%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET306-6 : 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 : n002.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 12:40:44 PM UTC 2026
% Result : Unsatisfiable 8.50s 22.55s
% Output : Refutation 9.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 29
% Syntax : Number of formulae : 102 ( 31 unt; 7 def)
% Number of atoms : 272 ( 37 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 332 ( 162 ~; 167 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 171 ( 0 sgn 171 !; 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(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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
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(f38,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(ordered_pair(X0,X1),X2),X3)
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X0),X2),flip(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
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,
range_of(universal_class) != universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_range_of_universal_class_1) ).
fof(f123,plain,
universal_class != range_of(universal_class),
inference(reorient_equations,[],[f122]) ).
fof(f125,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
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(f145,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(f149,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f38,f128,f128,f128,f128,f128,f128]) ).
fof(f186,plain,
universal_class != domain_of(domain_of(flip(cross_product(universal_class,universal_class)))),
inference(definition_unfolding,[],[f123,f125]) ).
fof(f191,definition,
sF0 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f192,plain,
cross_product(universal_class,universal_class) = sF0,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF1 = flip(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f194,plain,
flip(sF0) = sF1,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF2 = domain_of(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f196,plain,
domain_of(sF1) = sF2,
inference(reorient_equations,[],[f195]) ).
fof(f197,definition,
sF3 = domain_of(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f198,plain,
domain_of(sF2) = sF3,
inference(reorient_equations,[],[f197]) ).
fof(f199,plain,
universal_class != sF3,
inference(definition_folding,[],[f186,f198,f196,f194,f192]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(sF0,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3)) ),
inference(backward_demodulation,[],[f149,f192]) ).
fof(f223,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f250,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,f145]) ).
fof(f265,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f223,f3]) ).
fof(f273,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f265]) ).
fof(f310,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f273,f70]) ).
fof(f312,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f310,f7]) ).
fof(f313,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f312]) ).
fof(f315,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f313,f273]) ).
fof(f324,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(superposition,[],[f22,f315]) ).
fof(f333,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f324,f24]) ).
fof(f336,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[],[f333,f324]) ).
fof(f554,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),flip(X3))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),sF0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X0,X0))),X3)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f139,f212]) ).
fof(f556,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,unordered_pair(X2,X2))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),null_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| member(X2,domain_of(X3)) ),
inference(resolution,[],[f139,f250]) ).
fof(f559,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f139,f192]) ).
fof(f560,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3)
| ~ member(X1,unordered_pair(X2,X2))
| ~ member(X0,universal_class)
| ~ member(X2,universal_class)
| member(X2,domain_of(X3)) ),
inference(forward_subsumption_resolution,[],[f556,f336]) ).
fof(f580,definition,
( spl4_11
<=> ! [X2] : ~ member(X2,universal_class) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f581,plain,
( ! [X2] : ~ member(X2,universal_class)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f588,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X4,X4))
| ~ member(X2,universal_class)
| ~ member(X4,universal_class)
| member(X4,domain_of(flip(X3))) ),
inference(resolution,[],[f554,f560]) ).
fof(f591,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X4,X4))
| ~ member(X4,universal_class)
| member(X4,domain_of(flip(X3))) ),
inference(duplicate_literal_removal,[],[f588]) ).
fof(f602,plain,
( universal_class = null_class
| ~ spl4_11 ),
inference(resolution,[],[f581,f68]) ).
fof(f610,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),null_class)
| ~ spl4_11 ),
inference(backward_demodulation,[],[f11,f602]) ).
fof(f735,plain,
( $false
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f610,f336]) ).
fof(f736,plain,
~ spl4_11,
inference(avatar_contradiction_clause,[],[f735]) ).
fof(f989,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class)
| member(X3,domain_of(flip(sF0))) ),
inference(resolution,[],[f559,f591]) ).
fof(f992,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class)
| member(X3,domain_of(flip(sF0))) ),
inference(duplicate_literal_removal,[],[f989]) ).
fof(f999,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class)
| member(X3,domain_of(flip(sF0))) ),
inference(forward_subsumption_resolution,[],[f992,f11]) ).
fof(f1002,plain,
! [X2,X3,X0,X1] :
( member(X3,domain_of(sF1))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class) ),
inference(forward_demodulation,[],[f999,f194]) ).
fof(f1005,plain,
! [X2,X3,X0,X1] :
( member(X3,sF2)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class) ),
inference(forward_demodulation,[],[f1002,f196]) ).
fof(f1015,definition,
( spl4_17
<=> ! [X2,X1,X3] :
( member(X3,sF2)
| ~ member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0) ) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f1016,plain,
( ! [X2,X3,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))
| ~ member(X3,universal_class)
| member(X3,sF2)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1017,plain,
( spl4_11
| spl4_17 ),
inference(avatar_split_clause,[],[f1005,f1015,f580]) ).
fof(f1019,plain,
( ! [X0,X1] :
( ~ 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))),sF2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl4_17 ),
inference(resolution,[],[f1016,f10]) ).
fof(f1023,plain,
( ! [X0,X1] :
( ~ 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))),sF2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0) )
| ~ spl4_17 ),
inference(duplicate_literal_removal,[],[f1019]) ).
fof(f1027,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0) )
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f1023,f11]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| ~ member(X0,unordered_pair(X2,X2))
| ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| member(X2,domain_of(sF2)) )
| ~ spl4_17 ),
inference(resolution,[],[f1027,f560]) ).
fof(f1033,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF0)
| member(X2,sF3)
| ~ member(X0,unordered_pair(X2,X2))
| ~ member(X1,universal_class)
| ~ member(X2,universal_class) )
| ~ spl4_17 ),
inference(forward_demodulation,[],[f1029,f198]) ).
fof(f1035,plain,
( ! [X2,X0,X1] :
( member(X0,sF3)
| ~ member(X1,unordered_pair(X0,X0))
| ~ member(X2,universal_class)
| ~ member(X0,universal_class)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) )
| ~ spl4_17 ),
inference(resolution,[],[f1033,f559]) ).
fof(f1039,plain,
( ! [X2,X0,X1] :
( member(X0,sF3)
| ~ member(X1,unordered_pair(X0,X0))
| ~ member(X2,universal_class)
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl4_17 ),
inference(duplicate_literal_removal,[],[f1035]) ).
fof(f1041,definition,
( spl4_18
<=> ! [X0,X1] :
( member(X0,sF3)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl4_18])],[avatar_definition]) ).
fof(f1042,plain,
( ! [X0,X1] :
( ~ member(X1,unordered_pair(X0,X0))
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| member(X0,sF3) )
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f1041]) ).
fof(f1043,plain,
( spl4_11
| spl4_18
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f1039,f1015,f1041,f580]) ).
fof(f1045,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,universal_class)
| member(X0,sF3)
| ~ member(X0,universal_class) )
| ~ spl4_18 ),
inference(resolution,[],[f1042,f10]) ).
fof(f1055,plain,
( ! [X0] :
( member(X0,sF3)
| ~ member(X0,universal_class) )
| ~ spl4_18 ),
inference(duplicate_literal_removal,[],[f1045]) ).
fof(f1059,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,sF3),universal_class)
| subclass(X0,sF3) )
| ~ spl4_18 ),
inference(resolution,[],[f1055,f3]) ).
fof(f1101,plain,
( ! [X0,X1] :
( subclass(X0,sF3)
| ~ member(not_subclass_element(X0,sF3),X1)
| ~ subclass(X1,universal_class) )
| ~ spl4_18 ),
inference(resolution,[],[f1059,f1]) ).
fof(f1105,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,sF3),X1)
| subclass(X0,sF3) )
| ~ spl4_18 ),
inference(forward_subsumption_resolution,[],[f1101,f4]) ).
fof(f1106,plain,
( ! [X0] :
( subclass(X0,sF3)
| subclass(X0,sF3) )
| ~ spl4_18 ),
inference(resolution,[],[f1105,f2]) ).
fof(f1119,plain,
( ! [X0] : subclass(X0,sF3)
| ~ spl4_18 ),
inference(duplicate_literal_removal,[],[f1106]) ).
fof(f1120,plain,
( ! [X0] :
( ~ subclass(sF3,X0)
| sF3 = X0 )
| ~ spl4_18 ),
inference(resolution,[],[f1119,f7]) ).
fof(f1132,plain,
( universal_class = sF3
| ~ spl4_18 ),
inference(resolution,[],[f1120,f4]) ).
fof(f1144,plain,
( $false
| ~ spl4_18 ),
inference(forward_subsumption_resolution,[],[f1132,f199]) ).
fof(f1145,plain,
~ spl4_18,
inference(avatar_contradiction_clause,[],[f1144]) ).
cnf(s10,plain,
~ spl4_11,
inference(sat_conversion,[],[f736]) ).
cnf(s19,plain,
( spl4_11
| spl4_17 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s20,plain,
( spl4_11
| ~ spl4_17
| spl4_18 ),
inference(sat_conversion,[],[f1043]) ).
cnf(s27,plain,
~ spl4_18,
inference(sat_conversion,[],[f1145]) ).
cnf(s28,plain,
( spl4_11
| ~ spl4_17 ),
inference(rat,[],[s20,s27]) ).
cnf(s29,plain,
~ spl4_17,
inference(rat,[],[s28,s10]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s19,s29,s10]) ).
fof(f1146,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET306-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/20.66 % Computer : n002.cluster.edu
% 0.15/20.66 % Model : x86_64 x86_64
% 0.15/20.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/20.66 % Memory : 8046.5625MB
% 0.15/20.66 % OS : Linux 6.8.0-71-generic
% 0.15/20.66 % CPULimit : 300
% 0.15/20.66 % WCLimit : 300
% 0.15/20.66 % DateTime : Mon Sep 28 01:26:30 UTC 2026
% 0.15/20.66 % CPUTime :
% 0.15/20.66 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/20.72 Running first-order theorem proving
% 0.20/20.72 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
% 8.50/22.54 % (4071534)Input is clausal, will run a generic CNF schedule.
% 8.50/22.54 % (4071545)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1336917769:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.50/22.54 % (4071547)dis-21_1_sil=8000:lcm=predicate:random_seed=352542880: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)
% 8.50/22.54 % (4071545)Instruction limit reached!
% 8.50/22.54 % (4071545)------------------------------
% 8.50/22.54 % (4071545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071545)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071545)Termination reason: Instruction limit
% 8.50/22.54 % (4071545)Termination phase: Saturation
% 8.50/22.54 % (4071545)Time elapsed: 0.061 s
% 8.50/22.54 % (4071545)Peak memory usage: 88 MB
% 8.50/22.54 % (4071545)Instructions burned: 114 (million)
% 8.50/22.54 % (4071546)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1729308411:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.50/22.54 % (4071544)lrs+10_1_sil=8000:sp=occurrence:random_seed=569427137:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.50/22.54 % (4071541)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=3655312029:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.50/22.54 % (4071542)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3813039109:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.50/22.54 % (4071543)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1684970946:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.50/22.54 % (4071544)Refutation not found, incomplete strategy
% 8.50/22.54 % (4071544)------------------------------
% 8.50/22.54 % (4071544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071544)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071544)Termination reason: Refutation not found, incomplete strategy
% 8.50/22.54 % (4071544)Time elapsed: 0.002 s
% 8.50/22.54 % (4071544)Peak memory usage: 87 MB
% 8.50/22.54 % (4071547)Instruction limit reached!
% 8.50/22.54 % (4071547)------------------------------
% 8.50/22.54 % (4071547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071547)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071547)Termination reason: Instruction limit
% 8.50/22.54 % (4071547)Termination phase: Saturation
% 8.50/22.54 % (4071547)Time elapsed: 0.111 s
% 8.50/22.54 % (4071547)Peak memory usage: 89 MB
% 8.50/22.54 % (4071547)Instructions burned: 117 (million)
% 8.50/22.54 % (4071555)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=3857427907:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 8.50/22.54 % (4071555)Refutation not found, incomplete strategy
% 8.50/22.54 % (4071555)------------------------------
% 8.50/22.54 % (4071555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071555)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071555)Termination reason: Refutation not found, incomplete strategy
% 8.50/22.54 % (4071555)Time elapsed: 0.004 s
% 8.50/22.54 % (4071555)Peak memory usage: 88 MB
% 8.50/22.54 % (4071555)Instructions burned: 3 (million)
% 8.50/22.54 % (4071556)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2727898035: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)
% 8.50/22.54 % (4071546)Instruction limit reached!
% 8.50/22.54 % (4071546)------------------------------
% 8.50/22.54 % (4071546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071546)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071546)Termination reason: Instruction limit
% 8.50/22.54 % (4071546)Termination phase: Saturation
% 8.50/22.54 % (4071546)Time elapsed: 0.211 s
% 8.50/22.54 % (4071546)Peak memory usage: 90 MB
% 8.50/22.54 % (4071546)Instructions burned: 180 (million)
% 8.50/22.54 % (4071556)Instruction limit reached!
% 8.50/22.54 % (4071556)------------------------------
% 8.50/22.54 % (4071556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071556)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071556)Termination reason: Instruction limit
% 8.50/22.54 % (4071556)Termination phase: Saturation
% 8.50/22.54 % (4071556)Time elapsed: 0.139 s
% 8.50/22.54 % (4071556)Peak memory usage: 90 MB
% 8.50/22.54 % (4071556)Instructions burned: 190 (million)
% 8.50/22.54 % (4071544)------------------------------
% 8.50/22.54 % (4071544)------------------------------
% 8.50/22.54 % (4071559)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1245191631:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 8.50/22.54 % (4071559)Refutation not found, incomplete strategy
% 8.50/22.54 % (4071559)------------------------------
% 8.50/22.54 % (4071559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071559)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071559)Termination reason: Refutation not found, incomplete strategy
% 8.50/22.54 % (4071559)Time elapsed: 0.005 s
% 8.50/22.54 % (4071559)Peak memory usage: 88 MB
% 8.50/22.54 % (4071559)Instructions burned: 3 (million)
% 8.50/22.54 % (4071560)lrs+10_64_to=lpo:sil=8000:random_seed=3186096133:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.50/22.54 % (4071555)------------------------------
% 8.50/22.54 % (4071555)------------------------------
% 8.50/22.54 % (4071561)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3227870619:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 8.50/22.54 % (4071560)Instruction limit reached!
% 8.50/22.54 % (4071560)------------------------------
% 8.50/22.54 % (4071560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071560)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071560)Termination reason: Instruction limit
% 8.50/22.54 % (4071560)Termination phase: Saturation
% 8.50/22.54 % (4071560)Time elapsed: 0.132 s
% 8.50/22.54 % (4071560)Peak memory usage: 89 MB
% 8.50/22.54 % (4071560)Instructions burned: 126 (million)
% 8.50/22.54 % (4071564)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2959061974:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 8.50/22.54 % (4071543)First to succeed.
% 8.50/22.54 % (4071561)Instruction limit reached!
% 8.50/22.54 % (4071561)------------------------------
% 8.50/22.54 % (4071561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.54 % (4071561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.54 % (4071561)CaDiCaL version: 2.1.3
% 8.50/22.54 % (4071561)Termination reason: Instruction limit
% 8.50/22.54 % (4071561)Termination phase: Saturation
% 8.50/22.54 % (4071561)Time elapsed: 0.194 s
% 8.50/22.54 % (4071561)Peak memory usage: 89 MB
% 8.50/22.54 % (4071561)Instructions burned: 194 (million)
% 8.50/22.54 % (4071543)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4071534"
% 8.50/22.55 % (4071559)------------------------------
% 8.50/22.55 % (4071559)------------------------------
% 8.50/22.55 % (4071566)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3994952460:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 8.50/22.55 % (4071564)Instruction limit reached!
% 8.50/22.55 % (4071564)------------------------------
% 8.50/22.55 % (4071564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/22.55 % (4071564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/22.55 % (4071564)CaDiCaL version: 2.1.3
% 8.50/22.55 % (4071564)Termination reason: Instruction limit
% 8.50/22.55 % (4071564)Termination phase: Saturation
% 8.50/22.55 % (4071564)Time elapsed: 0.173 s
% 8.50/22.55 % (4071564)Peak memory usage: 91 MB
% 8.50/22.55 % (4071564)Instructions burned: 157 (million)
% 8.50/22.55 % (4071568)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=1371163746:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2989 on theBenchmark for (2989ds/106Mi)
% 8.50/22.55 % (4071543)Refutation found. Thanks to Tanya!
% 8.50/22.55 % SZS status Unsatisfiable for theBenchmark
% 8.50/22.55 % SZS output start Proof for theBenchmark
% See solution above
% 9.88/22.83 % (4071543)------------------------------
% 9.88/22.83 % (4071543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/22.83 % (4071543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/22.83 % (4071543)CaDiCaL version: 2.1.3
% 9.88/22.83 % (4071543)Termination reason: Refutation
% 9.88/22.83 % (4071543)Time elapsed: 0.813 s
% 9.88/22.83 % (4071543)Peak memory usage: 132 MB
% 9.88/22.83 % (4071543)Instructions burned: 1195 (million)
% 9.88/22.83 % (4071543)------------------------------
% 9.88/22.83 % (4071543)------------------------------
% 9.88/22.83 % (4071534)Success in time 1.281 s
% 9.88/22.83 % Vampire exiting
%------------------------------------------------------------------------------