%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET509-6 : 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 : n008.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 12:41:04 PM UTC 2026
% Result : Unsatisfiable 13.09s 3.00s
% Output : Refutation 14.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of formulae : 156 ( 30 unt; 11 def)
% Number of atoms : 351 ( 85 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 327 ( 132 ~; 186 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 100 ( 0 sgn 100 !; 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(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(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
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(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(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,
unordered_pair(universal_class,x) != singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_singleton_in_unordered_pair_1) ).
fof(f143,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(f185,plain,
unordered_pair(universal_class,x) != unordered_pair(x,x),
inference(definition_unfolding,[],[f122,f12]) ).
fof(f190,definition,
sF0 = unordered_pair(universal_class,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f191,plain,
unordered_pair(universal_class,x) = sF0,
inference(reorient_equations,[],[f190]) ).
fof(f192,definition,
sF1 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f193,plain,
unordered_pair(x,x) = sF1,
inference(reorient_equations,[],[f192]) ).
fof(f194,plain,
sF0 != sF1,
inference(definition_folding,[],[f185,f193,f191]) ).
fof(f195,plain,
( member(x,sF1)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f193]) ).
fof(f198,definition,
( spl2_1
<=> member(universal_class,universal_class) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f199,plain,
( member(universal_class,universal_class)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( ~ member(universal_class,universal_class)
| spl2_1 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f207,definition,
( spl2_3
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f208,plain,
( member(x,universal_class)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( ~ member(x,universal_class)
| spl2_3 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl2_4
<=> member(x,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f213,plain,
( member(x,sF1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f195,f211,f207]) ).
fof(f216,plain,
( member(x,sF0)
| ~ member(x,universal_class) ),
inference(superposition,[],[f10,f191]) ).
fof(f219,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f193]) ).
fof(f220,plain,
! [X0] :
( ~ member(X0,sF0)
| universal_class = X0
| x = X0 ),
inference(superposition,[],[f8,f191]) ).
fof(f221,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0 ),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f223,plain,
! [X0] :
( subclass(sF1,X0)
| x = not_subclass_element(sF1,X0) ),
inference(resolution,[],[f2,f221]) ).
fof(f224,plain,
! [X0] :
( ~ subclass(X0,sF1)
| x = not_subclass_element(sF1,X0)
| sF1 = X0 ),
inference(resolution,[],[f223,f7]) ).
fof(f230,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f234,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f238,plain,
! [X0] :
( subclass(sF0,X0)
| x = not_subclass_element(sF0,X0)
| universal_class = not_subclass_element(sF0,X0) ),
inference(resolution,[],[f220,f2]) ).
fof(f239,plain,
! [X0] :
( ~ subclass(X0,sF0)
| universal_class = not_subclass_element(sF0,X0)
| x = not_subclass_element(sF0,X0)
| sF0 = X0 ),
inference(resolution,[],[f238,f7]) ).
fof(f240,plain,
( x = not_subclass_element(sF0,sF1)
| universal_class = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF1,sF0)
| sF0 = sF1 ),
inference(resolution,[],[f238,f224]) ).
fof(f241,plain,
( x = not_subclass_element(sF0,sF1)
| universal_class = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF1,sF0) ),
inference(forward_subsumption_resolution,[],[f240,f194]) ).
fof(f243,definition,
( spl2_5
<=> x = not_subclass_element(sF1,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f244,plain,
( x != not_subclass_element(sF1,sF0)
| spl2_5 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( x = not_subclass_element(sF1,sF0)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f247,definition,
( spl2_6
<=> universal_class = not_subclass_element(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f248,plain,
( universal_class != not_subclass_element(sF0,sF1)
| spl2_6 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( universal_class = not_subclass_element(sF0,sF1)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f251,definition,
( spl2_7
<=> x = not_subclass_element(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f252,plain,
( x != not_subclass_element(sF0,sF1)
| spl2_7 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( x = not_subclass_element(sF0,sF1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( spl2_5
| spl2_6
| spl2_7 ),
inference(avatar_split_clause,[],[f241,f251,f247,f243]) ).
fof(f255,plain,
( ~ member(x,sF0)
| subclass(sF1,sF0)
| ~ spl2_5 ),
inference(superposition,[],[f3,f245]) ).
fof(f256,plain,
( member(x,sF1)
| subclass(sF1,sF0)
| ~ spl2_5 ),
inference(superposition,[],[f2,f245]) ).
fof(f258,definition,
( spl2_8
<=> subclass(sF1,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f260,plain,
( subclass(sF1,sF0)
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( spl2_8
| spl2_4
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f256,f243,f211,f258]) ).
fof(f263,definition,
( spl2_9
<=> member(x,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f265,plain,
( ~ member(x,sF0)
| spl2_9 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( spl2_8
| ~ spl2_9
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f255,f243,f263,f258]) ).
fof(f278,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f234,f3]) ).
fof(f285,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f301,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f68,f8]) ).
fof(f334,plain,
! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(equality_factoring,[],[f301]) ).
fof(f340,plain,
! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = null_class ),
inference(equality_resolution,[],[f334]) ).
fof(f351,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f352,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[],[f23,f3]) ).
fof(f355,plain,
! [X0] :
( null_class = intersection(unordered_pair(X0,X0),X0)
| unordered_pair(X0,X0) = null_class
| unordered_pair(X0,X0) = null_class ),
inference(superposition,[],[f70,f340]) ).
fof(f362,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f285,f70]) ).
fof(f364,plain,
! [X0] :
( null_class = intersection(unordered_pair(X0,X0),X0)
| unordered_pair(X0,X0) = null_class ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f380,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f362,f7]) ).
fof(f385,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f380]) ).
fof(f396,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f385,f285]) ).
fof(f417,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f143,f396]) ).
fof(f418,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f417]) ).
fof(f422,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f418,f68]) ).
fof(f428,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f418,f422]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f351,f4]) ).
fof(f443,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f438,f2]) ).
fof(f452,plain,
( ! [X0] :
( ~ member(x,X0)
| member(x,universal_class) )
| ~ spl2_4 ),
inference(resolution,[],[f438,f213]) ).
fof(f453,plain,
( ! [X0] : ~ member(x,X0)
| spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f452,f209]) ).
fof(f457,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(resolution,[],[f453,f213]) ).
fof(f458,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f459,plain,
( ~ member(x,universal_class)
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f216,f265]) ).
fof(f460,plain,
( $false
| ~ spl2_3
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f459,f208]) ).
fof(f461,plain,
( ~ spl2_3
| spl2_9 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f546,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f443,f2]) ).
fof(f557,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f546]) ).
fof(f587,plain,
( member(universal_class,universal_class)
| subclass(sF0,sF1)
| ~ spl2_6 ),
inference(superposition,[],[f557,f249]) ).
fof(f593,definition,
( spl2_19
<=> subclass(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f594,plain,
( ~ subclass(sF0,sF1)
| spl2_19 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f595,plain,
( subclass(sF0,sF1)
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f607,plain,
( subclass(sF0,sF1)
| spl2_1
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f587,f200]) ).
fof(f612,plain,
( spl2_19
| spl2_1
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f607,f247,f198,f593]) ).
fof(f742,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[],[f352,f230]) ).
fof(f751,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) ),
inference(duplicate_literal_removal,[],[f742]) ).
fof(f1052,plain,
! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[],[f751,f2]) ).
fof(f1069,plain,
! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f1052]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X1),X0)
| intersection(X0,X1) = X0 ),
inference(resolution,[],[f1069,f7]) ).
fof(f1085,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| intersection(X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f1071,f285]) ).
fof(f1086,plain,
! [X0] : intersection(X0,universal_class) = X0,
inference(resolution,[],[f1085,f4]) ).
fof(f1108,plain,
( null_class = unordered_pair(universal_class,universal_class)
| null_class = unordered_pair(universal_class,universal_class) ),
inference(superposition,[],[f364,f1086]) ).
fof(f1109,plain,
null_class = unordered_pair(universal_class,universal_class),
inference(duplicate_literal_removal,[],[f1108]) ).
fof(f1117,plain,
( member(universal_class,null_class)
| ~ member(universal_class,universal_class) ),
inference(superposition,[],[f9,f1109]) ).
fof(f1128,plain,
~ member(universal_class,universal_class),
inference(forward_subsumption_resolution,[],[f1117,f428]) ).
fof(f1131,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f1128,f199]) ).
fof(f1132,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f1131]) ).
fof(f1140,plain,
( ~ member(x,sF1)
| subclass(sF0,sF1)
| ~ spl2_7 ),
inference(superposition,[],[f3,f253]) ).
fof(f1142,plain,
( subclass(sF0,sF1)
| ~ spl2_4
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f1140,f213]) ).
fof(f1143,plain,
( spl2_19
| ~ spl2_4
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f1142,f251,f211,f593]) ).
fof(f1146,plain,
( x = not_subclass_element(sF1,sF0)
| sF0 = sF1
| ~ spl2_19 ),
inference(resolution,[],[f595,f224]) ).
fof(f1148,plain,
( ~ subclass(sF1,sF0)
| sF0 = sF1
| ~ spl2_19 ),
inference(resolution,[],[f595,f7]) ).
fof(f1149,plain,
( ~ subclass(sF1,sF0)
| ~ spl2_19 ),
inference(forward_subsumption_resolution,[],[f1148,f194]) ).
fof(f1150,plain,
( sF0 = sF1
| spl2_5
| ~ spl2_19 ),
inference(forward_subsumption_resolution,[],[f1146,f244]) ).
fof(f1151,plain,
( ~ spl2_8
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f1149,f593,f258]) ).
fof(f1152,plain,
( $false
| spl2_5
| ~ spl2_19 ),
inference(forward_subsumption_resolution,[],[f1150,f194]) ).
fof(f1153,plain,
( spl2_5
| ~ spl2_19 ),
inference(avatar_contradiction_clause,[],[f1152]) ).
fof(f1157,plain,
( universal_class = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF0,sF1)
| sF0 = sF1
| ~ spl2_8 ),
inference(resolution,[],[f260,f239]) ).
fof(f1160,plain,
( x = not_subclass_element(sF0,sF1)
| sF0 = sF1
| spl2_6
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f1157,f248]) ).
fof(f1161,plain,
( sF0 = sF1
| spl2_6
| spl2_7
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f1160,f252]) ).
fof(f1162,plain,
( $false
| spl2_6
| spl2_7
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f1161,f194]) ).
fof(f1163,plain,
( spl2_6
| spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f1162]) ).
fof(f1209,plain,
( member(x,universal_class)
| subclass(sF0,sF1)
| ~ spl2_7 ),
inference(superposition,[],[f557,f253]) ).
fof(f1216,plain,
( subclass(sF0,sF1)
| spl2_3
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f1209,f209]) ).
fof(f1219,plain,
( $false
| spl2_3
| ~ spl2_7
| spl2_19 ),
inference(forward_subsumption_resolution,[],[f1216,f594]) ).
fof(f1220,plain,
( spl2_3
| ~ spl2_7
| spl2_19 ),
inference(avatar_contradiction_clause,[],[f1219]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f214]) ).
cnf(s3,plain,
( spl2_5
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f254]) ).
cnf(s4,plain,
( spl2_4
| ~ spl2_5
| spl2_8 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( ~ spl2_5
| spl2_8
| ~ spl2_9 ),
inference(sat_conversion,[],[f266]) ).
cnf(s11,plain,
( spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f458]) ).
cnf(s12,plain,
( ~ spl2_3
| spl2_9 ),
inference(sat_conversion,[],[f461]) ).
cnf(s25,plain,
( spl2_1
| ~ spl2_6
| spl2_19 ),
inference(sat_conversion,[],[f612]) ).
cnf(s38,plain,
~ spl2_1,
inference(sat_conversion,[],[f1132]) ).
cnf(s41,plain,
( ~ spl2_4
| ~ spl2_7
| spl2_19 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s42,plain,
( ~ spl2_8
| ~ spl2_19 ),
inference(sat_conversion,[],[f1151]) ).
cnf(s43,plain,
( spl2_5
| ~ spl2_19 ),
inference(sat_conversion,[],[f1153]) ).
cnf(s44,plain,
( spl2_6
| spl2_7
| ~ spl2_8 ),
inference(sat_conversion,[],[f1163]) ).
cnf(s59,plain,
( spl2_3
| ~ spl2_7
| spl2_19 ),
inference(sat_conversion,[],[f1220]) ).
cnf(s62,plain,
( ~ spl2_6
| spl2_19 ),
inference(rat,[],[s25,s38]) ).
cnf(s68,plain,
( spl2_5
| spl2_3 ),
inference(rat,[],[s3,s59,s62,s43]) ).
cnf(s69,plain,
spl2_3,
inference(rat,[],[s44,s59,s62,s42,s4,s68,s11]) ).
cnf(s70,plain,
spl2_9,
inference(rat,[],[s12,s69]) ).
cnf(s71,plain,
spl2_4,
inference(rat,[],[s2,s69]) ).
cnf(s78,plain,
spl2_5,
inference(rat,[],[s3,s41,s62,s43,s71]) ).
cnf(s79,plain,
spl2_8,
inference(rat,[],[s5,s70,s78]) ).
cnf(s80,plain,
~ spl2_19,
inference(rat,[],[s42,s79]) ).
cnf(s81,plain,
~ spl2_6,
inference(rat,[],[s62,s80]) ).
cnf(s82,plain,
~ spl2_7,
inference(rat,[],[s41,s71,s80]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s44,s79,s81,s82]) ).
fof(f1221,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET509-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:02:09 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 13.09/3.00 % (1800293)Input is clausal, will run a generic CNF schedule.
% 13.09/3.00 % (1800305)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2123467884:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 13.09/3.00 % (1800302)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3535731707:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 13.09/3.00 % (1800303)lrs+10_1_sil=8000:sp=occurrence:random_seed=928839318:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 13.09/3.00 % (1800301)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2500306335:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 13.09/3.00 % (1800300)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=3273080261:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 13.09/3.00 % (1800304)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2216326398:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 13.09/3.00 % (1800303)Refutation not found, incomplete strategy
% 13.09/3.00 % (1800303)------------------------------
% 13.09/3.00 % (1800303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800303)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800303)Termination reason: Refutation not found, incomplete strategy
% 13.09/3.00 % (1800303)Time elapsed: 0.003 s
% 13.09/3.00 % (1800303)Peak memory usage: 87 MB
% 13.09/3.00 % (1800303)Instructions burned: 1 (million)
% 13.09/3.00 % (1800306)dis-21_1_sil=8000:lcm=predicate:random_seed=1366236759: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)
% 13.09/3.00 % (1800305)Instruction limit reached!
% 13.09/3.00 % (1800305)------------------------------
% 13.09/3.00 % (1800305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800305)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800305)Termination reason: Instruction limit
% 13.09/3.00 % (1800305)Termination phase: Saturation
% 13.09/3.00 % (1800305)Time elapsed: 0.111 s
% 13.09/3.00 % (1800305)Peak memory usage: 90 MB
% 13.09/3.00 % (1800305)Instructions burned: 181 (million)
% 13.09/3.00 % (1800304)Instruction limit reached!
% 13.09/3.00 % (1800304)------------------------------
% 13.09/3.00 % (1800304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800304)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800304)Termination reason: Instruction limit
% 13.09/3.00 % (1800304)Termination phase: Saturation
% 13.09/3.00 % (1800304)Time elapsed: 0.111 s
% 13.09/3.00 % (1800304)Peak memory usage: 88 MB
% 13.09/3.00 % (1800304)Instructions burned: 114 (million)
% 13.09/3.00 % (1800306)Instruction limit reached!
% 13.09/3.00 % (1800306)------------------------------
% 13.09/3.00 % (1800306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800306)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800306)Termination reason: Instruction limit
% 13.09/3.00 % (1800306)Termination phase: Saturation
% 13.09/3.00 % (1800306)Time elapsed: 0.113 s
% 13.09/3.00 % (1800306)Peak memory usage: 89 MB
% 13.09/3.00 % (1800306)Instructions burned: 118 (million)
% 13.09/3.00 % (1800314)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=231940412:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 13.09/3.00 % (1800314)Refutation not found, incomplete strategy
% 13.09/3.00 % (1800314)------------------------------
% 13.09/3.00 % (1800314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800314)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800314)Termination reason: Refutation not found, incomplete strategy
% 13.09/3.00 % (1800314)Time elapsed: 0.005 s
% 13.09/3.00 % (1800314)Peak memory usage: 88 MB
% 13.09/3.00 % (1800314)Instructions burned: 3 (million)
% 13.09/3.00 % (1800315)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=366974276:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 13.09/3.00 % (1800316)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3713823126:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 13.09/3.00 % (1800316)Refutation not found, incomplete strategy
% 13.09/3.00 % (1800316)------------------------------
% 13.09/3.00 % (1800316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800316)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800316)Termination reason: Refutation not found, incomplete strategy
% 13.09/3.00 % (1800316)Time elapsed: 0.004 s
% 13.09/3.00 % (1800316)Peak memory usage: 88 MB
% 13.09/3.00 % (1800316)Instructions burned: 3 (million)
% 13.09/3.00 % (1800303)------------------------------
% 13.09/3.00 % (1800303)------------------------------
% 13.09/3.00 % (1800315)Instruction limit reached!
% 13.09/3.00 % (1800315)------------------------------
% 13.09/3.00 % (1800315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800315)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800315)Termination reason: Instruction limit
% 13.09/3.00 % (1800315)Termination phase: Saturation
% 13.09/3.00 % (1800315)Time elapsed: 0.092 s
% 13.09/3.00 % (1800315)Peak memory usage: 90 MB
% 13.09/3.00 % (1800315)Instructions burned: 191 (million)
% 13.09/3.00 % (1800316)------------------------------
% 13.09/3.00 % (1800316)------------------------------
% 13.09/3.00 % (1800321)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3386283079:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 13.09/3.00 % (1800314)------------------------------
% 13.09/3.00 % (1800314)------------------------------
% 13.09/3.00 % (1800320)lrs+10_64_to=lpo:sil=8000:random_seed=2499117688:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 13.09/3.00 % (1800321)Instruction limit reached!
% 13.09/3.00 % (1800321)------------------------------
% 13.09/3.00 % (1800321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800321)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800321)Termination reason: Instruction limit
% 13.09/3.00 % (1800321)Termination phase: Saturation
% 13.09/3.00 % (1800321)Time elapsed: 0.100 s
% 13.09/3.00 % (1800321)Peak memory usage: 89 MB
% 13.09/3.00 % (1800321)Instructions burned: 194 (million)
% 13.09/3.00 % (1800320)Instruction limit reached!
% 13.09/3.00 % (1800320)------------------------------
% 13.09/3.00 % (1800320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800320)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800320)Termination reason: Instruction limit
% 13.09/3.00 % (1800320)Termination phase: Saturation
% 13.09/3.00 % (1800320)Time elapsed: 0.130 s
% 13.09/3.00 % (1800320)Peak memory usage: 89 MB
% 13.09/3.00 % (1800320)Instructions burned: 126 (million)
% 13.09/3.00 % (1800322)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3893698024:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 13.09/3.00 % (1800324)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3843646996:i=3394:sd=4:ss=included:sgt=64_2990 on theBenchmark for (2990ds/3394Mi)
% 13.09/3.00 % (1800326)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=412404735:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2990 on theBenchmark for (2990ds/106Mi)
% 13.09/3.00 % (1800326)Instruction limit reached!
% 13.09/3.00 % (1800326)------------------------------
% 13.09/3.00 % (1800326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800326)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800326)Termination reason: Instruction limit
% 13.09/3.00 % (1800326)Termination phase: Saturation
% 13.09/3.00 % (1800326)Time elapsed: 0.048 s
% 13.09/3.00 % (1800326)Peak memory usage: 94 MB
% 13.09/3.00 % (1800326)Instructions burned: 108 (million)
% 13.09/3.00 % (1800322)Instruction limit reached!
% 13.09/3.00 % (1800322)------------------------------
% 13.09/3.00 % (1800322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800322)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800322)Termination reason: Instruction limit
% 13.09/3.00 % (1800322)Termination phase: Saturation
% 13.09/3.00 % (1800322)Time elapsed: 0.174 s
% 13.09/3.00 % (1800322)Peak memory usage: 90 MB
% 13.09/3.00 % (1800322)Instructions burned: 158 (million)
% 13.09/3.00 % (1800327)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3730219250:i=107_2989 on theBenchmark for (2989ds/107Mi)
% 13.09/3.00 % (1800327)Refutation not found, incomplete strategy
% 13.09/3.00 % (1800327)------------------------------
% 13.09/3.00 % (1800327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800327)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800327)Termination reason: Refutation not found, incomplete strategy
% 13.09/3.00 % (1800327)Time elapsed: 0.009 s
% 13.09/3.00 % (1800327)Peak memory usage: 88 MB
% 13.09/3.00 % (1800327)Instructions burned: 8 (million)
% 13.09/3.00 % (1800331)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1779128485:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2987 on theBenchmark for (2987ds/242Mi)
% 13.09/3.00 % (1800300)First to succeed.
% 13.09/3.00 % (1800300)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1800293"
% 13.09/3.00 % (1800332)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3525400408:cond=fast:i=5208:av=off_2986 on theBenchmark for (2986ds/5208Mi)
% 13.09/3.00 % (1800302)Also succeeded, but the first one will report.
% 13.09/3.00 % (1800331)Instruction limit reached!
% 13.09/3.00 % (1800331)------------------------------
% 13.09/3.00 % (1800331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.09/3.00 % (1800331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.09/3.00 % (1800331)CaDiCaL version: 2.1.3
% 13.09/3.00 % (1800331)Termination reason: Instruction limit
% 13.09/3.00 % (1800331)Termination phase: Saturation
% 13.09/3.00 % (1800331)Time elapsed: 0.271 s
% 13.09/3.00 % (1800331)Peak memory usage: 90 MB
% 13.09/3.00 % (1800331)Instructions burned: 242 (million)
% 13.09/3.00 % (1800327)------------------------------
% 13.09/3.00 % (1800327)------------------------------
% 13.09/3.00 % (1800300)Refutation found. Thanks to Tanya!
% 13.09/3.00 % SZS status Unsatisfiable for theBenchmark
% 13.09/3.00 % SZS output start Proof for theBenchmark
% See solution above
% 14.56/3.27 % (1800300)------------------------------
% 14.56/3.27 % (1800300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.56/3.27 % (1800300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.56/3.27 % (1800300)CaDiCaL version: 2.1.3
% 14.56/3.27 % (1800300)Termination reason: Refutation
% 14.56/3.27 % (1800300)Time elapsed: 1.263 s
% 14.56/3.27 % (1800300)Peak memory usage: 131 MB
% 14.56/3.27 % (1800300)Instructions burned: 1157 (million)
% 14.56/3.27 % (1800300)------------------------------
% 14.56/3.27 % (1800300)------------------------------
% 14.56/3.27 % (1800293)Success in time 1.943 s
% 14.56/3.27 % Vampire exiting
%------------------------------------------------------------------------------