence:random_seed=2794096969:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.37/2.18 % (1102521)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1231423486:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.37/2.18 % (1102517)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=1388872916:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.37/2.18 % (1102520)Refutation not found, incomplete strategy
% 9.37/2.18 % (1102520)------------------------------
% 9.37/2.18 % (1102520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102520)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102520)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.18 % (1102520)Time elapsed: 0.002 s
% 9.37/2.18 % (1102520)Peak memory usage: 88 MB
% 9.37/2.18 % (1102520)Instructions burned: 1 (million)
% 9.37/2.18 % (1102523)dis-21_1_sil=8000:lcm=predicate:random_seed=958247923: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)
% 9.37/2.18 % (1102521)Instruction limit reached!
% 9.37/2.18 % (1102521)------------------------------
% 9.37/2.18 % (1102521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102521)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102521)Termination reason: Instruction limit
% 9.37/2.18 % (1102521)Termination phase: Saturation
% 9.37/2.18 % (1102521)Time elapsed: 0.069 s
% 9.37/2.18 % (1102521)Peak memory usage: 89 MB
% 9.37/2.18 % (1102521)Instructions burned: 115 (million)
% 9.37/2.18 % (1102523)Instruction limit reached!
% 9.37/2.18 % (1102523)------------------------------
% 9.37/2.18 % (1102523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102523)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102523)Termination reason: Instruction limit
% 9.37/2.18 % (1102523)Termination phase: Saturation
% 9.37/2.18 % (1102523)Time elapsed: 0.070 s
% 9.37/2.18 % (1102523)Peak memory usage: 89 MB
% 9.37/2.18 % (1102523)Instructions burned: 117 (million)
% 9.37/2.18 % (1102522)Instruction limit reached!
% 9.37/2.18 % (1102522)------------------------------
% 9.37/2.18 % (1102522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102522)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102522)Termination reason: Instruction limit
% 9.37/2.18 % (1102522)Termination phase: Saturation
% 9.37/2.18 % (1102522)Time elapsed: 0.137 s
% 9.37/2.18 % (1102522)Peak memory usage: 90 MB
% 9.37/2.18 % (1102522)Instructions burned: 181 (million)
% 9.37/2.18 % (1102531)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=2005317279:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 9.37/2.18 % (1102532)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2747867929: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)
% 9.37/2.18 % (1102520)------------------------------
% 9.37/2.18 % (1102520)------------------------------
% 9.37/2.18 % (1102533)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1511633957:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 9.37/2.18 % (1102533)Refutation not found, incomplete strategy
% 9.37/2.18 % (1102533)------------------------------
% 9.37/2.18 % (1102533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102533)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102533)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.18 % (1102533)Time elapsed: 0.004 s
% 9.37/2.18 % (1102533)Peak memory usage: 88 MB
% 9.37/2.18 % (1102533)Instructions burned: 5 (million)
% 9.37/2.18 % (1102531)Instruction limit reached!
% 9.37/2.18 % (1102531)------------------------------
% 9.37/2.18 % (1102531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102531)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102531)Termination reason: Instruction limit
% 9.37/2.18 % (1102531)Termination phase: Saturation
% 9.37/2.18 % (1102531)Time elapsed: 0.088 s
% 9.37/2.18 % (1102531)Peak memory usage: 89 MB
% 9.37/2.18 % (1102531)Instructions burned: 143 (million)
% 9.37/2.18 % (1102532)Instruction limit reached!
% 9.37/2.18 % (1102532)------------------------------
% 9.37/2.18 % (1102532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102532)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102532)Termination reason: Instruction limit
% 9.37/2.18 % (1102532)Termination phase: Saturation
% 9.37/2.18 % (1102532)Time elapsed: 0.096 s
% 9.37/2.18 % (1102532)Peak memory usage: 90 MB
% 9.37/2.18 % (1102532)Instructions burned: 191 (million)
% 9.37/2.18 % (1102536)lrs+10_64_to=lpo:sil=8000:random_seed=2146884627:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 9.37/2.18 % (1102538)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2860831403:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 9.37/2.18 % (1102539)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2688010887:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 9.37/2.18 % (1102536)Instruction limit reached!
% 9.37/2.18 % (1102536)------------------------------
% 9.37/2.18 % (1102536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102536)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102536)Termination reason: Instruction limit
% 9.37/2.18 % (1102536)Termination phase: Saturation
% 9.37/2.18 % (1102536)Time elapsed: 0.079 s
% 9.37/2.18 % (1102536)Peak memory usage: 89 MB
% 9.37/2.18 % (1102536)Instructions burned: 127 (million)
% 9.37/2.18 % (1102533)------------------------------
% 9.37/2.18 % (1102533)------------------------------
% 9.37/2.18 % (1102538)Instruction limit reached!
% 9.37/2.18 % (1102538)------------------------------
% 9.37/2.18 % (1102538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102538)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102538)Termination reason: Instruction limit
% 9.37/2.18 % (1102538)Termination phase: Saturation
% 9.37/2.18 % (1102538)Time elapsed: 0.120 s
% 9.37/2.18 % (1102538)Peak memory usage: 90 MB
% 9.37/2.18 % (1102538)Instructions burned: 194 (million)
% 9.37/2.18 % (1102539)Instruction limit reached!
% 9.37/2.18 % (1102539)------------------------------
% 9.37/2.18 % (1102539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102539)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102539)Termination reason: Instruction limit
% 9.37/2.18 % (1102539)Termination phase: Saturation
% 9.37/2.18 % (1102539)Time elapsed: 0.109 s
% 9.37/2.18 % (1102539)Peak memory usage: 91 MB
% 9.37/2.18 % (1102539)Instructions burned: 158 (million)
% 9.37/2.18 % (1102543)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2812145544:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 9.37/2.18 % (1102544)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=1602516735:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 9.37/2.18 % (1102546)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1806930792:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 9.37/2.18 % (1102545)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=683797110:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 9.37/2.18 % (1102544)Instruction limit reached!
% 9.37/2.18 % (1102544)------------------------------
% 9.37/2.18 % (1102544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102544)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102544)Termination reason: Instruction limit
% 9.37/2.18 % (1102544)Termination phase: Saturation
% 9.37/2.18 % (1102544)Time elapsed: 0.060 s
% 9.37/2.18 % (1102544)Peak memory usage: 89 MB
% 9.37/2.18 % (1102544)Instructions burned: 106 (million)
% 9.37/2.18 % (1102545)Instruction limit reached!
% 9.37/2.18 % (1102545)------------------------------
% 9.37/2.18 % (1102545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102545)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102545)Termination reason: Instruction limit
% 9.37/2.18 % (1102545)Termination phase: Saturation
% 9.37/2.18 % (1102545)Time elapsed: 0.071 s
% 9.37/2.18 % (1102545)Peak memory usage: 89 MB
% 9.37/2.18 % (1102545)Instructions burned: 107 (million)
% 9.37/2.18 % (1102546)Instruction limit reached!
% 9.37/2.18 % (1102546)------------------------------
% 9.37/2.18 % (1102546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102546)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102546)Termination reason: Instruction limit
% 9.37/2.18 % (1102546)Termination phase: Saturation
% 9.37/2.18 % (1102546)Time elapsed: 0.158 s
% 9.37/2.18 % (1102546)Peak memory usage: 91 MB
% 9.37/2.18 % (1102546)Instructions burned: 243 (million)
% 9.37/2.18 % (1102551)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2280293074:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 9.37/2.18 % (1102552)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=4000831522:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 9.37/2.18 % (1102519)First to succeed.
% 9.37/2.18 % (1102519)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1102512"
% 9.37/2.18 % (1102554)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2830487657:i=499:bd=all_2990 on theBenchmark for (2990ds/499Mi)
% 9.37/2.18 % (1102552)Instruction limit reached!
% 9.37/2.18 % (1102552)------------------------------
% 9.37/2.18 % (1102552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.18 % (1102552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.18 % (1102552)CaDiCaL version: 2.1.3
% 9.37/2.18 % (1102552)Termination reason: Instruction limit
% 9.37/2.18 % (1102552)Termination phase: Saturation
% 9.37/2.18 % (1102552)Time elapsed: 0.093 s
% 9.37/2.18 % (1102552)Peak memory usage: 90 MB
% 9.37/2.18 % (1102552)Instructions burned: 135 (million)
% 9.37/2.18 % (1102557)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=33249517:i=191:fgj=on:bd=all_2988 on theBenchmark for (2988ds/191Mi)
% 9.37/2.18 % (1102519)Refutation found. Thanks to Tanya!
% 9.37/2.18 % SZS status Unsatisfiable for theBenchmark
% 9.37/2.18 % SZS output start Proof for theBenchmark
% See solution above
% 10.00/2.40 % (1102519)------------------------------
% 10.00/2.40 % (1102519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.00/2.40 % (1102519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.00/2.40 % (1102519)CaDiCaL version: 2.1.3
% 10.00/2.40 % (1102519)Termination reason: Refutation
% 10.00/2.40 % (1102519)Time elapsed: 0.920 s
% 10.00/2.40 % (1102519)Peak memory usage: 133 MB
% 10.00/2.40 % (1102519)Instructions burned: 1397 (million)
% 10.00/2.40 % (1102519)------------------------------
% 10.00/2.40 % (1102519)------------------------------
% 10.00/2.40 % (1102512)Success in time 1.319 s
% 10.00/2.40 % Vampire exiting
%------------------------------------------------------------------------------