%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET267-6 : 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 : n013.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 12:40:39 PM UTC 2026
% Result : Unsatisfiable 6.55s 2.20s
% Output : Refutation 6.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 27
% Syntax : Number of formulae : 106 ( 27 unt; 8 def)
% Number of atoms : 297 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 335 ( 144 ~; 187 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 135 ( 0 sgn 135 !; 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(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(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(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(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f31,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| restrict(X1,singleton(X0),universal_class) = null_class
| member(X0,domain_of(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| member(X0,domain_of(X1)) ),
inference(reorient_equations,[],[f31]) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f122,negated_conjecture,
~ subclass(complement(domain_of(x)),domain_of(complement(x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_monotonic4_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(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(f189,definition,
sF0 = domain_of(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f190,plain,
domain_of(x) = sF0,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f192,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF2 = complement(x),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f194,plain,
complement(x) = sF2,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF3 = domain_of(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f196,plain,
domain_of(sF2) = sF3,
inference(reorient_equations,[],[f195]) ).
fof(f197,plain,
~ subclass(sF1,sF3),
inference(definition_folding,[],[f122,f196,f194,f192,f190]) ).
fof(f198,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f24,f2]) ).
fof(f206,plain,
! [X0] :
( member(X0,sF2)
| ~ member(X0,universal_class)
| member(X0,x) ),
inference(superposition,[],[f25,f194]) ).
fof(f207,plain,
! [X0] :
( ~ member(X0,sF2)
| ~ member(X0,x) ),
inference(superposition,[],[f24,f194]) ).
fof(f229,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f68,f22]) ).
fof(f230,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f68,f21]) ).
fof(f255,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(f358,plain,
! [X0,X1] :
( ~ member(regular(intersection(X0,complement(X1))),X1)
| null_class = intersection(X0,complement(X1)) ),
inference(resolution,[],[f229,f24]) ).
fof(f382,plain,
! [X0] :
( null_class = intersection(X0,complement(X0))
| null_class = intersection(X0,complement(X0)) ),
inference(resolution,[],[f358,f230]) ).
fof(f391,plain,
! [X0] : null_class = intersection(X0,complement(X0)),
inference(duplicate_literal_removal,[],[f382]) ).
fof(f396,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(superposition,[],[f21,f391]) ).
fof(f529,definition,
( spl4_11
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f530,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f649,plain,
! [X2,X0,X1] :
( member(regular(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))),null_class)
| ~ member(regular(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))),X2)
| ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(resolution,[],[f255,f229]) ).
fof(f761,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))),X2)
| ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f649,f530]) ).
fof(f853,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,x) ),
inference(resolution,[],[f396,f207]) ).
fof(f910,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,domain_of(sF2))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),universal_class)
| member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),x) )
| ~ spl4_11 ),
inference(resolution,[],[f761,f206]) ).
fof(f914,plain,
( ! [X0,X1] :
( member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),x)
| ~ member(X0,universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),universal_class)
| member(X0,sF3) )
| ~ spl4_11 ),
inference(forward_demodulation,[],[f910,f196]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),universal_class)
| member(X0,sF3)
| ~ member(X0,universal_class)
| member(X0,domain_of(x))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)) )
| ~ spl4_11 ),
inference(resolution,[],[f914,f761]) ).
fof(f918,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),universal_class)
| member(X0,sF3)
| member(X0,domain_of(x)) )
| ~ spl4_11 ),
inference(duplicate_literal_removal,[],[f916]) ).
fof(f921,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),universal_class)
| ~ member(X0,universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF0)
| member(X0,sF3) )
| ~ spl4_11 ),
inference(forward_demodulation,[],[f918,f190]) ).
fof(f1461,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f11,f139]) ).
fof(f1564,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| null_class = intersection(universal_class,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF0)
| member(X0,sF3)
| null_class = intersection(universal_class,cross_product(unordered_pair(X0,X0),universal_class)) )
| ~ spl4_11 ),
inference(resolution,[],[f921,f230]) ).
fof(f1567,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF0)
| member(X0,sF3)
| ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),X2)
| ~ subclass(X2,universal_class) )
| ~ spl4_11 ),
inference(resolution,[],[f921,f1]) ).
fof(f1568,plain,
( ! [X0] :
( null_class = intersection(universal_class,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class)
| member(X0,sF0)
| member(X0,sF3) )
| ~ spl4_11 ),
inference(duplicate_literal_removal,[],[f1564]) ).
fof(f1569,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))),X2)
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF0)
| member(X0,sF3)
| ~ member(X0,universal_class) )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f1567,f4]) ).
fof(f1583,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| member(X1,sF0)
| member(X1,sF3)
| ~ member(X1,universal_class)
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) )
| ~ spl4_11 ),
inference(resolution,[],[f1569,f229]) ).
fof(f1596,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| member(X1,sF0)
| member(X1,sF3)
| ~ member(X1,universal_class) )
| ~ spl4_11 ),
inference(duplicate_literal_removal,[],[f1583]) ).
fof(f1602,plain,
( ! [X2,X0,X1] :
( member(X0,null_class)
| ~ member(X0,cross_product(unordered_pair(X2,X2),universal_class))
| ~ member(X0,X1)
| member(X2,sF0)
| member(X2,sF3)
| ~ member(X2,universal_class) )
| ~ spl4_11 ),
inference(superposition,[],[f23,f1596]) ).
fof(f1607,plain,
( ! [X2,X0,X1] :
( ~ member(X0,cross_product(unordered_pair(X2,X2),universal_class))
| ~ member(X0,X1)
| member(X2,sF0)
| member(X2,sF3)
| ~ member(X2,universal_class) )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f1602,f530]) ).
fof(f1656,plain,
( ! [X0,X1] :
( member(X0,null_class)
| ~ member(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| member(X1,sF0)
| member(X1,sF3) )
| ~ spl4_11 ),
inference(superposition,[],[f23,f1568]) ).
fof(f1661,plain,
( ! [X0,X1] :
( member(X0,null_class)
| ~ member(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,sF0)
| member(X1,sF3) )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f1656,f1461]) ).
fof(f1662,plain,
( ! [X0,X1] :
( ~ member(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,sF0)
| member(X1,sF3) )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f1661,f1607]) ).
fof(f1849,definition,
( spl4_36
<=> member(not_subclass_element(sF1,sF3),universal_class) ),
introduced(definition,[new_symbols(definition,[spl4_36])],[avatar_definition]) ).
fof(f1850,plain,
( member(not_subclass_element(sF1,sF3),universal_class)
| ~ spl4_36 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f1851,plain,
( ~ member(not_subclass_element(sF1,sF3),universal_class)
| spl4_36 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f1862,plain,
( ! [X0] :
( ~ member(not_subclass_element(sF1,sF3),X0)
| ~ subclass(X0,universal_class) )
| spl4_36 ),
inference(resolution,[],[f1851,f1]) ).
fof(f1863,plain,
( ! [X0] : ~ member(not_subclass_element(sF1,sF3),X0)
| spl4_36 ),
inference(forward_subsumption_resolution,[],[f1862,f4]) ).
fof(f1864,plain,
( subclass(sF1,sF3)
| spl4_36 ),
inference(resolution,[],[f1863,f2]) ).
fof(f1877,plain,
( $false
| spl4_36 ),
inference(forward_subsumption_resolution,[],[f1864,f197]) ).
fof(f1878,plain,
spl4_36,
inference(avatar_contradiction_clause,[],[f1877]) ).
fof(f1924,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,unordered_pair(X2,X2))
| ~ member(X2,universal_class)
| member(X2,sF0)
| member(X2,sF3) )
| ~ spl4_11 ),
inference(resolution,[],[f138,f1662]) ).
fof(f1929,definition,
( spl4_42
<=> ! [X2,X1] :
( ~ member(X1,unordered_pair(X2,X2))
| member(X2,sF3)
| member(X2,sF0)
| ~ member(X2,universal_class) ) ),
introduced(definition,[new_symbols(definition,[spl4_42])],[avatar_definition]) ).
fof(f1930,plain,
( ! [X2,X1] :
( ~ member(X1,unordered_pair(X2,X2))
| member(X2,sF3)
| member(X2,sF0)
| ~ member(X2,universal_class) )
| ~ spl4_42 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f1932,definition,
( spl4_43
<=> ! [X0] : ~ member(X0,universal_class) ),
introduced(definition,[new_symbols(definition,[spl4_43])],[avatar_definition]) ).
fof(f1933,plain,
( ! [X0] : ~ member(X0,universal_class)
| ~ spl4_43 ),
inference(avatar_component_clause,[],[f1932]) ).
fof(f1934,plain,
( spl4_42
| spl4_43
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f1924,f529,f1932,f1929]) ).
fof(f1965,plain,
( ! [X0] :
( member(X0,sF3)
| member(X0,sF0)
| ~ member(X0,universal_class)
| ~ member(X0,universal_class) )
| ~ spl4_42 ),
inference(resolution,[],[f1930,f10]) ).
fof(f1976,plain,
( ! [X0] :
( member(X0,sF3)
| member(X0,sF0)
| ~ member(X0,universal_class) )
| ~ spl4_42 ),
inference(duplicate_literal_removal,[],[f1965]) ).
fof(f1987,plain,
( universal_class = null_class
| ~ spl4_43 ),
inference(resolution,[],[f1933,f68]) ).
fof(f1997,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),null_class)
| ~ spl4_43 ),
inference(backward_demodulation,[],[f11,f1987]) ).
fof(f2202,plain,
( $false
| ~ spl4_11
| ~ spl4_43 ),
inference(forward_subsumption_resolution,[],[f1997,f530]) ).
fof(f2203,plain,
( ~ spl4_11
| ~ spl4_43 ),
inference(avatar_contradiction_clause,[],[f2202]) ).
fof(f2310,plain,
( ! [X0] :
( member(not_subclass_element(X0,sF3),sF0)
| ~ member(not_subclass_element(X0,sF3),universal_class)
| subclass(X0,sF3) )
| ~ spl4_42 ),
inference(resolution,[],[f1976,f3]) ).
fof(f2330,plain,
( ~ member(not_subclass_element(complement(sF0),sF3),universal_class)
| subclass(complement(sF0),sF3)
| subclass(complement(sF0),sF3)
| ~ spl4_42 ),
inference(resolution,[],[f2310,f198]) ).
fof(f2331,plain,
( ~ member(not_subclass_element(complement(sF0),sF3),universal_class)
| subclass(complement(sF0),sF3)
| ~ spl4_42 ),
inference(duplicate_literal_removal,[],[f2330]) ).
fof(f2334,plain,
( ~ member(not_subclass_element(sF1,sF3),universal_class)
| subclass(complement(sF0),sF3)
| ~ spl4_42 ),
inference(forward_demodulation,[],[f2331,f192]) ).
fof(f2337,plain,
( subclass(complement(sF0),sF3)
| ~ spl4_36
| ~ spl4_42 ),
inference(forward_subsumption_resolution,[],[f2334,f1850]) ).
fof(f2341,plain,
( subclass(sF1,sF3)
| ~ spl4_36
| ~ spl4_42 ),
inference(forward_demodulation,[],[f2337,f192]) ).
fof(f2342,plain,
( $false
| ~ spl4_36
| ~ spl4_42 ),
inference(forward_subsumption_resolution,[],[f2341,f197]) ).
fof(f2343,plain,
( ~ spl4_36
| ~ spl4_42 ),
inference(avatar_contradiction_clause,[],[f2342]) ).
fof(f2384,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[],[f853,f396]) ).
fof(f2434,plain,
spl4_11,
inference(avatar_split_clause,[],[f2384,f529]) ).
cnf(s29,plain,
spl4_36,
inference(sat_conversion,[],[f1878]) ).
cnf(s33,plain,
( ~ spl4_11
| spl4_42
| spl4_43 ),
inference(sat_conversion,[],[f1934]) ).
cnf(s41,plain,
( ~ spl4_11
| ~ spl4_43 ),
inference(sat_conversion,[],[f2203]) ).
cnf(s46,plain,
( ~ spl4_36
| ~ spl4_42 ),
inference(sat_conversion,[],[f2343]) ).
cnf(s59,plain,
spl4_11,
inference(sat_conversion,[],[f2434]) ).
cnf(s72,plain,
~ spl4_43,
inference(rat,[],[s41,s59]) ).
cnf(s75,plain,
spl4_42,
inference(rat,[],[s33,s72,s59]) ).
cnf(s76,plain,
~ spl4_36,
inference(rat,[],[s46,s75]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s29,s76]) ).
fof(f2457,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET267-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 01:15:06 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.55/2.20 % (720706)Input is clausal, will run a generic CNF schedule.
% 6.55/2.20 % (720715)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=15670518:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.55/2.20 % (720715)Refutation not found, incomplete strategy
% 6.55/2.20 % (720715)------------------------------
% 6.55/2.20 % (720715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720715)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720715)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.20 % (720715)Time elapsed: 0.001 s
% 6.55/2.20 % (720715)Peak memory usage: 88 MB
% 6.55/2.20 % (720715)Instructions burned: 1 (million)
% 6.55/2.20 % (720717)dis-21_1_sil=8000:lcm=predicate:random_seed=1018080318: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)
% 6.55/2.20 % (720714)lrs+10_1_sil=8000:sp=occurrence:random_seed=3460948785:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.55/2.20 % (720711)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=307105162:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.55/2.20 % (720716)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2468645158:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.55/2.20 % (720713)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=948363729:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.55/2.20 % (720712)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3179689653:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.55/2.20 % (720714)Refutation not found, incomplete strategy
% 6.55/2.20 % (720714)------------------------------
% 6.55/2.20 % (720714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720714)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720714)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.20 % (720714)Time elapsed: 0.002 s
% 6.55/2.20 % (720714)Peak memory usage: 87 MB
% 6.55/2.20 % (720714)Instructions burned: 1 (million)
% 6.55/2.20 % (720717)Instruction limit reached!
% 6.55/2.20 % (720717)------------------------------
% 6.55/2.20 % (720717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720717)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720717)Termination reason: Instruction limit
% 6.55/2.20 % (720717)Termination phase: Saturation
% 6.55/2.20 % (720717)Time elapsed: 0.072 s
% 6.55/2.20 % (720717)Peak memory usage: 89 MB
% 6.55/2.20 % (720717)Instructions burned: 117 (million)
% 6.55/2.20 % (720715)------------------------------
% 6.55/2.20 % (720715)------------------------------
% 6.55/2.20 % (720716)Instruction limit reached!
% 6.55/2.20 % (720716)------------------------------
% 6.55/2.20 % (720716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720716)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720716)Termination reason: Instruction limit
% 6.55/2.20 % (720716)Termination phase: Saturation
% 6.55/2.20 % (720716)Time elapsed: 0.131 s
% 6.55/2.20 % (720716)Peak memory usage: 90 MB
% 6.55/2.20 % (720716)Instructions burned: 180 (million)
% 6.55/2.20 % (720725)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=1260440550:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.55/2.20 % (720725)Refutation not found, incomplete strategy
% 6.55/2.20 % (720725)------------------------------
% 6.55/2.20 % (720725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720725)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720725)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.20 % (720725)Time elapsed: 0.003 s
% 6.55/2.20 % (720725)Peak memory usage: 88 MB
% 6.55/2.20 % (720725)Instructions burned: 2 (million)
% 6.55/2.20 % (720726)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3101138789: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)
% 6.55/2.20 % (720726)Refutation not found, incomplete strategy
% 6.55/2.20 % (720726)------------------------------
% 6.55/2.20 % (720726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720726)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720726)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.20 % (720726)Time elapsed: 0.006 s
% 6.55/2.20 % (720726)Peak memory usage: 88 MB
% 6.55/2.20 % (720726)Instructions burned: 20 (million)
% 6.55/2.20 % (720714)------------------------------
% 6.55/2.20 % (720714)------------------------------
% 6.55/2.20 % (720727)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=134039053:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.55/2.20 % (720726)------------------------------
% 6.55/2.20 % (720726)------------------------------
% 6.55/2.20 % (720727)Instruction limit reached!
% 6.55/2.20 % (720727)------------------------------
% 6.55/2.20 % (720727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720727)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720727)Termination reason: Instruction limit
% 6.55/2.20 % (720727)Termination phase: Saturation
% 6.55/2.20 % (720727)Time elapsed: 0.129 s
% 6.55/2.20 % (720727)Peak memory usage: 89 MB
% 6.55/2.20 % (720727)Instructions burned: 219 (million)
% 6.55/2.20 % (720730)lrs+10_64_to=lpo:sil=8000:random_seed=2199053603:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.55/2.20 % (720725)------------------------------
% 6.55/2.20 % (720725)------------------------------
% 6.55/2.20 % (720732)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2066578332:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.55/2.20 % (720730)Instruction limit reached!
% 6.55/2.20 % (720730)------------------------------
% 6.55/2.20 % (720730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720730)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720730)Termination reason: Instruction limit
% 6.55/2.20 % (720730)Termination phase: Saturation
% 6.55/2.20 % (720730)Time elapsed: 0.078 s
% 6.55/2.20 % (720730)Peak memory usage: 90 MB
% 6.55/2.20 % (720730)Instructions burned: 126 (million)
% 6.55/2.20 % (720732)Instruction limit reached!
% 6.55/2.20 % (720732)------------------------------
% 6.55/2.20 % (720732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720732)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720732)Termination reason: Instruction limit
% 6.55/2.20 % (720732)Termination phase: Saturation
% 6.55/2.20 % (720732)Time elapsed: 0.059 s
% 6.55/2.20 % (720732)Peak memory usage: 89 MB
% 6.55/2.20 % (720732)Instructions burned: 195 (million)
% 6.55/2.20 % (720733)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3877422682:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 6.55/2.20 % (720735)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3939511524:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.55/2.20 % (720737)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=2204597678:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.55/2.20 % (720738)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1951577592:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 6.55/2.20 % (720733)Instruction limit reached!
% 6.55/2.20 % (720733)------------------------------
% 6.55/2.20 % (720733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720733)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720733)Termination reason: Instruction limit
% 6.55/2.20 % (720733)Termination phase: Saturation
% 6.55/2.20 % (720733)Time elapsed: 0.107 s
% 6.55/2.20 % (720733)Peak memory usage: 91 MB
% 6.55/2.20 % (720733)Instructions burned: 158 (million)
% 6.55/2.20 % (720738)Instruction limit reached!
% 6.55/2.20 % (720738)------------------------------
% 6.55/2.20 % (720738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720738)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720738)Termination reason: Instruction limit
% 6.55/2.20 % (720738)Termination phase: Saturation
% 6.55/2.20 % (720738)Time elapsed: 0.039 s
% 6.55/2.20 % (720738)Peak memory usage: 89 MB
% 6.55/2.20 % (720738)Instructions burned: 110 (million)
% 6.55/2.20 % (720737)Instruction limit reached!
% 6.55/2.20 % (720737)------------------------------
% 6.55/2.20 % (720737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720737)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720737)Termination reason: Instruction limit
% 6.55/2.20 % (720737)Termination phase: Saturation
% 6.55/2.20 % (720737)Time elapsed: 0.063 s
% 6.55/2.20 % (720737)Peak memory usage: 90 MB
% 6.55/2.20 % (720737)Instructions burned: 107 (million)
% 6.55/2.20 % (720743)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2026475526:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 6.55/2.20 % (720744)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=707539494:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 6.55/2.20 % (720745)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=2367961698:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 6.55/2.20 % (720745)Refutation not found, incomplete strategy
% 6.55/2.20 % (720745)------------------------------
% 6.55/2.20 % (720745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720745)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720745)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.20 % (720745)Time elapsed: 0.004 s
% 6.55/2.20 % (720745)Peak memory usage: 88 MB
% 6.55/2.20 % (720745)Instructions burned: 4 (million)
% 6.55/2.20 % (720713)First to succeed.
% 6.55/2.20 % (720713)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-720706"
% 6.55/2.20 % (720743)Instruction limit reached!
% 6.55/2.20 % (720743)------------------------------
% 6.55/2.20 % (720743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.20 % (720743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.20 % (720743)CaDiCaL version: 2.1.3
% 6.55/2.20 % (720743)Termination reason: Instruction limit
% 6.55/2.20 % (720743)Termination phase: Saturation
% 6.55/2.20 % (720743)Time elapsed: 0.164 s
% 6.55/2.20 % (720743)Peak memory usage: 91 MB
% 6.55/2.20 % (720743)Instructions burned: 245 (million)
% 6.55/2.20 % (720711)Also succeeded, but the first one will report.
% 6.55/2.20 % (720745)------------------------------
% 6.55/2.20 % (720745)------------------------------
% 6.55/2.20 % (720749)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=4174930885:i=499:bd=all_2988 on theBenchmark for (2988ds/499Mi)
% 6.55/2.20 % (720713)Refutation found. Thanks to Tanya!
% 6.55/2.20 % SZS status Unsatisfiable for theBenchmark
% 6.55/2.20 % SZS output start Proof for theBenchmark
% See solution above
% 6.55/2.29 % (720713)------------------------------
% 6.55/2.29 % (720713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/2.29 % (720713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/2.29 % (720713)CaDiCaL version: 2.1.3
% 6.55/2.29 % (720713)Termination reason: Refutation
% 6.55/2.29 % (720713)Time elapsed: 0.896 s
% 6.55/2.29 % (720713)Peak memory usage: 130 MB
% 6.55/2.29 % (720713)Instructions burned: 1358 (million)
% 6.55/2.29 % (720713)------------------------------
% 6.55/2.29 % (720713)------------------------------
% 6.55/2.29 % (720706)Success in time 1.332 s
% 6.55/2.29 % Vampire exiting
%------------------------------------------------------------------------------