%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET272-6 : 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 : n015.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 12:40:40 PM UTC 2026
% Result : Unsatisfiable 7.98s 1.96s
% Output : Refutation 9.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of formulae : 119 ( 27 unt; 6 def)
% Number of atoms : 303 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 358 ( 174 ~; 184 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-3 aty)
% Number of variables : 193 ( 193 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,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(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
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(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(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
restrict(xr,intersection(domain_of(xr),x),y) != restrict(xr,x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property3_1) ).
fof(f127,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f127]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f127]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f127]) ).
fof(f139,plain,
! [X2,X0,X1] :
( 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,f127]) ).
fof(f144,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(f185,plain,
intersection(xr,cross_product(intersection(domain_of(xr),x),y)) != intersection(xr,cross_product(x,y)),
inference(definition_unfolding,[],[f122,f28,f28]) ).
fof(f190,definition,
sF0 = domain_of(xr),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f191,plain,
domain_of(xr) = sF0,
inference(reorient_equations,[],[f190]) ).
fof(f192,definition,
sF1 = intersection(sF0,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f193,plain,
intersection(sF0,x) = sF1,
inference(reorient_equations,[],[f192]) ).
fof(f194,definition,
sF2 = cross_product(sF1,y),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f195,plain,
cross_product(sF1,y) = sF2,
inference(reorient_equations,[],[f194]) ).
fof(f196,definition,
sF3 = intersection(xr,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f197,plain,
intersection(xr,sF2) = sF3,
inference(reorient_equations,[],[f196]) ).
fof(f198,definition,
sF4 = cross_product(x,y),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f199,plain,
cross_product(x,y) = sF4,
inference(reorient_equations,[],[f198]) ).
fof(f200,definition,
sF5 = intersection(xr,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f201,plain,
intersection(xr,sF4) = sF5,
inference(reorient_equations,[],[f200]) ).
fof(f202,plain,
sF3 != sF5,
inference(definition_folding,[],[f185,f201,f199,f197,f195,f193,f191]) ).
fof(f204,plain,
! [X0] :
( member(X0,xr)
| ~ member(X0,sF5) ),
inference(superposition,[],[f21,f201]) ).
fof(f206,plain,
! [X0] :
( member(X0,sF4)
| ~ member(X0,sF5) ),
inference(superposition,[],[f22,f201]) ).
fof(f207,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f2,f22]) ).
fof(f208,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f2,f21]) ).
fof(f210,plain,
! [X0] :
( member(X0,x)
| ~ member(X0,sF1) ),
inference(superposition,[],[f22,f193]) ).
fof(f223,plain,
! [X0] :
( member(X0,sF3)
| ~ member(X0,sF2)
| ~ member(X0,xr) ),
inference(superposition,[],[f23,f197]) ).
fof(f224,plain,
! [X0] :
( member(X0,sF5)
| ~ member(X0,sF4)
| ~ member(X0,xr) ),
inference(superposition,[],[f23,f201]) ).
fof(f225,plain,
! [X0] :
( member(X0,sF1)
| ~ member(X0,x)
| ~ member(X0,sF0) ),
inference(superposition,[],[f23,f193]) ).
fof(f226,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF3),sF2)
| ~ member(not_subclass_element(X0,sF3),xr)
| subclass(X0,sF3) ),
inference(resolution,[],[f223,f3]) ).
fof(f239,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF5),sF4)
| ~ member(not_subclass_element(X0,sF5),xr)
| subclass(X0,sF5) ),
inference(resolution,[],[f224,f3]) ).
fof(f257,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(second(X0),X2)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f137,f139]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(first(X0),X1)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f136,f139]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X2,X1))
| member(second(X0),X1)
| ~ member(X0,sF4) ),
inference(superposition,[],[f257,f199]) ).
fof(f261,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X2,X1))
| member(second(X0),X1)
| ~ member(X0,sF2) ),
inference(superposition,[],[f257,f195]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| member(first(X0),X1)
| ~ member(X0,sF4) ),
inference(superposition,[],[f258,f199]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| member(first(X0),X1)
| ~ member(X0,sF2) ),
inference(superposition,[],[f258,f195]) ).
fof(f277,plain,
! [X0] :
( ~ member(X0,sF2)
| member(second(X0),y)
| ~ member(X0,sF2) ),
inference(superposition,[],[f261,f195]) ).
fof(f278,plain,
! [X0] :
( member(second(X0),y)
| ~ member(X0,sF2) ),
inference(duplicate_literal_removal,[],[f277]) ).
fof(f281,plain,
! [X0] :
( ~ member(X0,sF4)
| member(second(X0),y)
| ~ member(X0,sF4) ),
inference(superposition,[],[f260,f199]) ).
fof(f283,plain,
! [X0] :
( member(second(X0),y)
| ~ member(X0,sF4) ),
inference(duplicate_literal_removal,[],[f281]) ).
fof(f287,plain,
! [X0] :
( ~ member(X0,sF2)
| member(first(X0),sF1)
| ~ member(X0,sF2) ),
inference(superposition,[],[f264,f195]) ).
fof(f288,plain,
! [X0] :
( member(first(X0),sF1)
| ~ member(X0,sF2) ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f291,plain,
! [X0] :
( ~ member(X0,sF4)
| member(first(X0),x)
| ~ member(X0,sF4) ),
inference(superposition,[],[f263,f199]) ).
fof(f293,plain,
! [X0] :
( member(first(X0),x)
| ~ member(X0,sF4) ),
inference(duplicate_literal_removal,[],[f291]) ).
fof(f327,plain,
! [X2,X3,X0,X1,X4] :
( member(X0,cross_product(X1,X2))
| ~ member(second(X0),X2)
| ~ member(first(X0),X1)
| ~ member(X0,cross_product(X3,X4)) ),
inference(superposition,[],[f138,f139]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(second(X0),y)
| ~ member(first(X0),x)
| member(X0,sF4) ),
inference(superposition,[],[f327,f199]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(second(X0),y)
| ~ member(first(X0),sF1)
| member(X0,sF2) ),
inference(superposition,[],[f327,f195]) ).
fof(f395,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f208,f3]) ).
fof(f413,plain,
! [X0] :
( member(not_subclass_element(sF3,X0),xr)
| subclass(sF3,X0) ),
inference(superposition,[],[f208,f197]) ).
fof(f418,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f395]) ).
fof(f459,plain,
! [X0] :
( member(not_subclass_element(sF3,X0),sF2)
| subclass(sF3,X0) ),
inference(superposition,[],[f207,f197]) ).
fof(f483,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f418,f70]) ).
fof(f492,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f483,f7]) ).
fof(f493,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f492]) ).
fof(f494,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f493,f418]) ).
fof(f501,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(superposition,[],[f22,f494]) ).
fof(f515,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,f144]) ).
fof(f548,plain,
! [X0] :
( ~ member(X0,sF4)
| ~ member(second(X0),y)
| ~ member(first(X0),sF1)
| member(X0,sF2) ),
inference(superposition,[],[f340,f199]) ).
fof(f550,plain,
! [X0] :
( ~ member(first(X0),sF1)
| ~ member(X0,sF4)
| member(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f548,f283]) ).
fof(f553,plain,
! [X0] :
( ~ member(X0,sF4)
| member(X0,sF2)
| ~ member(first(X0),x)
| ~ member(first(X0),sF0) ),
inference(resolution,[],[f550,f225]) ).
fof(f556,plain,
! [X0] :
( ~ member(first(X0),sF0)
| member(X0,sF2)
| ~ member(X0,sF4) ),
inference(forward_subsumption_resolution,[],[f553,f293]) ).
fof(f567,plain,
! [X0] :
( ~ member(X0,sF2)
| ~ member(second(X0),y)
| ~ member(first(X0),x)
| member(X0,sF4) ),
inference(superposition,[],[f339,f195]) ).
fof(f568,plain,
! [X0] :
( ~ member(first(X0),x)
| ~ member(X0,sF2)
| member(X0,sF4) ),
inference(forward_subsumption_resolution,[],[f567,f278]) ).
fof(f572,plain,
! [X0] :
( ~ member(X0,sF2)
| member(X0,sF4)
| ~ member(first(X0),sF1) ),
inference(resolution,[],[f568,f210]) ).
fof(f576,plain,
! [X0] :
( member(X0,sF4)
| ~ member(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f572,f288]) ).
fof(f577,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF5),sF2)
| ~ member(not_subclass_element(X0,sF5),xr)
| subclass(X0,sF5) ),
inference(resolution,[],[f576,f239]) ).
fof(f581,plain,
( ~ member(not_subclass_element(sF3,sF5),xr)
| subclass(sF3,sF5)
| subclass(sF3,sF5) ),
inference(resolution,[],[f577,f459]) ).
fof(f590,plain,
( ~ member(not_subclass_element(sF3,sF5),xr)
| subclass(sF3,sF5) ),
inference(duplicate_literal_removal,[],[f581]) ).
fof(f601,plain,
subclass(sF3,sF5),
inference(forward_subsumption_resolution,[],[f590,f413]) ).
fof(f602,plain,
( ~ subclass(sF5,sF3)
| sF3 = sF5 ),
inference(resolution,[],[f601,f7]) ).
fof(f603,plain,
~ subclass(sF5,sF3),
inference(forward_subsumption_resolution,[],[f602,f202]) ).
fof(f635,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f501,f24]) ).
fof(f657,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[],[f635,f501]) ).
fof(f1195,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,[],[f515,f138]) ).
fof(f1202,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)) ),
inference(forward_subsumption_resolution,[],[f1195,f657]) ).
fof(f1217,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| member(X0,domain_of(xr))
| ~ member(X1,universal_class)
| ~ member(X2,unordered_pair(X0,X0))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF5) ),
inference(resolution,[],[f1202,f204]) ).
fof(f1221,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),sF5)
| ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| ~ member(X2,unordered_pair(X0,X0))
| member(X0,sF0) ),
inference(forward_demodulation,[],[f1217,f191]) ).
fof(f1718,plain,
! [X2,X3,X0,X1] :
( ~ member(first(X0),unordered_pair(X1,X1))
| ~ member(X1,universal_class)
| ~ member(second(X0),universal_class)
| ~ member(X0,sF5)
| member(X1,sF0)
| ~ member(X0,cross_product(X2,X3)) ),
inference(superposition,[],[f1221,f139]) ).
fof(f1853,plain,
! [X2,X0,X1] :
( ~ member(first(X0),universal_class)
| ~ member(second(X0),universal_class)
| ~ member(X0,sF5)
| member(first(X0),sF0)
| ~ member(X0,cross_product(X1,X2))
| ~ member(first(X0),universal_class) ),
inference(resolution,[],[f1718,f10]) ).
fof(f1857,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(second(X0),universal_class)
| ~ member(X0,sF5)
| member(first(X0),sF0)
| ~ member(first(X0),universal_class) ),
inference(duplicate_literal_removal,[],[f1853]) ).
fof(f1875,plain,
! [X0] :
( ~ member(X0,sF4)
| ~ member(second(X0),universal_class)
| ~ member(X0,sF5)
| member(first(X0),sF0)
| ~ member(first(X0),universal_class) ),
inference(superposition,[],[f1857,f199]) ).
fof(f1959,plain,
! [X0] :
( member(first(X0),sF0)
| ~ member(X0,sF5)
| ~ member(second(X0),universal_class)
| ~ member(first(X0),universal_class) ),
inference(forward_subsumption_resolution,[],[f1875,f206]) ).
fof(f2156,plain,
! [X0] :
( ~ member(X0,sF5)
| ~ member(second(X0),universal_class)
| ~ member(first(X0),universal_class)
| member(X0,sF2)
| ~ member(X0,sF4) ),
inference(resolution,[],[f1959,f556]) ).
fof(f2157,plain,
! [X0] :
( ~ member(second(X0),universal_class)
| ~ member(X0,sF5)
| ~ member(first(X0),universal_class)
| member(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f2156,f206]) ).
fof(f2203,plain,
! [X0,X1] :
( ~ member(X0,sF5)
| ~ member(first(X0),universal_class)
| member(X0,sF2)
| ~ member(second(X0),X1)
| ~ subclass(X1,universal_class) ),
inference(resolution,[],[f2157,f1]) ).
fof(f2204,plain,
! [X0,X1] :
( ~ member(second(X0),X1)
| ~ member(first(X0),universal_class)
| member(X0,sF2)
| ~ member(X0,sF5) ),
inference(forward_subsumption_resolution,[],[f2203,f4]) ).
fof(f2206,plain,
! [X0] :
( ~ member(first(X0),universal_class)
| member(X0,sF2)
| ~ member(X0,sF5)
| ~ member(X0,sF4) ),
inference(resolution,[],[f2204,f283]) ).
fof(f2223,plain,
! [X0] :
( ~ member(first(X0),universal_class)
| member(X0,sF2)
| ~ member(X0,sF5) ),
inference(forward_subsumption_resolution,[],[f2206,f206]) ).
fof(f2226,plain,
! [X0,X1] :
( member(X0,sF2)
| ~ member(X0,sF5)
| ~ member(first(X0),X1)
| ~ subclass(X1,universal_class) ),
inference(resolution,[],[f2223,f1]) ).
fof(f2227,plain,
! [X0,X1] :
( ~ member(first(X0),X1)
| ~ member(X0,sF5)
| member(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f2226,f4]) ).
fof(f2229,plain,
! [X0] :
( ~ member(X0,sF5)
| member(X0,sF2)
| ~ member(X0,sF4) ),
inference(resolution,[],[f2227,f293]) ).
fof(f2250,plain,
! [X0] :
( member(X0,sF2)
| ~ member(X0,sF5) ),
inference(forward_subsumption_resolution,[],[f2229,f206]) ).
fof(f2343,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF3),xr)
| subclass(X0,sF3)
| ~ member(not_subclass_element(X0,sF3),sF5) ),
inference(resolution,[],[f226,f2250]) ).
fof(f2352,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF3),sF5)
| subclass(X0,sF3) ),
inference(forward_subsumption_resolution,[],[f2343,f204]) ).
fof(f2353,plain,
( subclass(sF5,sF3)
| subclass(sF5,sF3) ),
inference(resolution,[],[f2352,f2]) ).
fof(f2366,plain,
subclass(sF5,sF3),
inference(duplicate_literal_removal,[],[f2353]) ).
fof(f2367,plain,
$false,
inference(forward_subsumption_resolution,[],[f2366,f603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET272-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 01:19:46 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.98/1.96 % (2179345)Input is clausal, will run a generic CNF schedule.
% 7.98/1.96 % (2179355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3549296641:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.98/1.96 % (2179352)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1908193034:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.98/1.96 % (2179356)dis-21_1_sil=8000:lcm=predicate:random_seed=2484862528: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)
% 7.98/1.96 % (2179351)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1663990301:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.98/1.96 % (2179350)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=324339750:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.98/1.96 % (2179353)lrs+10_1_sil=8000:sp=occurrence:random_seed=1412112115:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.98/1.96 % (2179354)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2997831086:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.98/1.96 % (2179353)Refutation not found, incomplete strategy
% 7.98/1.96 % (2179353)------------------------------
% 7.98/1.96 % (2179353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179353)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179353)Termination reason: Refutation not found, incomplete strategy
% 7.98/1.96 % (2179353)Time elapsed: 0.002 s
% 7.98/1.96 % (2179353)Peak memory usage: 88 MB
% 7.98/1.96 % (2179353)Instructions burned: 1 (million)
% 7.98/1.96 % (2179354)Instruction limit reached!
% 7.98/1.96 % (2179354)------------------------------
% 7.98/1.96 % (2179354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179354)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179354)Termination reason: Instruction limit
% 7.98/1.96 % (2179354)Termination phase: Saturation
% 7.98/1.96 % (2179354)Time elapsed: 0.066 s
% 7.98/1.96 % (2179354)Peak memory usage: 88 MB
% 7.98/1.96 % (2179354)Instructions burned: 115 (million)
% 7.98/1.96 % (2179356)Instruction limit reached!
% 7.98/1.96 % (2179356)------------------------------
% 7.98/1.96 % (2179356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179356)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179356)Termination reason: Instruction limit
% 7.98/1.96 % (2179356)Termination phase: Saturation
% 7.98/1.96 % (2179356)Time elapsed: 0.068 s
% 7.98/1.96 % (2179356)Peak memory usage: 89 MB
% 7.98/1.96 % (2179356)Instructions burned: 117 (million)
% 7.98/1.96 % (2179355)Instruction limit reached!
% 7.98/1.96 % (2179355)------------------------------
% 7.98/1.96 % (2179355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179355)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179355)Termination reason: Instruction limit
% 7.98/1.96 % (2179355)Termination phase: Saturation
% 7.98/1.96 % (2179355)Time elapsed: 0.121 s
% 7.98/1.96 % (2179355)Peak memory usage: 90 MB
% 7.98/1.96 % (2179355)Instructions burned: 181 (million)
% 7.98/1.96 % (2179365)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1944588223: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)
% 7.98/1.96 % (2179364)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=2010874110:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 7.98/1.96 % (2179364)Refutation not found, incomplete strategy
% 7.98/1.96 % (2179364)------------------------------
% 7.98/1.96 % (2179364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179364)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179364)Termination reason: Refutation not found, incomplete strategy
% 7.98/1.96 % (2179364)Time elapsed: 0.003 s
% 7.98/1.96 % (2179364)Peak memory usage: 88 MB
% 7.98/1.96 % (2179364)Instructions burned: 3 (million)
% 7.98/1.96 % (2179365)Refutation not found, incomplete strategy
% 7.98/1.96 % (2179365)------------------------------
% 7.98/1.96 % (2179365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179365)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179365)Termination reason: Refutation not found, incomplete strategy
% 7.98/1.96 % (2179365)Time elapsed: 0.011 s
% 7.98/1.96 % (2179365)Peak memory usage: 88 MB
% 7.98/1.96 % (2179365)Instructions burned: 20 (million)
% 7.98/1.96 % (2179366)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2548847653:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.98/1.96 % (2179353)------------------------------
% 7.98/1.96 % (2179353)------------------------------
% 7.98/1.96 % (2179366)Instruction limit reached!
% 7.98/1.96 % (2179366)------------------------------
% 7.98/1.96 % (2179366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179366)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179366)Termination reason: Instruction limit
% 7.98/1.96 % (2179366)Termination phase: Saturation
% 7.98/1.96 % (2179366)Time elapsed: 0.065 s
% 7.98/1.96 % (2179366)Peak memory usage: 88 MB
% 7.98/1.96 % (2179366)Instructions burned: 222 (million)
% 7.98/1.96 % (2179370)lrs+10_64_to=lpo:sil=8000:random_seed=946672057:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 7.98/1.96 % (2179371)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1288102980:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 7.98/1.96 % (2179364)------------------------------
% 7.98/1.96 % (2179364)------------------------------
% 7.98/1.96 % (2179365)------------------------------
% 7.98/1.96 % (2179365)------------------------------
% 7.98/1.96 % (2179370)Instruction limit reached!
% 7.98/1.96 % (2179370)------------------------------
% 7.98/1.96 % (2179370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179370)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179370)Termination reason: Instruction limit
% 7.98/1.96 % (2179370)Termination phase: Saturation
% 7.98/1.96 % (2179370)Time elapsed: 0.082 s
% 7.98/1.96 % (2179370)Peak memory usage: 89 MB
% 7.98/1.96 % (2179370)Instructions burned: 127 (million)
% 7.98/1.96 % (2179371)Instruction limit reached!
% 7.98/1.96 % (2179371)------------------------------
% 7.98/1.96 % (2179371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179371)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179371)Termination reason: Instruction limit
% 7.98/1.96 % (2179371)Termination phase: Saturation
% 7.98/1.96 % (2179371)Time elapsed: 0.063 s
% 7.98/1.96 % (2179371)Peak memory usage: 89 MB
% 7.98/1.96 % (2179371)Instructions burned: 194 (million)
% 7.98/1.96 % (2179377)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2517901087:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 7.98/1.96 % (2179377)Refutation not found, incomplete strategy
% 7.98/1.96 % (2179377)------------------------------
% 7.98/1.96 % (2179377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179377)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179377)Termination reason: Refutation not found, incomplete strategy
% 7.98/1.96 % (2179377)Time elapsed: 0.003 s
% 7.98/1.96 % (2179377)Peak memory usage: 88 MB
% 7.98/1.96 % (2179377)Instructions burned: 8 (million)
% 7.98/1.96 % (2179374)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=420886712:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 7.98/1.96 % (2179375)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=161165673:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 7.98/1.96 % (2179376)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=865237750:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 7.98/1.96 % (2179376)Instruction limit reached!
% 7.98/1.96 % (2179376)------------------------------
% 7.98/1.96 % (2179376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179376)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179376)Termination reason: Instruction limit
% 7.98/1.96 % (2179376)Termination phase: Saturation
% 7.98/1.96 % (2179376)Time elapsed: 0.064 s
% 7.98/1.96 % (2179376)Peak memory usage: 89 MB
% 7.98/1.96 % (2179376)Instructions burned: 106 (million)
% 7.98/1.96 % (2179374)Instruction limit reached!
% 7.98/1.96 % (2179374)------------------------------
% 7.98/1.96 % (2179374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179374)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179374)Termination reason: Instruction limit
% 7.98/1.96 % (2179374)Termination phase: Saturation
% 7.98/1.96 % (2179374)Time elapsed: 0.107 s
% 7.98/1.96 % (2179374)Peak memory usage: 91 MB
% 7.98/1.96 % (2179374)Instructions burned: 157 (million)
% 7.98/1.96 % (2179377)------------------------------
% 7.98/1.96 % (2179377)------------------------------
% 7.98/1.96 % (2179382)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=943197237:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 7.98/1.96 % (2179384)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=197822539:i=134:sd=2:doe=on:ss=axioms:sgt=14_2990 on theBenchmark for (2990ds/134Mi)
% 7.98/1.96 % (2179383)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3506597612:cond=fast:i=5208:av=off_2990 on theBenchmark for (2990ds/5208Mi)
% 7.98/1.96 % (2179352)First to succeed.
% 7.98/1.96 % (2179352)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2179345"
% 7.98/1.96 % (2179384)Instruction limit reached!
% 7.98/1.96 % (2179384)------------------------------
% 7.98/1.96 % (2179384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179384)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179384)Termination reason: Instruction limit
% 7.98/1.96 % (2179384)Termination phase: Saturation
% 7.98/1.96 % (2179384)Time elapsed: 0.050 s
% 7.98/1.96 % (2179384)Peak memory usage: 90 MB
% 7.98/1.96 % (2179384)Instructions burned: 134 (million)
% 7.98/1.96 % (2179382)Instruction limit reached!
% 7.98/1.96 % (2179382)------------------------------
% 7.98/1.96 % (2179382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/1.96 % (2179382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/1.96 % (2179382)CaDiCaL version: 2.1.3
% 7.98/1.96 % (2179382)Termination reason: Instruction limit
% 7.98/1.96 % (2179382)Termination phase: Saturation
% 7.98/1.96 % (2179382)Time elapsed: 0.165 s
% 7.98/1.96 % (2179382)Peak memory usage: 90 MB
% 7.98/1.96 % (2179382)Instructions burned: 243 (million)
% 7.98/1.96 % (2179388)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2072533143:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 7.98/1.96 % (2179352)Refutation found. Thanks to Tanya!
% 7.98/1.96 % SZS status Unsatisfiable for theBenchmark
% 7.98/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 9.83/2.15 % (2179352)------------------------------
% 9.83/2.15 % (2179352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.83/2.15 % (2179352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/2.15 % (2179352)CaDiCaL version: 2.1.3
% 9.83/2.15 % (2179352)Termination reason: Refutation
% 9.83/2.15 % (2179352)Time elapsed: 0.901 s
% 9.83/2.15 % (2179352)Peak memory usage: 130 MB
% 9.83/2.15 % (2179352)Instructions burned: 1341 (million)
% 9.83/2.15 % (2179352)------------------------------
% 9.83/2.15 % (2179352)------------------------------
% 9.83/2.15 % (2179345)Success in time 1.335 s
% 9.83/2.15 % Vampire exiting
%------------------------------------------------------------------------------