%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET292-6 : 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 : 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 5.23s 1.67s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 22
% Syntax : Number of formulae : 108 ( 29 unt; 5 def)
% Number of atoms : 236 ( 96 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 220 ( 92 ~; 126 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 136 ( 0 sgn 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
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(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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f36,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
fof(f37,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| member(ordered_pair(ordered_pair(X1,X0),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
inverse(null_class) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_null_class_1) ).
fof(f123,plain,
null_class != inverse(null_class),
inference(reorient_equations,[],[f122]) ).
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(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(X0,X2) ),
inference(definition_unfolding,[],[f14,f128]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f128]) ).
fof(f144,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f148,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))),flip(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))),X3) ),
inference(definition_unfolding,[],[f37,f128,f128,f128,f128]) ).
fof(f186,plain,
null_class != domain_of(flip(cross_product(null_class,universal_class))),
inference(definition_unfolding,[],[f123,f39]) ).
fof(f191,definition,
sF0 = cross_product(null_class,universal_class),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f192,plain,
cross_product(null_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,plain,
null_class != sF2,
inference(definition_folding,[],[f186,f196,f194,f192]) ).
fof(f203,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f1,f68]) ).
fof(f206,plain,
! [X2,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))),sF1)
| 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))),sF0) ),
inference(superposition,[],[f148,f194]) ).
fof(f209,plain,
! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class ),
inference(resolution,[],[f140,f68]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0)))))
| null_class = X0 ),
inference(resolution,[],[f140,f203]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = null_class ),
inference(superposition,[],[f137,f209]) ).
fof(f220,definition,
( spl3_1
<=> null_class = sF0 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f221,plain,
( null_class != sF0
| spl3_1 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( null_class = sF0
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f229,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,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = null_class
| cross_product(X0,X1) = null_class ),
inference(resolution,[],[f215,f68]) ).
fof(f237,plain,
! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = null_class ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f281,plain,
! [X0] :
( regular(flip(X0)) = unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(second(regular(flip(X0))),second(regular(flip(X0))))))
| null_class = flip(X0) ),
inference(resolution,[],[f211,f36]) ).
fof(f304,definition,
( spl3_7
<=> sF0 = sF1 ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f305,plain,
( sF0 != sF1
| spl3_7 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f306,plain,
( sF0 = sF1
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f329,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f229,f3]) ).
fof(f336,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f353,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f336,f70]) ).
fof(f443,plain,
( sF2 = domain_of(sF0)
| ~ spl3_7 ),
inference(superposition,[],[f196,f306]) ).
fof(f653,plain,
! [X2,X0,X1] :
( ~ member(regular(flip(X0)),cross_product(X1,X2))
| member(first(regular(flip(X0))),X1)
| null_class = flip(X0) ),
inference(superposition,[],[f137,f281]) ).
fof(f661,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f353,f7]) ).
fof(f663,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f661]) ).
fof(f664,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f663,f336]) ).
fof(f668,plain,
! [X2,X0,X1] :
( member(first(regular(flip(X0))),X1)
| null_class = flip(X0)
| ~ subclass(flip(X0),cross_product(X1,X2))
| null_class = flip(X0) ),
inference(resolution,[],[f653,f203]) ).
fof(f671,plain,
! [X2,X0,X1] :
( ~ subclass(flip(X0),cross_product(X1,X2))
| null_class = flip(X0)
| member(first(regular(flip(X0))),X1) ),
inference(duplicate_literal_removal,[],[f668]) ).
fof(f688,plain,
! [X0] :
( member(first(regular(flip(X0))),cross_product(universal_class,universal_class))
| null_class = flip(X0) ),
inference(resolution,[],[f671,f36]) ).
fof(f695,plain,
! [X0] :
( first(regular(flip(X0))) = unordered_pair(unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))),unordered_pair(first(first(regular(flip(X0)))),unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0)))))))
| null_class = flip(X0) ),
inference(resolution,[],[f688,f140]) ).
fof(f706,plain,
! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))))),unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0)))))))),unordered_pair(unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))))),unordered_pair(X1,X1))),X2)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(X2))
| null_class = flip(X0) ),
inference(superposition,[],[f148,f695]) ).
fof(f744,plain,
! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))),unordered_pair(first(first(regular(flip(X0)))),unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))))),unordered_pair(unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))),unordered_pair(first(first(regular(flip(X0)))),unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0)))))))),unordered_pair(unordered_pair(unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))),unordered_pair(first(first(regular(flip(X0)))),unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))))),unordered_pair(X1,X1))),X2)
| null_class = flip(X0)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(X2))) ),
inference(resolution,[],[f706,f148]) ).
fof(f786,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f144,f664]) ).
fof(f787,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f786]) ).
fof(f791,plain,
! [X0] : null_class = cross_product(domain_of(null_class),X0),
inference(resolution,[],[f787,f237]) ).
fof(f793,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f787,f68]) ).
fof(f800,plain,
! [X0] : null_class = cross_product(null_class,X0),
inference(forward_demodulation,[],[f791,f793]) ).
fof(f803,plain,
null_class = sF0,
inference(superposition,[],[f800,f192]) ).
fof(f819,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f803,f221]) ).
fof(f820,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f819]) ).
fof(f829,plain,
( ! [X0] : ~ member(X0,domain_of(sF0))
| ~ spl3_1 ),
inference(superposition,[],[f787,f222]) ).
fof(f831,plain,
( ! [X0] : ~ member(X0,sF2)
| ~ spl3_1
| ~ spl3_7 ),
inference(forward_demodulation,[],[f829,f443]) ).
fof(f836,plain,
( null_class = sF2
| ~ spl3_1
| ~ spl3_7 ),
inference(resolution,[],[f831,f68]) ).
fof(f847,plain,
( $false
| ~ spl3_1
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f836,f197]) ).
fof(f848,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f847]) ).
fof(f877,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f787,f793]) ).
fof(f879,plain,
( ! [X0] : ~ member(X0,sF0)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f877,f222]) ).
fof(f1446,plain,
! [X0,X1] :
( null_class = flip(X0)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(sF1)))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))))),unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0)))))))),unordered_pair(unordered_pair(unordered_pair(second(first(regular(flip(X0)))),second(first(regular(flip(X0))))),unordered_pair(second(first(regular(flip(X0)))),unordered_pair(first(first(regular(flip(X0)))),first(first(regular(flip(X0))))))),unordered_pair(X1,X1))),sF0) ),
inference(resolution,[],[f744,f206]) ).
fof(f1448,plain,
! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),X2)
| null_class = flip(X0)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(X2)))
| null_class = flip(X0) ),
inference(superposition,[],[f744,f695]) ).
fof(f1449,plain,
! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),X2)
| null_class = flip(X0)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(X2))) ),
inference(duplicate_literal_removal,[],[f1448]) ).
fof(f1450,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(X2)))
| member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),X2)
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1449,f222]) ).
fof(f1452,plain,
( ! [X0,X1] :
( null_class = flip(X0)
| ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(sF1))) )
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f1446,f879]) ).
fof(f1470,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(first(regular(flip(X0))),first(regular(flip(X0)))),unordered_pair(first(regular(flip(X0))),unordered_pair(X1,X1))),flip(flip(sF1)))
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1452,f222]) ).
fof(f1485,plain,
( ! [X0] :
( ~ member(regular(flip(X0)),flip(flip(sF1)))
| flip(X0) = sF0
| null_class = flip(X0) )
| ~ spl3_1 ),
inference(superposition,[],[f1470,f281]) ).
fof(f1486,plain,
( ! [X0] :
( flip(X0) = sF0
| ~ member(regular(flip(X0)),flip(flip(sF1)))
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1485,f222]) ).
fof(f1487,plain,
( ! [X0] :
( ~ member(regular(flip(X0)),flip(flip(sF1)))
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f1486]) ).
fof(f1491,plain,
( sF0 = flip(flip(sF1))
| null_class = flip(flip(sF1))
| ~ spl3_1 ),
inference(resolution,[],[f1487,f68]) ).
fof(f1497,plain,
( sF0 = flip(flip(sF1))
| sF0 = flip(flip(sF1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1491,f222]) ).
fof(f1498,plain,
( sF0 = flip(flip(sF1))
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f1497]) ).
fof(f1531,plain,
( ! [X0,X1] :
( ~ member(regular(flip(X0)),flip(flip(X1)))
| member(regular(flip(X0)),X1)
| flip(X0) = sF0
| null_class = flip(X0) )
| ~ spl3_1 ),
inference(superposition,[],[f1450,f281]) ).
fof(f1536,plain,
( ! [X0,X1] :
( flip(X0) = sF0
| ~ member(regular(flip(X0)),flip(flip(X1)))
| member(regular(flip(X0)),X1)
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1531,f222]) ).
fof(f1537,plain,
( ! [X0,X1] :
( ~ member(regular(flip(X0)),flip(flip(X1)))
| flip(X0) = sF0
| member(regular(flip(X0)),X1) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f1536]) ).
fof(f1539,plain,
( ! [X0] :
( sF0 = flip(flip(X0))
| member(regular(flip(flip(X0))),X0)
| null_class = flip(flip(X0)) )
| ~ spl3_1 ),
inference(resolution,[],[f1537,f68]) ).
fof(f1542,plain,
( ! [X0] :
( ~ member(regular(flip(X0)),flip(sF1))
| flip(X0) = sF0
| member(regular(flip(X0)),sF0) )
| ~ spl3_1 ),
inference(superposition,[],[f1537,f194]) ).
fof(f1546,plain,
( ! [X0] :
( ~ member(regular(flip(X0)),flip(sF1))
| flip(X0) = sF0 )
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f1542,f879]) ).
fof(f1550,plain,
( ! [X0] :
( sF0 = flip(flip(X0))
| sF0 = flip(flip(X0))
| member(regular(flip(flip(X0))),X0) )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1539,f222]) ).
fof(f1551,plain,
( ! [X0] :
( member(regular(flip(flip(X0))),X0)
| sF0 = flip(flip(X0)) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f1550]) ).
fof(f1726,plain,
( member(regular(flip(sF0)),flip(sF1))
| sF0 = flip(sF0)
| ~ spl3_1 ),
inference(superposition,[],[f1551,f1498]) ).
fof(f1731,plain,
( sF0 = flip(sF0)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f1726,f1546]) ).
fof(f1744,plain,
( sF0 = sF1
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1731,f194]) ).
fof(f1749,plain,
( $false
| ~ spl3_1
| spl3_7 ),
inference(forward_subsumption_resolution,[],[f1744,f305]) ).
fof(f1750,plain,
( ~ spl3_1
| spl3_7 ),
inference(avatar_contradiction_clause,[],[f1749]) ).
cnf(s18,plain,
spl3_1,
inference(sat_conversion,[],[f820]) ).
cnf(s19,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(sat_conversion,[],[f848]) ).
cnf(s37,plain,
( ~ spl3_1
| spl3_7 ),
inference(sat_conversion,[],[f1750]) ).
cnf(s38,plain,
spl3_7,
inference(rat,[],[s37,s18]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s19,s38,s18]) ).
fof(f1752,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET292-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 01:23:57 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
% 5.23/1.67 % (1103535)Input is clausal, will run a generic CNF schedule.
% 5.23/1.67 % (1103540)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=2206731884:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.23/1.67 % (1103546)dis-21_1_sil=8000:lcm=predicate:random_seed=4218697660: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)
% 5.23/1.67 % (1103543)lrs+10_1_sil=8000:sp=occurrence:random_seed=2352596486:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.23/1.67 % (1103542)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=358582693:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.23/1.67 % (1103541)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1594468251:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.23/1.67 % (1103544)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4017419938:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.23/1.67 % (1103545)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3866617084:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.23/1.67 % (1103543)Refutation not found, incomplete strategy
% 5.23/1.67 % (1103543)------------------------------
% 5.23/1.67 % (1103543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103543)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103543)Termination reason: Refutation not found, incomplete strategy
% 5.23/1.67 % (1103543)Time elapsed: 0.001 s
% 5.23/1.67 % (1103543)Peak memory usage: 87 MB
% 5.23/1.67 % (1103544)Instruction limit reached!
% 5.23/1.67 % (1103544)------------------------------
% 5.23/1.67 % (1103544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103544)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103544)Termination reason: Instruction limit
% 5.23/1.67 % (1103544)Termination phase: Saturation
% 5.23/1.67 % (1103544)Time elapsed: 0.066 s
% 5.23/1.67 % (1103544)Peak memory usage: 88 MB
% 5.23/1.67 % (1103544)Instructions burned: 114 (million)
% 5.23/1.67 % (1103546)Instruction limit reached!
% 5.23/1.67 % (1103546)------------------------------
% 5.23/1.67 % (1103546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103546)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103546)Termination reason: Instruction limit
% 5.23/1.67 % (1103546)Termination phase: Saturation
% 5.23/1.67 % (1103546)Time elapsed: 0.070 s
% 5.23/1.67 % (1103546)Peak memory usage: 89 MB
% 5.23/1.67 % (1103546)Instructions burned: 119 (million)
% 5.23/1.67 % (1103545)Instruction limit reached!
% 5.23/1.67 % (1103545)------------------------------
% 5.23/1.67 % (1103545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103545)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103545)Termination reason: Instruction limit
% 5.23/1.67 % (1103545)Termination phase: Saturation
% 5.23/1.67 % (1103545)Time elapsed: 0.133 s
% 5.23/1.67 % (1103545)Peak memory usage: 90 MB
% 5.23/1.67 % (1103545)Instructions burned: 181 (million)
% 5.23/1.67 % (1103554)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=1836491448:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.23/1.67 % (1103555)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=158085387: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)
% 5.23/1.67 % (1103554)Refutation not found, incomplete strategy
% 5.23/1.67 % (1103554)------------------------------
% 5.23/1.67 % (1103554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103554)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103554)Termination reason: Refutation not found, incomplete strategy
% 5.23/1.67 % (1103554)Time elapsed: 0.004 s
% 5.23/1.67 % (1103554)Peak memory usage: 88 MB
% 5.23/1.67 % (1103554)Instructions burned: 4 (million)
% 5.23/1.67 % (1103543)------------------------------
% 5.23/1.67 % (1103543)------------------------------
% 5.23/1.67 % (1103556)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4138032806:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 5.23/1.67 % (1103556)Refutation not found, incomplete strategy
% 5.23/1.67 % (1103556)------------------------------
% 5.23/1.67 % (1103556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103556)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103556)Termination reason: Refutation not found, incomplete strategy
% 5.23/1.67 % (1103556)Time elapsed: 0.003 s
% 5.23/1.67 % (1103556)Peak memory usage: 88 MB
% 5.23/1.67 % (1103556)Instructions burned: 3 (million)
% 5.23/1.67 % (1103555)Instruction limit reached!
% 5.23/1.67 % (1103555)------------------------------
% 5.23/1.67 % (1103555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103555)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103555)Termination reason: Instruction limit
% 5.23/1.67 % (1103555)Termination phase: Saturation
% 5.23/1.67 % (1103555)Time elapsed: 0.106 s
% 5.23/1.67 % (1103555)Peak memory usage: 91 MB
% 5.23/1.67 % (1103555)Instructions burned: 190 (million)
% 5.23/1.67 % (1103559)lrs+10_64_to=lpo:sil=8000:random_seed=3235415339:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.23/1.67 % (1103554)------------------------------
% 5.23/1.67 % (1103554)------------------------------
% 5.23/1.67 % (1103540)First to succeed.
% 5.23/1.67 % (1103540)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1103535"
% 5.23/1.67 % (1103559)Instruction limit reached!
% 5.23/1.67 % (1103559)------------------------------
% 5.23/1.67 % (1103559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103559)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103559)Termination reason: Instruction limit
% 5.23/1.67 % (1103559)Termination phase: Saturation
% 5.23/1.67 % (1103559)Time elapsed: 0.080 s
% 5.23/1.67 % (1103559)Peak memory usage: 89 MB
% 5.23/1.67 % (1103559)Instructions burned: 127 (million)
% 5.23/1.67 % (1103561)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3960417265:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.23/1.67 % (1103556)------------------------------
% 5.23/1.67 % (1103556)------------------------------
% 5.23/1.67 % (1103561)Instruction limit reached!
% 5.23/1.67 % (1103561)------------------------------
% 5.23/1.67 % (1103561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.67 % (1103561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.67 % (1103561)CaDiCaL version: 2.1.3
% 5.23/1.67 % (1103561)Termination reason: Instruction limit
% 5.23/1.67 % (1103561)Termination phase: Saturation
% 5.23/1.67 % (1103561)Time elapsed: 0.127 s
% 5.23/1.67 % (1103561)Peak memory usage: 90 MB
% 5.23/1.67 % (1103561)Instructions burned: 195 (million)
% 5.23/1.67 % (1103564)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=532447650:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 5.23/1.67 % (1103563)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3059402093:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 5.23/1.67 % (1103540)Refutation found. Thanks to Tanya!
% 5.23/1.67 % SZS status Unsatisfiable for theBenchmark
% 5.23/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 6.34/1.87 % (1103540)------------------------------
% 6.34/1.87 % (1103540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.87 % (1103540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.87 % (1103540)CaDiCaL version: 2.1.3
% 6.34/1.87 % (1103540)Termination reason: Refutation
% 6.34/1.87 % (1103540)Time elapsed: 0.518 s
% 6.34/1.87 % (1103540)Peak memory usage: 132 MB
% 6.34/1.87 % (1103540)Instructions burned: 1248 (million)
% 6.34/1.87 % (1103540)------------------------------
% 6.34/1.87 % (1103540)------------------------------
% 6.34/1.87 % (1103535)Success in time 0.818 s
% 6.34/1.87 % Vampire exiting
%------------------------------------------------------------------------------