TSTP Solution File: SET972+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET972+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:09:13 EDT 2024
% Result : Theorem 0.57s 0.76s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 171 ( 10 unt; 0 def)
% Number of atoms : 506 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 586 ( 251 ~; 266 |; 38 &)
% ( 25 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 21 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 192 ( 174 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f318,plain,
$false,
inference(avatar_sat_refutation,[],[f68,f103,f104,f106,f108,f124,f135,f154,f155,f162,f163,f182,f184,f197,f215,f223,f224,f225,f226,f233,f234,f246,f253,f254,f261,f271,f273,f289,f306,f317]) ).
fof(f317,plain,
( ~ spl7_20
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f279,f82,f243]) ).
fof(f243,plain,
( spl7_20
<=> in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_20])]) ).
fof(f82,plain,
( spl7_6
<=> in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f279,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| ~ spl7_6 ),
inference(resolution,[],[f84,f50]) ).
fof(f50,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( ~ in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( ~ in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) )
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',d4_xboole_0) ).
fof(f84,plain,
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f306,plain,
( spl7_9
| spl7_12
| ~ spl7_13
| ~ spl7_14 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f305,plain,
( $false
| spl7_9
| spl7_12
| ~ spl7_13
| ~ spl7_14 ),
inference(subsumption_resolution,[],[f304,f142]) ).
fof(f142,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f141,plain,
( spl7_14
<=> in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).
fof(f304,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| spl7_9
| spl7_12
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f303,f288]) ).
fof(f288,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| spl7_12
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f216,f138]) ).
fof(f138,plain,
( in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f137,plain,
( spl7_13
<=> in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
fof(f216,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl7_12 ),
inference(resolution,[],[f122,f44]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',l55_zfmisc_1) ).
fof(f122,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| spl7_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f121,plain,
( spl7_12
<=> in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f303,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| spl7_9
| ~ spl7_13 ),
inference(resolution,[],[f298,f49]) ).
fof(f49,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f298,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_difference(sK0,sK1))
| spl7_9
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f296,f138]) ).
fof(f296,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_difference(sK0,sK1))
| ~ in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl7_9 ),
inference(resolution,[],[f97,f44]) ).
fof(f97,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_difference(sK0,sK1)))
| spl7_9 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl7_9
<=> in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_difference(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
fof(f289,plain,
( ~ spl7_18
| ~ spl7_16
| spl7_20 ),
inference(avatar_split_clause,[],[f285,f243,f194,f212]) ).
fof(f212,plain,
( spl7_18
<=> in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).
fof(f194,plain,
( spl7_16
<=> in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_16])]) ).
fof(f285,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ spl7_16
| spl7_20 ),
inference(subsumption_resolution,[],[f283,f195]) ).
fof(f195,plain,
( in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl7_16 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f283,plain,
( ~ in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| spl7_20 ),
inference(resolution,[],[f244,f44]) ).
fof(f244,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| spl7_20 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f273,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f272,plain,
( $false
| ~ spl7_4 ),
inference(resolution,[],[f76,f34]) ).
fof(f34,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',t36_xboole_1) ).
fof(f76,plain,
( ! [X0,X1] : ~ subset(set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,X1))
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl7_4
<=> ! [X0,X1] : ~ subset(set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f271,plain,
( spl7_18
| ~ spl7_20 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f270,plain,
( $false
| spl7_18
| ~ spl7_20 ),
inference(subsumption_resolution,[],[f266,f213]) ).
fof(f213,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| spl7_18 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f266,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ spl7_20 ),
inference(resolution,[],[f245,f42]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f245,plain,
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| ~ spl7_20 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f261,plain,
( ~ spl7_16
| ~ spl7_17
| spl7_19 ),
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f260,plain,
( $false
| ~ spl7_16
| ~ spl7_17
| spl7_19 ),
inference(subsumption_resolution,[],[f259,f209]) ).
fof(f209,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl7_17 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f208,plain,
( spl7_17
<=> in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_17])]) ).
fof(f259,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl7_16
| spl7_19 ),
inference(subsumption_resolution,[],[f257,f195]) ).
fof(f257,plain,
( ~ in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| spl7_19 ),
inference(resolution,[],[f241,f44]) ).
fof(f241,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| spl7_19 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f239,plain,
( spl7_19
<=> in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).
fof(f254,plain,
( spl7_17
| ~ spl7_15 ),
inference(avatar_split_clause,[],[f247,f190,f208]) ).
fof(f190,plain,
( spl7_15
<=> in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_difference(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).
fof(f247,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl7_15 ),
inference(resolution,[],[f191,f51]) ).
fof(f51,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f191,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_difference(sK0,sK1))
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f253,plain,
( ~ spl7_18
| ~ spl7_15 ),
inference(avatar_split_clause,[],[f248,f190,f212]) ).
fof(f248,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ spl7_15 ),
inference(resolution,[],[f191,f50]) ).
fof(f246,plain,
( ~ spl7_19
| spl7_20
| spl7_6 ),
inference(avatar_split_clause,[],[f237,f82,f243,f239]) ).
fof(f237,plain,
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| spl7_6 ),
inference(resolution,[],[f83,f49]) ).
fof(f83,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl7_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f234,plain,
( spl7_15
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f227,f78,f190]) ).
fof(f78,plain,
( spl7_5
<=> in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_difference(sK0,sK1),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f227,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_difference(sK0,sK1))
| ~ spl7_5 ),
inference(resolution,[],[f80,f42]) ).
fof(f80,plain,
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_difference(sK0,sK1),sK2))
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f233,plain,
( spl7_16
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f228,f78,f194]) ).
fof(f228,plain,
( in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl7_5 ),
inference(resolution,[],[f80,f43]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f226,plain,
( spl7_3
| spl7_4
| spl7_5
| spl7_6
| spl7_1 ),
inference(avatar_split_clause,[],[f185,f61,f82,f78,f75,f72]) ).
fof(f72,plain,
( spl7_3
<=> ! [X2,X3] : ~ subset(cartesian_product2(set_difference(sK0,sK1),sK2),cartesian_product2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f61,plain,
( spl7_1
<=> sQ6_eqProxy(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f185,plain,
( ! [X2,X3,X0,X1] :
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_difference(sK0,sK1),sK2))
| ~ subset(set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,X1))
| ~ subset(cartesian_product2(set_difference(sK0,sK1),sK2),cartesian_product2(X2,X3)) )
| spl7_1 ),
inference(resolution,[],[f63,f58]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ6_eqProxy(X0,X3)
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0)
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(equality_proxy_replacement,[],[f45,f52]) ).
fof(f52,plain,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ6_eqProxy])]) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0)
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ( ( ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0) )
& ( in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0) ) )
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f30,f31]) ).
fof(f31,plain,
! [X0,X3] :
( ? [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) )
& ( in(ordered_pair(X6,X7),X3)
| in(ordered_pair(X6,X7),X0) ) )
=> ( ( ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0) )
& ( in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ? [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) )
& ( in(ordered_pair(X6,X7),X3)
| in(ordered_pair(X6,X7),X0) ) )
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ? [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<~> in(ordered_pair(X6,X7),X3) )
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ? [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<~> in(ordered_pair(X6,X7),X3) )
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',t110_zfmisc_1) ).
fof(f63,plain,
( ~ sQ6_eqProxy(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl7_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f225,plain,
( spl7_3
| spl7_4
| ~ spl7_5
| ~ spl7_6
| spl7_1 ),
inference(avatar_split_clause,[],[f186,f61,f82,f78,f75,f72]) ).
fof(f186,plain,
( ! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_difference(sK0,sK1),sK2))
| ~ subset(set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,X1))
| ~ subset(cartesian_product2(set_difference(sK0,sK1),sK2),cartesian_product2(X2,X3)) )
| spl7_1 ),
inference(resolution,[],[f63,f57]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ6_eqProxy(X0,X3)
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0)
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(equality_proxy_replacement,[],[f46,f52]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X3)
| ~ in(ordered_pair(sK4(X0,X3),sK5(X0,X3)),X0)
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f224,plain,
( spl7_16
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f219,f82,f194]) ).
fof(f219,plain,
( in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl7_6 ),
inference(resolution,[],[f198,f43]) ).
fof(f198,plain,
( in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| ~ spl7_6 ),
inference(resolution,[],[f84,f51]) ).
fof(f223,plain,
( ~ spl7_6
| spl7_17 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f222,plain,
( $false
| ~ spl7_6
| spl7_17 ),
inference(subsumption_resolution,[],[f218,f210]) ).
fof(f210,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| spl7_17 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f218,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl7_6 ),
inference(resolution,[],[f198,f42]) ).
fof(f215,plain,
( ~ spl7_17
| spl7_18
| spl7_15 ),
inference(avatar_split_clause,[],[f206,f190,f212,f208]) ).
fof(f206,plain,
( in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| spl7_15 ),
inference(resolution,[],[f192,f49]) ).
fof(f192,plain,
( ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_difference(sK0,sK1))
| spl7_15 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f197,plain,
( ~ spl7_15
| ~ spl7_16
| spl7_5 ),
inference(avatar_split_clause,[],[f187,f78,f194,f190]) ).
fof(f187,plain,
( ~ in(sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_difference(sK0,sK1))
| spl7_5 ),
inference(resolution,[],[f79,f44]) ).
fof(f79,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK5(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_difference(sK0,sK1),sK2))
| spl7_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f184,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f183,plain,
( $false
| ~ spl7_3 ),
inference(resolution,[],[f73,f47]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',reflexivity_r1_tarski) ).
fof(f73,plain,
( ! [X2,X3] : ~ subset(cartesian_product2(set_difference(sK0,sK1),sK2),cartesian_product2(X2,X3))
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f182,plain,
( ~ spl7_9
| ~ spl7_12 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f181,plain,
( $false
| ~ spl7_9
| ~ spl7_12 ),
inference(subsumption_resolution,[],[f178,f174]) ).
fof(f174,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ spl7_9 ),
inference(resolution,[],[f165,f50]) ).
fof(f165,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_difference(sK0,sK1))
| ~ spl7_9 ),
inference(resolution,[],[f98,f43]) ).
fof(f98,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_difference(sK0,sK1)))
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f178,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ spl7_12 ),
inference(resolution,[],[f123,f43]) ).
fof(f123,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f163,plain,
( spl7_13
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f156,f117,f137]) ).
fof(f117,plain,
( spl7_11
<=> in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f156,plain,
( in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl7_11 ),
inference(resolution,[],[f118,f42]) ).
fof(f118,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f162,plain,
( spl7_14
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f157,f117,f141]) ).
fof(f157,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ spl7_11 ),
inference(resolution,[],[f118,f43]) ).
fof(f155,plain,
( ~ spl7_12
| ~ spl7_10 ),
inference(avatar_split_clause,[],[f150,f100,f121]) ).
fof(f100,plain,
( spl7_10
<=> in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
fof(f150,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| ~ spl7_10 ),
inference(resolution,[],[f102,f50]) ).
fof(f102,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f154,plain,
( ~ spl7_10
| spl7_11 ),
inference(avatar_contradiction_clause,[],[f153]) ).
fof(f153,plain,
( $false
| ~ spl7_10
| spl7_11 ),
inference(subsumption_resolution,[],[f149,f119]) ).
fof(f119,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| spl7_11 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f149,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| ~ spl7_10 ),
inference(resolution,[],[f102,f51]) ).
fof(f135,plain,
( ~ spl7_9
| spl7_11 ),
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f134,plain,
( $false
| ~ spl7_9
| spl7_11 ),
inference(subsumption_resolution,[],[f133,f109]) ).
fof(f109,plain,
( in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl7_9 ),
inference(resolution,[],[f98,f42]) ).
fof(f133,plain,
( ~ in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl7_9
| spl7_11 ),
inference(subsumption_resolution,[],[f131,f125]) ).
fof(f125,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ spl7_9 ),
inference(resolution,[],[f110,f51]) ).
fof(f110,plain,
( in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_difference(sK0,sK1))
| ~ spl7_9 ),
inference(resolution,[],[f98,f43]) ).
fof(f131,plain,
( ~ in(sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ in(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl7_11 ),
inference(resolution,[],[f119,f44]) ).
fof(f124,plain,
( ~ spl7_11
| spl7_12
| spl7_10 ),
inference(avatar_split_clause,[],[f115,f100,f121,f117]) ).
fof(f115,plain,
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| spl7_10 ),
inference(resolution,[],[f101,f49]) ).
fof(f101,plain,
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| spl7_10 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f108,plain,
~ spl7_8,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f107,plain,
( $false
| ~ spl7_8 ),
inference(resolution,[],[f94,f34]) ).
fof(f94,plain,
( ! [X0,X1] : ~ subset(set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,X1))
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl7_8
<=> ! [X0,X1] : ~ subset(set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f106,plain,
~ spl7_7,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f105,plain,
( $false
| ~ spl7_7 ),
inference(resolution,[],[f91,f47]) ).
fof(f91,plain,
( ! [X2,X3] : ~ subset(cartesian_product2(sK2,set_difference(sK0,sK1)),cartesian_product2(X2,X3))
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f90,plain,
( spl7_7
<=> ! [X2,X3] : ~ subset(cartesian_product2(sK2,set_difference(sK0,sK1)),cartesian_product2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f104,plain,
( spl7_7
| spl7_8
| ~ spl7_9
| ~ spl7_10
| spl7_2 ),
inference(avatar_split_clause,[],[f88,f65,f100,f96,f93,f90]) ).
fof(f65,plain,
( spl7_2
<=> sQ6_eqProxy(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f88,plain,
( ! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_difference(sK0,sK1)))
| ~ subset(set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,X1))
| ~ subset(cartesian_product2(sK2,set_difference(sK0,sK1)),cartesian_product2(X2,X3)) )
| spl7_2 ),
inference(resolution,[],[f67,f57]) ).
fof(f67,plain,
( ~ sQ6_eqProxy(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| spl7_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f103,plain,
( spl7_7
| spl7_8
| spl7_9
| spl7_10
| spl7_2 ),
inference(avatar_split_clause,[],[f87,f65,f100,f96,f93,f90]) ).
fof(f87,plain,
( ! [X2,X3,X0,X1] :
( in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(ordered_pair(sK4(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK5(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_difference(sK0,sK1)))
| ~ subset(set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,X1))
| ~ subset(cartesian_product2(sK2,set_difference(sK0,sK1)),cartesian_product2(X2,X3)) )
| spl7_2 ),
inference(resolution,[],[f67,f58]) ).
fof(f68,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f53,f65,f61]) ).
fof(f53,plain,
( ~ sQ6_eqProxy(cartesian_product2(sK2,set_difference(sK0,sK1)),set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ6_eqProxy(cartesian_product2(set_difference(sK0,sK1),sK2),set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
inference(equality_proxy_replacement,[],[f33,f52,f52]) ).
fof(f33,plain,
( cartesian_product2(sK2,set_difference(sK0,sK1)) != set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_difference(sK0,sK1),sK2) != set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( cartesian_product2(sK2,set_difference(sK0,sK1)) != set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_difference(sK0,sK1),sK2) != set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2] :
( cartesian_product2(X2,set_difference(X0,X1)) != set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| cartesian_product2(set_difference(X0,X1),X2) != set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
=> ( cartesian_product2(sK2,set_difference(sK0,sK1)) != set_difference(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_difference(sK0,sK1),sK2) != set_difference(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( cartesian_product2(X2,set_difference(X0,X1)) != set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| cartesian_product2(set_difference(X0,X1),X2) != set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693',t125_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET972+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 16:29:22 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.34 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.lgHDL0TL7S/Vampire---4.8_10693
% 0.57/0.75 % (10802)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75 % (10807)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75 % (10805)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.75 % (10804)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75 % (10806)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75 % (10808)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.75 % (10803)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.75 % (10809)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.75 % (10807)Refutation not found, incomplete strategy% (10807)------------------------------
% 0.57/0.75 % (10807)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (10807)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (10807)Memory used [KB]: 959
% 0.57/0.75 % (10807)Time elapsed: 0.003 s
% 0.57/0.75 % (10807)Instructions burned: 3 (million)
% 0.57/0.75 % (10805)Refutation not found, incomplete strategy% (10805)------------------------------
% 0.57/0.75 % (10805)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (10805)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (10805)Memory used [KB]: 972
% 0.57/0.75 % (10805)Time elapsed: 0.003 s
% 0.57/0.75 % (10805)Instructions burned: 3 (million)
% 0.57/0.75 % (10807)------------------------------
% 0.57/0.75 % (10807)------------------------------
% 0.57/0.75 % (10808)Refutation not found, incomplete strategy% (10808)------------------------------
% 0.57/0.75 % (10808)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (10808)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (10808)Memory used [KB]: 1027
% 0.57/0.75 % (10808)Time elapsed: 0.003 s
% 0.57/0.75 % (10808)Instructions burned: 3 (million)
% 0.57/0.75 % (10805)------------------------------
% 0.57/0.75 % (10805)------------------------------
% 0.57/0.76 % (10808)------------------------------
% 0.57/0.76 % (10808)------------------------------
% 0.57/0.76 % (10802)Refutation not found, incomplete strategy% (10802)------------------------------
% 0.57/0.76 % (10802)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76 % (10802)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.76
% 0.57/0.76 % (10802)Memory used [KB]: 1061
% 0.57/0.76 % (10802)Time elapsed: 0.005 s
% 0.57/0.76 % (10802)Instructions burned: 11 (million)
% 0.57/0.76 % (10802)------------------------------
% 0.57/0.76 % (10802)------------------------------
% 0.57/0.76 % (10809)First to succeed.
% 0.57/0.76 % (10811)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.57/0.76 % (10810)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.57/0.76 % (10806)Also succeeded, but the first one will report.
% 0.57/0.76 % (10812)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.57/0.76 % (10811)Refutation not found, incomplete strategy% (10811)------------------------------
% 0.57/0.76 % (10811)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76 % (10811)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.76
% 0.57/0.76 % (10811)Memory used [KB]: 1031
% 0.57/0.76 % (10811)Time elapsed: 0.003 s
% 0.57/0.76 % (10811)Instructions burned: 3 (million)
% 0.57/0.76 % (10811)------------------------------
% 0.57/0.76 % (10811)------------------------------
% 0.57/0.76 % (10810)Refutation not found, incomplete strategy% (10810)------------------------------
% 0.57/0.76 % (10810)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76 % (10810)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.76
% 0.57/0.76 % (10810)Memory used [KB]: 1065
% 0.57/0.76 % (10810)Time elapsed: 0.005 s
% 0.57/0.76 % (10810)Instructions burned: 7 (million)
% 0.57/0.76 % (10813)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.57/0.76 % (10809)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10801"
% 0.57/0.76 % (10810)------------------------------
% 0.57/0.76 % (10810)------------------------------
% 0.57/0.76 % (10809)Refutation found. Thanks to Tanya!
% 0.57/0.76 % SZS status Theorem for Vampire---4
% 0.57/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76 % (10809)------------------------------
% 0.57/0.76 % (10809)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76 % (10809)Termination reason: Refutation
% 0.57/0.76
% 0.57/0.76 % (10809)Memory used [KB]: 1106
% 0.57/0.76 % (10809)Time elapsed: 0.010 s
% 0.57/0.76 % (10809)Instructions burned: 17 (million)
% 0.57/0.76 % (10801)Success in time 0.404 s
% 0.57/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------