%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET066+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 : n018.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 12:39:54 PM UTC 2026
% Result : Theorem 5.91s 1.89s
% Output : Refutation 7.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 157 ( 20 unt; 14 def)
% Number of atoms : 404 ( 71 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 398 ( 151 ~; 212 |; 18 &)
% ( 16 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
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(f44,conjecture,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f60,plain,
? [X0,X1] : unordered_pair(X0,X1) != unordered_pair(X1,X0),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f64]) ).
fof(f66,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(f67,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,[],[f66]) ).
fof(f103,plain,
unordered_pair(sK6,sK7) != unordered_pair(sK7,sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f110,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f67]) ).
fof(f113,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f191,plain,
unordered_pair(sK6,sK7) != unordered_pair(sK7,sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f231,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f232,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f113]) ).
fof(f235,definition,
sF8 = unordered_pair(sK6,sK7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f236,plain,
unordered_pair(sK6,sK7) = sF8,
inference(reorient_equations,[],[f235]) ).
fof(f237,definition,
sF9 = unordered_pair(sK7,sK6),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f238,plain,
unordered_pair(sK7,sK6) = sF9,
inference(reorient_equations,[],[f237]) ).
fof(f239,plain,
sF8 != sF9,
inference(definition_folding,[],[f191,f238,f236]) ).
fof(f240,plain,
! [X0] :
( ~ member(X0,sF8)
| sK7 = X0
| sK6 = X0 ),
inference(superposition,[],[f111,f236]) ).
fof(f241,plain,
! [X0] :
( ~ member(X0,sF9)
| sK6 = X0
| sK7 = X0 ),
inference(superposition,[],[f111,f238]) ).
fof(f243,plain,
( member(sK7,sF8)
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f232,f236]) ).
fof(f244,plain,
( member(sK6,sF9)
| ~ member(sK6,universal_class) ),
inference(superposition,[],[f232,f238]) ).
fof(f246,definition,
( spl10_1
<=> member(sK6,universal_class) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f247,plain,
( member(sK6,universal_class)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ member(sK6,universal_class)
| spl10_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl10_2
<=> member(sK6,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f252,plain,
( member(sK6,sF9)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f244,f250,f246]) ).
fof(f255,definition,
( spl10_3
<=> member(sK7,universal_class) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f256,plain,
( member(sK7,universal_class)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ member(sK7,universal_class)
| spl10_3 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl10_4
<=> member(sK7,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f262,plain,
( ~ spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f243,f259,f255]) ).
fof(f264,plain,
( member(sK6,sF8)
| ~ member(sK6,universal_class) ),
inference(superposition,[],[f231,f236]) ).
fof(f265,plain,
( member(sK7,sF9)
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f231,f238]) ).
fof(f268,plain,
! [X0] :
( ~ member(X0,sF8)
| member(X0,universal_class) ),
inference(superposition,[],[f112,f236]) ).
fof(f269,plain,
! [X0] :
( ~ member(X0,sF9)
| member(X0,universal_class) ),
inference(superposition,[],[f112,f238]) ).
fof(f275,plain,
! [X0] :
( subclass(sF8,X0)
| sK7 = sK0(sF8,X0)
| sK6 = sK0(sF8,X0) ),
inference(resolution,[],[f105,f240]) ).
fof(f276,plain,
! [X0] :
( member(sK0(sF8,X0),universal_class)
| subclass(sF8,X0) ),
inference(resolution,[],[f105,f268]) ).
fof(f277,plain,
! [X0] :
( subclass(sF9,X0)
| sK6 = sK0(sF9,X0)
| sK7 = sK0(sF9,X0) ),
inference(resolution,[],[f105,f241]) ).
fof(f278,plain,
! [X0] :
( member(sK0(sF9,X0),universal_class)
| subclass(sF9,X0) ),
inference(resolution,[],[f105,f269]) ).
fof(f280,plain,
! [X0] :
( ~ subclass(X0,sF8)
| sK6 = sK0(sF8,X0)
| sK7 = sK0(sF8,X0)
| sF8 = X0 ),
inference(resolution,[],[f275,f110]) ).
fof(f287,plain,
( sK6 = sK0(sF8,sF9)
| sK7 = sK0(sF8,sF9)
| sF8 = sF9
| sK6 = sK0(sF9,sF8)
| sK7 = sK0(sF9,sF8) ),
inference(resolution,[],[f280,f277]) ).
fof(f289,plain,
( sK6 = sK0(sF8,sF9)
| sK7 = sK0(sF8,sF9)
| sK6 = sK0(sF9,sF8)
| sK7 = sK0(sF9,sF8) ),
inference(forward_subsumption_resolution,[],[f287,f239]) ).
fof(f291,definition,
( spl10_5
<=> sK7 = sK0(sF9,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f292,plain,
( sK7 != sK0(sF9,sF8)
| spl10_5 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( sK7 = sK0(sF9,sF8)
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,definition,
( spl10_6
<=> sK6 = sK0(sF9,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f296,plain,
( sK6 != sK0(sF9,sF8)
| spl10_6 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( sK6 = sK0(sF9,sF8)
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,definition,
( spl10_7
<=> sK7 = sK0(sF8,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f300,plain,
( sK7 != sK0(sF8,sF9)
| spl10_7 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f301,plain,
( sK7 = sK0(sF8,sF9)
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f303,definition,
( spl10_8
<=> sK6 = sK0(sF8,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f305,plain,
( sK6 = sK0(sF8,sF9)
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f306,plain,
( spl10_5
| spl10_6
| spl10_7
| spl10_8 ),
inference(avatar_split_clause,[],[f289,f303,f299,f295,f291]) ).
fof(f307,plain,
( member(sK7,universal_class)
| subclass(sF9,sF8)
| ~ spl10_5 ),
inference(superposition,[],[f278,f293]) ).
fof(f308,plain,
( member(sK7,sF9)
| subclass(sF9,sF8)
| ~ spl10_5 ),
inference(superposition,[],[f105,f293]) ).
fof(f309,plain,
( ~ member(sK7,sF8)
| subclass(sF9,sF8)
| ~ spl10_5 ),
inference(superposition,[],[f106,f293]) ).
fof(f311,definition,
( spl10_9
<=> subclass(sF9,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f312,plain,
( ~ subclass(sF9,sF8)
| spl10_9 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f313,plain,
( subclass(sF9,sF8)
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f314,plain,
( spl10_9
| ~ spl10_4
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f309,f291,f259,f311]) ).
fof(f316,definition,
( spl10_10
<=> member(sK7,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f317,plain,
( ~ member(sK7,sF9)
| spl10_10 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( member(sK7,sF9)
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f319,plain,
( spl10_9
| spl10_10
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f308,f291,f316,f311]) ).
fof(f320,plain,
( subclass(sF9,sF8)
| spl10_3
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f307,f257]) ).
fof(f321,plain,
( spl10_9
| spl10_3
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f320,f291,f255,f311]) ).
fof(f322,plain,
( member(sK6,universal_class)
| subclass(sF9,sF8)
| ~ spl10_6 ),
inference(superposition,[],[f278,f297]) ).
fof(f324,plain,
( ~ member(sK6,sF8)
| subclass(sF9,sF8)
| ~ spl10_6 ),
inference(superposition,[],[f106,f297]) ).
fof(f326,definition,
( spl10_11
<=> member(sK6,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f328,plain,
( ~ member(sK6,sF8)
| spl10_11 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f329,plain,
( spl10_9
| ~ spl10_11
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f324,f295,f326,f311]) ).
fof(f331,plain,
( subclass(sF9,sF8)
| spl10_1
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f322,f248]) ).
fof(f332,plain,
( spl10_9
| spl10_1
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f331,f295,f246,f311]) ).
fof(f333,plain,
( member(sK7,universal_class)
| subclass(sF8,sF9)
| ~ spl10_7 ),
inference(superposition,[],[f276,f301]) ).
fof(f335,plain,
( ~ member(sK7,sF9)
| subclass(sF8,sF9)
| ~ spl10_7 ),
inference(superposition,[],[f106,f301]) ).
fof(f337,definition,
( spl10_12
<=> subclass(sF8,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
fof(f338,plain,
( ~ subclass(sF8,sF9)
| spl10_12 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f339,plain,
( subclass(sF8,sF9)
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f340,plain,
( spl10_12
| ~ spl10_10
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f335,f299,f316,f337]) ).
fof(f342,plain,
( subclass(sF8,sF9)
| spl10_3
| ~ spl10_7 ),
inference(forward_subsumption_resolution,[],[f333,f257]) ).
fof(f343,plain,
( spl10_12
| spl10_3
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f342,f299,f255,f337]) ).
fof(f344,plain,
( ~ member(sK7,universal_class)
| spl10_10 ),
inference(forward_subsumption_resolution,[],[f265,f317]) ).
fof(f345,plain,
( $false
| ~ spl10_3
| spl10_10 ),
inference(forward_subsumption_resolution,[],[f344,f256]) ).
fof(f346,plain,
( ~ spl10_3
| spl10_10 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f348,plain,
( member(sK7,universal_class)
| ~ spl10_10 ),
inference(resolution,[],[f318,f269]) ).
fof(f349,plain,
( ~ subclass(sF9,sF8)
| sF8 = sF9
| ~ spl10_12 ),
inference(resolution,[],[f339,f110]) ).
fof(f350,plain,
( ~ subclass(sF9,sF8)
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f349,f239]) ).
fof(f351,plain,
( ~ spl10_9
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f350,f337,f311]) ).
fof(f352,plain,
( sK6 = sK0(sF9,sF8)
| sK7 = sK0(sF9,sF8)
| spl10_9 ),
inference(resolution,[],[f312,f277]) ).
fof(f353,plain,
( sK7 = sK0(sF9,sF8)
| spl10_6
| spl10_9 ),
inference(forward_subsumption_resolution,[],[f352,f296]) ).
fof(f354,plain,
( $false
| spl10_5
| spl10_6
| spl10_9 ),
inference(forward_subsumption_resolution,[],[f353,f292]) ).
fof(f355,plain,
( spl10_5
| spl10_6
| spl10_9 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f356,plain,
( ~ member(sK6,universal_class)
| spl10_11 ),
inference(forward_subsumption_resolution,[],[f264,f328]) ).
fof(f357,plain,
( $false
| ~ spl10_1
| spl10_11 ),
inference(forward_subsumption_resolution,[],[f356,f247]) ).
fof(f358,plain,
( ~ spl10_1
| spl10_11 ),
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f363,plain,
( sK6 = sK0(sF8,sF9)
| sK7 = sK0(sF8,sF9)
| sF8 = sF9
| ~ spl10_9 ),
inference(resolution,[],[f313,f280]) ).
fof(f365,plain,
( sK6 = sK0(sF8,sF9)
| sF8 = sF9
| spl10_7
| ~ spl10_9 ),
inference(forward_subsumption_resolution,[],[f363,f300]) ).
fof(f366,plain,
( sK6 = sK0(sF8,sF9)
| spl10_7
| ~ spl10_9 ),
inference(forward_subsumption_resolution,[],[f365,f239]) ).
fof(f367,plain,
( spl10_8
| spl10_7
| ~ spl10_9 ),
inference(avatar_split_clause,[],[f366,f311,f299,f303]) ).
fof(f368,plain,
( member(sK6,universal_class)
| subclass(sF8,sF9)
| ~ spl10_8 ),
inference(superposition,[],[f276,f305]) ).
fof(f370,plain,
( ~ member(sK6,sF9)
| subclass(sF8,sF9)
| ~ spl10_8 ),
inference(superposition,[],[f106,f305]) ).
fof(f371,plain,
( subclass(sF8,sF9)
| ~ spl10_2
| ~ spl10_8 ),
inference(forward_subsumption_resolution,[],[f370,f252]) ).
fof(f372,plain,
( $false
| ~ spl10_2
| ~ spl10_8
| spl10_12 ),
inference(forward_subsumption_resolution,[],[f371,f338]) ).
fof(f373,plain,
( ~ spl10_2
| ~ spl10_8
| spl10_12 ),
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f374,plain,
( $false
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f348,f257]) ).
fof(f375,plain,
( spl10_3
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f374]) ).
fof(f376,plain,
( subclass(sF8,sF9)
| spl10_1
| ~ spl10_8 ),
inference(forward_subsumption_resolution,[],[f368,f248]) ).
fof(f377,plain,
( $false
| spl10_1
| ~ spl10_8
| spl10_12 ),
inference(forward_subsumption_resolution,[],[f376,f338]) ).
fof(f378,plain,
( spl10_1
| ~ spl10_8
| spl10_12 ),
inference(avatar_contradiction_clause,[],[f377]) ).
cnf(s1,plain,
( ~ spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s2,plain,
( ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s3,plain,
( spl10_5
| spl10_6
| spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f306]) ).
cnf(s4,plain,
( ~ spl10_4
| ~ spl10_5
| spl10_9 ),
inference(sat_conversion,[],[f314]) ).
cnf(s5,plain,
( ~ spl10_5
| spl10_9
| spl10_10 ),
inference(sat_conversion,[],[f319]) ).
cnf(s6,plain,
( spl10_3
| ~ spl10_5
| spl10_9 ),
inference(sat_conversion,[],[f321]) ).
cnf(s7,plain,
( ~ spl10_6
| spl10_9
| ~ spl10_11 ),
inference(sat_conversion,[],[f329]) ).
cnf(s9,plain,
( spl10_1
| ~ spl10_6
| spl10_9 ),
inference(sat_conversion,[],[f332]) ).
cnf(s10,plain,
( ~ spl10_7
| ~ spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f340]) ).
cnf(s12,plain,
( spl10_3
| ~ spl10_7
| spl10_12 ),
inference(sat_conversion,[],[f343]) ).
cnf(s13,plain,
( ~ spl10_3
| spl10_10 ),
inference(sat_conversion,[],[f346]) ).
cnf(s14,plain,
( ~ spl10_9
| ~ spl10_12 ),
inference(sat_conversion,[],[f351]) ).
cnf(s15,plain,
( spl10_5
| spl10_6
| spl10_9 ),
inference(sat_conversion,[],[f355]) ).
cnf(s16,plain,
( ~ spl10_1
| spl10_11 ),
inference(sat_conversion,[],[f358]) ).
cnf(s17,plain,
( spl10_7
| spl10_8
| ~ spl10_9 ),
inference(sat_conversion,[],[f367]) ).
cnf(s18,plain,
( ~ spl10_2
| ~ spl10_8
| spl10_12 ),
inference(sat_conversion,[],[f373]) ).
cnf(s19,plain,
( spl10_3
| ~ spl10_10 ),
inference(sat_conversion,[],[f375]) ).
cnf(s20,plain,
( spl10_1
| ~ spl10_8
| spl10_12 ),
inference(sat_conversion,[],[f378]) ).
cnf(s21,plain,
( ~ spl10_9
| spl10_3
| spl10_1 ),
inference(rat,[],[s17,s20,s12,s14]) ).
cnf(s22,plain,
( spl10_3
| spl10_1 ),
inference(rat,[],[s5,s15,s9,s21,s19]) ).
cnf(s23,plain,
( ~ spl10_9
| spl10_1 ),
inference(rat,[],[s17,s20,s10,s14,s13,s22]) ).
cnf(s24,plain,
spl10_1,
inference(rat,[],[s4,s15,s9,s23,s2,s22]) ).
cnf(s25,plain,
spl10_11,
inference(rat,[],[s16,s24]) ).
cnf(s26,plain,
spl10_2,
inference(rat,[],[s1,s24]) ).
cnf(s27,plain,
( ~ spl10_7
| spl10_12 ),
inference(rat,[],[s13,s10,s12]) ).
cnf(s28,plain,
( spl10_6
| spl10_5 ),
inference(rat,[],[s27,s3,s18,s14,s15,s26]) ).
cnf(s29,plain,
~ spl10_9,
inference(rat,[],[s17,s27,s18,s14,s26]) ).
cnf(s30,plain,
~ spl10_6,
inference(rat,[],[s7,s25,s29]) ).
cnf(s31,plain,
spl10_5,
inference(rat,[],[s28,s30]) ).
cnf(s32,plain,
spl10_3,
inference(rat,[],[s6,s29,s31]) ).
cnf(s34,plain,
~ spl10_4,
inference(rat,[],[s4,s29,s31]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s2,s34,s32]) ).
fof(f379,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET066+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.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 00:30:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/1.89 % (2886503)Detected formulas, will run a generic FOF schedule.
% 5.91/1.89 % (2886512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2794253615:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.91/1.89 % (2886512)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886512)------------------------------
% 5.91/1.89 % (2886512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886512)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886512)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886512)Time elapsed: 0.001 s
% 5.91/1.89 % (2886512)Peak memory usage: 88 MB
% 5.91/1.89 % (2886512)Instructions burned: 1 (million)
% 5.91/1.89 % (2886513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1589785673:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.91/1.89 % (2886514)dis-21_1_sil=8000:lcm=predicate:random_seed=3395399954: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)
% 5.91/1.89 % (2886509)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=657362285:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.91/1.89 % (2886508)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=1586063916:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.91/1.89 % (2886510)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=2064636642:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.91/1.89 % (2886511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=190014832:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.91/1.89 % (2886511)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886511)------------------------------
% 5.91/1.89 % (2886511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886511)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886511)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886511)Time elapsed: 0.001 s
% 5.91/1.89 % (2886511)Peak memory usage: 88 MB
% 5.91/1.89 % (2886514)Instruction limit reached!
% 5.91/1.89 % (2886514)------------------------------
% 5.91/1.89 % (2886514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886514)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886514)Termination reason: Instruction limit
% 5.91/1.89 % (2886514)Termination phase: Saturation
% 5.91/1.89 % (2886514)Time elapsed: 0.077 s
% 5.91/1.89 % (2886514)Peak memory usage: 89 MB
% 5.91/1.89 % (2886514)Instructions burned: 129 (million)
% 5.91/1.89 % (2886513)Instruction limit reached!
% 5.91/1.89 % (2886513)------------------------------
% 5.91/1.89 % (2886513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886513)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886513)Termination reason: Instruction limit
% 5.91/1.89 % (2886513)Termination phase: Saturation
% 5.91/1.89 % (2886513)Time elapsed: 0.100 s
% 5.91/1.89 % (2886513)Peak memory usage: 90 MB
% 5.91/1.89 % (2886513)Instructions burned: 140 (million)
% 5.91/1.89 % (2886512)------------------------------
% 5.91/1.89 % (2886512)------------------------------
% 5.91/1.89 % (2886522)lrs+10_1_sil=8000:sp=occurrence:random_seed=3587362644:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.91/1.89 % (2886524)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1843002415:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.91/1.89 % (2886523)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3963429893:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.91/1.89 % (2886523)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886523)------------------------------
% 5.91/1.89 % (2886523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886523)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886523)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886523)Time elapsed: 0.002 s
% 5.91/1.89 % (2886523)Peak memory usage: 88 MB
% 5.91/1.89 % (2886523)Instructions burned: 1 (million)
% 5.91/1.89 % (2886511)------------------------------
% 5.91/1.89 % (2886511)------------------------------
% 5.91/1.89 % (2886524)Instruction limit reached!
% 5.91/1.89 % (2886524)------------------------------
% 5.91/1.89 % (2886524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886524)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886524)Termination reason: Instruction limit
% 5.91/1.89 % (2886524)Termination phase: Saturation
% 5.91/1.89 % (2886524)Time elapsed: 0.098 s
% 5.91/1.89 % (2886524)Peak memory usage: 92 MB
% 5.91/1.89 % (2886524)Instructions burned: 326 (million)
% 5.91/1.89 % (2886522)Instruction limit reached!
% 5.91/1.89 % (2886522)------------------------------
% 5.91/1.89 % (2886522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886522)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886522)Termination reason: Instruction limit
% 5.91/1.89 % (2886522)Termination phase: Saturation
% 5.91/1.89 % (2886522)Time elapsed: 0.176 s
% 5.91/1.89 % (2886522)Peak memory usage: 91 MB
% 5.91/1.89 % (2886522)Instructions burned: 286 (million)
% 5.91/1.89 % (2886528)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=2251156758:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.91/1.89 % (2886529)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2261089338:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.91/1.89 % (2886529)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886529)------------------------------
% 5.91/1.89 % (2886529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886529)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886529)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886529)Time elapsed: 0.001 s
% 5.91/1.89 % (2886529)Peak memory usage: 88 MB
% 5.91/1.89 % (2886529)Instructions burned: 2 (million)
% 5.91/1.89 % (2886523)------------------------------
% 5.91/1.89 % (2886523)------------------------------
% 5.91/1.89 % (2886530)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=718718333:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.91/1.89 % (2886528)Instruction limit reached!
% 5.91/1.89 % (2886528)------------------------------
% 5.91/1.89 % (2886528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886528)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886528)Termination reason: Instruction limit
% 5.91/1.89 % (2886528)Termination phase: Saturation
% 5.91/1.89 % (2886528)Time elapsed: 0.144 s
% 5.91/1.89 % (2886528)Peak memory usage: 91 MB
% 5.91/1.89 % (2886528)Instructions burned: 248 (million)
% 5.91/1.89 % (2886529)------------------------------
% 5.91/1.89 % (2886529)------------------------------
% 5.91/1.89 % (2886510)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886510)------------------------------
% 5.91/1.89 % (2886510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886510)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886510)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886510)Time elapsed: 0.603 s
% 5.91/1.89 % (2886510)Peak memory usage: 127 MB
% 5.91/1.89 % (2886510)Instructions burned: 891 (million)
% 5.91/1.89 % (2886533)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3702451638:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.91/1.89 % (2886533)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886533)------------------------------
% 5.91/1.89 % (2886533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886533)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886533)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886533)Time elapsed: 0.001 s
% 5.91/1.89 % (2886533)Peak memory usage: 88 MB
% 5.91/1.89 % (2886508)First to succeed.
% 5.91/1.89 % (2886508)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2886503"
% 5.91/1.89 % (2886535)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2725068849:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.91/1.89 % (2886535)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886535)------------------------------
% 5.91/1.89 % (2886535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886535)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886535)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886535)Time elapsed: 0.003 s
% 5.91/1.89 % (2886535)Peak memory usage: 88 MB
% 5.91/1.89 % (2886535)Instructions burned: 4 (million)
% 5.91/1.89 % (2886536)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3666269601:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.91/1.89 % (2886536)Refutation not found, incomplete strategy
% 5.91/1.89 % (2886536)------------------------------
% 5.91/1.89 % (2886536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.89 % (2886536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.89 % (2886536)CaDiCaL version: 2.1.3
% 5.91/1.89 % (2886536)Termination reason: Refutation not found, incomplete strategy
% 5.91/1.89 % (2886536)Time elapsed: 0.001 s
% 5.91/1.89 % (2886536)Peak memory usage: 88 MB
% 5.91/1.89 % (2886536)Instructions burned: 1 (million)
% 5.91/1.89 % (2886536)------------------------------
% 5.91/1.89 % (2886536)------------------------------
% 5.91/1.89 % (2886510)------------------------------
% 5.91/1.89 % (2886510)------------------------------
% 5.91/1.89 % (2886533)------------------------------
% 5.91/1.89 % (2886533)------------------------------
% 5.91/1.89 % (2886508)Refutation found. Thanks to Tanya!
% 5.91/1.89 % SZS status Theorem for theBenchmark
% 5.91/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 7.96/2.08 % (2886508)------------------------------
% 7.96/2.08 % (2886508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/2.08 % (2886508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/2.08 % (2886508)CaDiCaL version: 2.1.3
% 7.96/2.08 % (2886508)Termination reason: Refutation
% 7.96/2.08 % (2886508)Time elapsed: 0.642 s
% 7.96/2.08 % (2886508)Peak memory usage: 129 MB
% 7.96/2.08 % (2886508)Instructions burned: 949 (million)
% 7.96/2.08 % (2886508)------------------------------
% 7.96/2.08 % (2886508)------------------------------
% 7.96/2.08 % (2886503)Success in time 1.046 s
% 7.96/2.08 % Vampire exiting
%------------------------------------------------------------------------------