%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET018+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:35 PM UTC 2026
% Result : Theorem 4.69s 1.55s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 135 ( 27 unt; 13 def)
% Number of atoms : 313 ( 55 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 325 ( 147 ~; 141 |; 20 &)
% ( 15 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 103 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f44,conjecture,
! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X1,universal_class) )
=> X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X1,universal_class) )
=> X1 = X3 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X1,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f48,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X1,universal_class) ),
inference(flattening,[],[f47]) ).
fof(f54,plain,
( sK1 != sK3
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3)
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f48]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(flattening,[],[f57]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
member(sK1,universal_class),
inference(cnf_transformation,[],[f54]) ).
fof(f71,plain,
ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ),
inference(cnf_transformation,[],[f58]) ).
fof(f89,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f99,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f103,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X2 ),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f69]) ).
fof(f109,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f89,f99,f99]) ).
fof(f111,plain,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),
inference(definition_unfolding,[],[f71,f109,f109]) ).
fof(f112,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)
| ~ member(X1,X3) ),
inference(definition_unfolding,[],[f79,f109]) ).
fof(f113,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,[],[f78,f109]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f77,f109]) ).
fof(f127,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f107]) ).
fof(f128,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f106]) ).
fof(f129,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(X0,X1))
| ~ member(sK2,X0)
| ~ member(sK3,X1) ),
inference(superposition,[],[f112,f111]) ).
fof(f130,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(X0,X1))
| member(sK2,X0) ),
inference(superposition,[],[f113,f111]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(X0,X1))
| member(sK3,X1) ),
inference(superposition,[],[f114,f111]) ).
fof(f139,plain,
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))))
| ~ member(unordered_pair(sK2,unordered_pair(sK3,sK3)),universal_class) ),
inference(superposition,[],[f128,f111]) ).
fof(f143,plain,
member(unordered_pair(sK2,unordered_pair(sK3,sK3)),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1)))),
inference(forward_subsumption_resolution,[],[f139,f103]) ).
fof(f213,definition,
( spl5_7
<=> member(sK0,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f214,plain,
( member(sK0,universal_class)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f215,plain,
( ~ member(sK0,universal_class)
| spl5_7 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f219,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
inference(resolution,[],[f143,f104]) ).
fof(f222,definition,
( spl5_8
<=> unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f224,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl5_9
<=> unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f228,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( spl5_8
| spl5_9 ),
inference(avatar_split_clause,[],[f219,f226,f222]) ).
fof(f235,plain,
! [X0,X1] :
( member(sK2,X0)
| ~ member(sK0,X0)
| ~ member(sK1,X1) ),
inference(resolution,[],[f130,f112]) ).
fof(f246,plain,
! [X0,X1] :
( ~ member(sK2,X0)
| ~ member(sK3,X1)
| member(sK1,X1) ),
inference(resolution,[],[f129,f114]) ).
fof(f260,plain,
( member(unordered_pair(sK3,sK3),unordered_pair(sK0,sK0))
| ~ member(unordered_pair(sK3,sK3),universal_class)
| ~ spl5_8 ),
inference(superposition,[],[f128,f224]) ).
fof(f263,plain,
( member(unordered_pair(sK3,sK3),unordered_pair(sK0,sK0))
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f260,f103]) ).
fof(f319,plain,
( member(unordered_pair(sK3,sK3),unordered_pair(sK0,unordered_pair(sK1,sK1)))
| ~ member(unordered_pair(sK3,sK3),universal_class)
| ~ spl5_9 ),
inference(superposition,[],[f128,f228]) ).
fof(f322,plain,
( member(unordered_pair(sK3,sK3),unordered_pair(sK0,unordered_pair(sK1,sK1)))
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f319,f103]) ).
fof(f339,plain,
( unordered_pair(sK1,sK1) = unordered_pair(sK3,sK3)
| sK0 = unordered_pair(sK3,sK3)
| ~ spl5_9 ),
inference(resolution,[],[f322,f104]) ).
fof(f342,definition,
( spl5_10
<=> sK0 = unordered_pair(sK3,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f344,plain,
( sK0 = unordered_pair(sK3,sK3)
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f346,definition,
( spl5_11
<=> unordered_pair(sK1,sK1) = unordered_pair(sK3,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f348,plain,
( unordered_pair(sK1,sK1) = unordered_pair(sK3,sK3)
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f349,plain,
( spl5_10
| spl5_11
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f339,f226,f346,f342]) ).
fof(f359,definition,
( spl5_12
<=> member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
fof(f360,plain,
( member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(universal_class,universal_class))
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f361,plain,
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),cross_product(universal_class,universal_class))
| spl5_12 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f444,plain,
( member(sK3,sK0)
| ~ member(sK3,universal_class)
| ~ spl5_10 ),
inference(superposition,[],[f128,f344]) ).
fof(f446,plain,
( member(sK0,universal_class)
| ~ spl5_10 ),
inference(superposition,[],[f103,f344]) ).
fof(f448,plain,
( $false
| spl5_7
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f446,f215]) ).
fof(f449,plain,
( spl5_7
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f448]) ).
fof(f451,definition,
( spl5_16
<=> member(sK3,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
fof(f453,plain,
( ~ member(sK3,universal_class)
| spl5_16 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f455,definition,
( spl5_17
<=> member(sK3,sK0) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
fof(f459,plain,
( ~ spl5_16
| spl5_17
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f444,f342,f455,f451]) ).
fof(f589,plain,
( ~ member(sK0,universal_class)
| ~ member(sK1,universal_class)
| spl5_12 ),
inference(resolution,[],[f361,f112]) ).
fof(f648,plain,
( sK0 = unordered_pair(sK3,sK3)
| sK0 = unordered_pair(sK3,sK3)
| ~ spl5_8 ),
inference(resolution,[],[f263,f104]) ).
fof(f650,plain,
( sK0 = unordered_pair(sK3,sK3)
| ~ spl5_8 ),
inference(duplicate_literal_removal,[],[f648]) ).
fof(f661,plain,
( ~ member(sK1,universal_class)
| ~ spl5_7
| spl5_12 ),
inference(forward_subsumption_resolution,[],[f589,f214]) ).
fof(f701,plain,
( $false
| ~ spl5_7
| spl5_12 ),
inference(forward_subsumption_resolution,[],[f661,f70]) ).
fof(f702,plain,
( ~ spl5_7
| spl5_12 ),
inference(avatar_contradiction_clause,[],[f701]) ).
fof(f737,definition,
( spl5_23
<=> ! [X0] : ~ member(sK1,X0) ),
introduced(definition,[new_symbols(definition,[spl5_23])],[avatar_definition]) ).
fof(f738,plain,
( ! [X0] : ~ member(sK1,X0)
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f866,plain,
( $false
| ~ spl5_23 ),
inference(resolution,[],[f738,f70]) ).
fof(f871,plain,
~ spl5_23,
inference(avatar_contradiction_clause,[],[f866]) ).
fof(f893,definition,
( spl5_27
<=> ! [X1] :
( ~ member(sK3,X1)
| member(sK1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition]) ).
fof(f894,plain,
( ! [X1] :
( member(sK1,X1)
| ~ member(sK3,X1) )
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f1055,definition,
( spl5_36
<=> ! [X0] :
( member(sK2,X0)
| ~ member(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_36])],[avatar_definition]) ).
fof(f1056,plain,
( ! [X0] :
( member(sK2,X0)
| ~ member(sK0,X0) )
| ~ spl5_36 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1057,plain,
( spl5_23
| spl5_36 ),
inference(avatar_split_clause,[],[f235,f1055,f737]) ).
fof(f1228,plain,
( ! [X0] :
( ~ member(X0,sK0)
| sK3 = X0
| sK3 = X0 )
| ~ spl5_10 ),
inference(superposition,[],[f104,f344]) ).
fof(f1233,plain,
( ! [X0] :
( ~ member(X0,sK0)
| sK3 = X0 )
| ~ spl5_10 ),
inference(duplicate_literal_removal,[],[f1228]) ).
fof(f1476,plain,
( sK1 = sK3
| ~ member(sK3,sK0)
| ~ spl5_10
| ~ spl5_27 ),
inference(resolution,[],[f1233,f894]) ).
fof(f1480,plain,
( ~ member(sK3,sK0)
| ~ spl5_10
| ~ spl5_27 ),
inference(forward_subsumption_resolution,[],[f1476,f72]) ).
fof(f1490,definition,
( spl5_45
<=> ! [X0] : ~ member(sK0,X0) ),
introduced(definition,[new_symbols(definition,[spl5_45])],[avatar_definition]) ).
fof(f1491,plain,
( ! [X0] : ~ member(sK0,X0)
| ~ spl5_45 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f1493,plain,
( $false
| ~ spl5_7
| ~ spl5_45 ),
inference(resolution,[],[f1491,f214]) ).
fof(f1499,plain,
( ~ spl5_7
| ~ spl5_45 ),
inference(avatar_contradiction_clause,[],[f1493]) ).
fof(f1658,plain,
( spl5_10
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f650,f222,f342]) ).
fof(f1663,plain,
( ~ spl5_17
| ~ spl5_10
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f1480,f893,f342,f455]) ).
fof(f1714,definition,
( spl5_49
<=> ! [X0] : ~ member(sK2,X0) ),
introduced(definition,[new_symbols(definition,[spl5_49])],[avatar_definition]) ).
fof(f1715,plain,
( ! [X0] : ~ member(sK2,X0)
| ~ spl5_49 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f1716,plain,
( spl5_27
| spl5_49 ),
inference(avatar_split_clause,[],[f246,f1714,f893]) ).
fof(f1741,plain,
( ! [X0] : ~ member(sK0,X0)
| ~ spl5_36
| ~ spl5_49 ),
inference(resolution,[],[f1056,f1715]) ).
fof(f1749,plain,
( spl5_45
| ~ spl5_36
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f1741,f1714,f1055,f1490]) ).
fof(f1944,plain,
( member(sK3,universal_class)
| ~ spl5_12 ),
inference(resolution,[],[f360,f131]) ).
fof(f1976,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK1,sK1))
| sK3 = X0
| sK3 = X0 )
| ~ spl5_11 ),
inference(superposition,[],[f104,f348]) ).
fof(f1981,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK1,sK1))
| sK3 = X0 )
| ~ spl5_11 ),
inference(duplicate_literal_removal,[],[f1976]) ).
fof(f2011,plain,
( $false
| ~ spl5_12
| spl5_16 ),
inference(forward_subsumption_resolution,[],[f1944,f453]) ).
fof(f2012,plain,
( ~ spl5_12
| spl5_16 ),
inference(avatar_contradiction_clause,[],[f2011]) ).
fof(f2220,plain,
( sK1 = sK3
| ~ member(sK1,universal_class)
| ~ spl5_11 ),
inference(resolution,[],[f1981,f127]) ).
fof(f2228,plain,
( ~ member(sK1,universal_class)
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f2220,f72]) ).
fof(f2231,plain,
( $false
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f2228,f70]) ).
fof(f2232,plain,
~ spl5_11,
inference(avatar_contradiction_clause,[],[f2231]) ).
cnf(s5,plain,
( spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f229]) ).
cnf(s8,plain,
( ~ spl5_9
| spl5_10
| spl5_11 ),
inference(sat_conversion,[],[f349]) ).
cnf(s13,plain,
( spl5_7
| ~ spl5_10 ),
inference(sat_conversion,[],[f449]) ).
cnf(s15,plain,
( ~ spl5_10
| ~ spl5_16
| spl5_17 ),
inference(sat_conversion,[],[f459]) ).
cnf(s21,plain,
( ~ spl5_7
| spl5_12 ),
inference(sat_conversion,[],[f702]) ).
cnf(s25,plain,
~ spl5_23,
inference(sat_conversion,[],[f871]) ).
cnf(s35,plain,
( spl5_23
| spl5_36 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s44,plain,
( ~ spl5_7
| ~ spl5_45 ),
inference(sat_conversion,[],[f1499]) ).
cnf(s50,plain,
( ~ spl5_8
| spl5_10 ),
inference(sat_conversion,[],[f1658]) ).
cnf(s51,plain,
( ~ spl5_10
| ~ spl5_17
| ~ spl5_27 ),
inference(sat_conversion,[],[f1663]) ).
cnf(s56,plain,
( spl5_27
| spl5_49 ),
inference(sat_conversion,[],[f1716]) ).
cnf(s59,plain,
( ~ spl5_36
| spl5_45
| ~ spl5_49 ),
inference(sat_conversion,[],[f1749]) ).
cnf(s72,plain,
( ~ spl5_12
| spl5_16 ),
inference(sat_conversion,[],[f2012]) ).
cnf(s92,plain,
~ spl5_11,
inference(sat_conversion,[],[f2232]) ).
cnf(s93,plain,
spl5_36,
inference(rat,[],[s35,s25]) ).
cnf(s94,plain,
( ~ spl5_9
| spl5_10 ),
inference(rat,[],[s8,s92]) ).
cnf(s95,plain,
spl5_10,
inference(rat,[],[s5,s94,s50]) ).
cnf(s96,plain,
spl5_7,
inference(rat,[],[s13,s95]) ).
cnf(s97,plain,
~ spl5_45,
inference(rat,[],[s44,s96]) ).
cnf(s98,plain,
spl5_12,
inference(rat,[],[s21,s96]) ).
cnf(s99,plain,
~ spl5_49,
inference(rat,[],[s59,s93,s97]) ).
cnf(s102,plain,
spl5_16,
inference(rat,[],[s72,s98]) ).
cnf(s104,plain,
spl5_27,
inference(rat,[],[s56,s99]) ).
cnf(s108,plain,
spl5_17,
inference(rat,[],[s15,s95,s102]) ).
cnf(s110,plain,
$false,
inference(rat,[],[s51,s95,s104,s108]) ).
fof(f2233,plain,
$false,
inference(avatar_sat_refutation,[],[s110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:11:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 4.69/1.54 % (4036471)Detected formulas, will run a generic FOF schedule.
% 4.69/1.54 % (4036480)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1082380094:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.69/1.54 % (4036480)Refutation not found, incomplete strategy
% 4.69/1.54 % (4036480)------------------------------
% 4.69/1.54 % (4036480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.54 % (4036480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.54 % (4036480)CaDiCaL version: 2.1.3
% 4.69/1.54 % (4036480)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.54 % (4036480)Time elapsed: 0.001 s
% 4.69/1.54 % (4036480)Peak memory usage: 88 MB
% 4.69/1.54 % (4036480)Instructions burned: 1 (million)
% 4.69/1.54 % (4036479)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3306302581:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.69/1.54 % (4036481)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3451245422:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.69/1.54 % (4036482)dis-21_1_sil=8000:lcm=predicate:random_seed=2666641192:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.69/1.54 % (4036476)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=4080715704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.69/1.54 % (4036478)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3918038246:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.69/1.54 % (4036477)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2407832986:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.69/1.54 % (4036479)Refutation not found, incomplete strategy
% 4.69/1.54 % (4036479)------------------------------
% 4.69/1.54 % (4036479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.54 % (4036479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.54 % (4036479)CaDiCaL version: 2.1.3
% 4.69/1.54 % (4036479)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.54 % (4036479)Time elapsed: 0.002 s
% 4.69/1.54 % (4036479)Peak memory usage: 88 MB
% 4.69/1.54 % (4036479)Instructions burned: 1 (million)
% 4.69/1.54 % (4036482)Instruction limit reached!
% 4.69/1.54 % (4036482)------------------------------
% 4.69/1.54 % (4036482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.54 % (4036482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.54 % (4036482)CaDiCaL version: 2.1.3
% 4.69/1.54 % (4036482)Termination reason: Instruction limit
% 4.69/1.54 % (4036482)Termination phase: Saturation
% 4.69/1.54 % (4036482)Time elapsed: 0.081 s
% 4.69/1.54 % (4036482)Peak memory usage: 89 MB
% 4.69/1.54 % (4036482)Instructions burned: 130 (million)
% 4.69/1.54 % (4036480)------------------------------
% 4.69/1.54 % (4036480)------------------------------
% 4.69/1.54 % (4036481)Instruction limit reached!
% 4.69/1.54 % (4036481)------------------------------
% 4.69/1.55 % (4036481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.55 % (4036481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.55 % (4036481)CaDiCaL version: 2.1.3
% 4.69/1.55 % (4036481)Termination reason: Instruction limit
% 4.69/1.55 % (4036481)Termination phase: Saturation
% 4.69/1.55 % (4036481)Time elapsed: 0.103 s
% 4.69/1.55 % (4036481)Peak memory usage: 90 MB
% 4.69/1.55 % (4036481)Instructions burned: 139 (million)
% 4.69/1.55 % (4036491)lrs+10_1_sil=32000:urr=on:br=off:random_seed=193407991:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.69/1.55 % (4036490)lrs+10_1_sil=8000:sp=occurrence:random_seed=1209390623:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.69/1.55 % (4036490)Refutation not found, incomplete strategy
% 4.69/1.55 % (4036490)------------------------------
% 4.69/1.55 % (4036490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.55 % (4036490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.55 % (4036490)CaDiCaL version: 2.1.3
% 4.69/1.55 % (4036490)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.55 % (4036490)Time elapsed: 0.002 s
% 4.69/1.55 % (4036490)Peak memory usage: 88 MB
% 4.69/1.55 % (4036490)Instructions burned: 1 (million)
% 4.69/1.55 % (4036479)------------------------------
% 4.69/1.55 % (4036479)------------------------------
% 4.69/1.55 % (4036491)Instruction limit reached!
% 4.69/1.55 % (4036491)------------------------------
% 4.69/1.55 % (4036491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.55 % (4036491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.55 % (4036491)CaDiCaL version: 2.1.3
% 4.69/1.55 % (4036491)Termination reason: Instruction limit
% 4.69/1.55 % (4036491)Termination phase: Saturation
% 4.69/1.55 % (4036491)Time elapsed: 0.040 s
% 4.69/1.55 % (4036491)Peak memory usage: 90 MB
% 4.69/1.55 % (4036491)Instructions burned: 160 (million)
% 4.69/1.55 % (4036492)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1547333872:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.69/1.55 % (4036496)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2303743360:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.69/1.55 % (4036496)First to succeed.
% 4.69/1.55 % (4036495)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2987387328:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.69/1.55 % (4036496)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4036471"
% 4.69/1.55 % (4036492)Instruction limit reached!
% 4.69/1.55 % (4036492)------------------------------
% 4.69/1.55 % (4036492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.55 % (4036492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.55 % (4036492)CaDiCaL version: 2.1.3
% 4.69/1.55 % (4036492)Termination reason: Instruction limit
% 4.69/1.55 % (4036492)Termination phase: Saturation
% 4.69/1.55 % (4036492)Time elapsed: 0.200 s
% 4.69/1.55 % (4036492)Peak memory usage: 91 MB
% 4.69/1.55 % (4036492)Instructions burned: 326 (million)
% 4.69/1.55 % (4036490)------------------------------
% 4.69/1.55 % (4036490)------------------------------
% 4.69/1.55 % (4036495)Instruction limit reached!
% 4.69/1.55 % (4036495)------------------------------
% 4.69/1.55 % (4036495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.55 % (4036495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.55 % (4036495)CaDiCaL version: 2.1.3
% 4.69/1.55 % (4036495)Termination reason: Instruction limit
% 4.69/1.55 % (4036495)Termination phase: Saturation
% 4.69/1.55 % (4036495)Time elapsed: 0.134 s
% 4.69/1.55 % (4036495)Peak memory usage: 93 MB
% 4.69/1.55 % (4036495)Instructions burned: 249 (million)
% 4.69/1.55 % (4036496)Refutation found. Thanks to Tanya!
% 4.69/1.55 % SZS status Theorem for theBenchmark
% 4.69/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.79/1.74 % (4036496)------------------------------
% 5.79/1.74 % (4036496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.79/1.74 % (4036496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.79/1.74 % (4036496)CaDiCaL version: 2.1.3
% 5.79/1.74 % (4036496)Termination reason: Refutation
% 5.79/1.74 % (4036496)Time elapsed: 0.036 s
% 5.79/1.74 % (4036496)Peak memory usage: 90 MB
% 5.79/1.74 % (4036496)Instructions burned: 115 (million)
% 5.79/1.74 % (4036496)------------------------------
% 5.79/1.74 % (4036496)------------------------------
% 5.79/1.74 % (4036471)Success in time 0.747 s
% 5.79/1.74 % Vampire exiting
%------------------------------------------------------------------------------