TSTP Solution File: SET967+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET967+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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n026.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 09:09:11 EDT 2024
% Result : Theorem 0.63s 0.80s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 38
% Syntax : Number of formulae : 260 ( 1 unt; 0 def)
% Number of atoms : 879 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1007 ( 388 ~; 521 |; 56 &)
% ( 32 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 27 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 338 ( 308 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f766,plain,
$false,
inference(avatar_sat_refutation,[],[f93,f141,f142,f149,f174,f175,f268,f269,f289,f290,f299,f308,f320,f322,f361,f365,f444,f459,f478,f480,f508,f511,f514,f543,f567,f602,f611,f617,f625,f628,f629,f631,f636,f654,f670,f671,f681,f682,f683,f707,f719,f724,f726,f728,f756,f762,f763,f764,f765]) ).
fof(f765,plain,
( ~ spl11_63
| spl11_6 ),
inference(avatar_split_clause,[],[f758,f110,f564]) ).
fof(f564,plain,
( spl11_63
<=> in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).
fof(f110,plain,
( spl11_6
<=> in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f758,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| spl11_6 ),
inference(resolution,[],[f111,f66]) ).
fof(f66,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f30,f31]) ).
fof(f31,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(f30,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815',d2_xboole_0) ).
fof(f111,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl11_6 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f764,plain,
( spl11_49
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f695,f106,f475]) ).
fof(f475,plain,
( spl11_49
<=> in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).
fof(f106,plain,
( spl11_5
<=> in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f695,plain,
( in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl11_5 ),
inference(resolution,[],[f108,f54]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,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,[],[f35]) ).
fof(f35,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,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815',l55_zfmisc_1) ).
fof(f108,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f763,plain,
( ~ spl11_62
| spl11_6 ),
inference(avatar_split_clause,[],[f759,f110,f560]) ).
fof(f560,plain,
( spl11_62
<=> in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).
fof(f759,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| spl11_6 ),
inference(resolution,[],[f111,f65]) ).
fof(f65,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f46]) ).
fof(f46,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f762,plain,
( spl11_48
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f694,f106,f471]) ).
fof(f471,plain,
( spl11_48
<=> in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).
fof(f694,plain,
( in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(sK0,sK1))
| ~ spl11_5 ),
inference(resolution,[],[f108,f53]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f756,plain,
( spl11_7
| ~ spl11_6
| spl11_1
| spl11_4
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f755,f106,f102,f86,f110,f116]) ).
fof(f116,plain,
( spl11_7
<=> ! [X2,X3] : ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f86,plain,
( spl11_1
<=> sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f102,plain,
( spl11_4
<=> in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f755,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_1
| spl11_4
| ~ spl11_5 ),
inference(subsumption_resolution,[],[f754,f108]) ).
fof(f754,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_1
| spl11_4 ),
inference(resolution,[],[f735,f88]) ).
fof(f88,plain,
( ~ sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl11_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( sQ10_eqProxy(X0,set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ in(ordered_pair(sK6(X0,set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(X0,set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),X0)
| ~ in(ordered_pair(sK6(X0,set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(X0,set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X1,X2),sK9(X0)) )
| spl11_4 ),
inference(resolution,[],[f103,f78]) ).
fof(f78,plain,
! [X0,X1,X8,X9] :
( in(sK8(X1),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| sQ10_eqProxy(X0,X1)
| ~ sQ10_eqProxy(ordered_pair(X8,X9),sK9(X0)) ),
inference(equality_proxy_replacement,[],[f61,f68,f68]) ).
fof(f68,plain,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ10_eqProxy])]) ).
fof(f61,plain,
! [X0,X1,X8,X9] :
( X0 = X1
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| ordered_pair(X8,X9) != sK9(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) )
& ( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) ) )
| ( ! [X5,X6] : ordered_pair(X5,X6) != sK8(X1)
& in(sK8(X1),X1) )
| ( ! [X8,X9] : ordered_pair(X8,X9) != sK9(X0)
& in(sK9(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f37,f40,f39,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
=> ( ( ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) )
& ( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X1] :
( ? [X4] :
( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
=> ( ! [X6,X5] : ordered_pair(X5,X6) != sK8(X1)
& in(sK8(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ? [X7] :
( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) )
=> ( ! [X9,X8] : ordered_pair(X8,X9) != sK9(X0)
& in(sK9(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
| ? [X4] :
( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
| ? [X7] :
( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<~> in(ordered_pair(X2,X3),X1) )
| ? [X4] :
( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
| ? [X7] :
( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<~> in(ordered_pair(X2,X3),X1) )
| ? [X4] :
( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
| ? [X7] :
( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X4] :
~ ( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
& ! [X7] :
~ ( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) ) )
=> X0 = X1 ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X0) ) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815',t112_zfmisc_1) ).
fof(f103,plain,
( ~ in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl11_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f728,plain,
( spl11_7
| spl11_8
| ~ spl11_6
| spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f727,f106,f86,f110,f119,f116]) ).
fof(f119,plain,
( spl11_8
<=> ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f727,plain,
( ! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_1
| ~ spl11_5 ),
inference(subsumption_resolution,[],[f690,f108]) ).
fof(f690,plain,
( ! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_1 ),
inference(resolution,[],[f88,f76]) ).
fof(f76,plain,
! [X0,X1,X8,X6,X9,X5] :
( sQ10_eqProxy(X0,X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ~ sQ10_eqProxy(ordered_pair(X5,X6),sK8(X1))
| ~ sQ10_eqProxy(ordered_pair(X8,X9),sK9(X0)) ),
inference(equality_proxy_replacement,[],[f63,f68,f68,f68]) ).
fof(f63,plain,
! [X0,X1,X8,X6,X9,X5] :
( X0 = X1
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ordered_pair(X5,X6) != sK8(X1)
| ordered_pair(X8,X9) != sK9(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f726,plain,
( spl11_3
| spl11_4
| ~ spl11_6
| spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f725,f106,f86,f110,f102,f98]) ).
fof(f98,plain,
( spl11_3
<=> in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f725,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_1
| ~ spl11_5 ),
inference(subsumption_resolution,[],[f689,f108]) ).
fof(f689,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_1 ),
inference(resolution,[],[f88,f79]) ).
fof(f79,plain,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| in(sK9(X0),X0) ),
inference(equality_proxy_replacement,[],[f60,f68]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| in(sK9(X0),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f724,plain,
( ~ spl11_6
| spl11_8
| spl11_1
| spl11_3
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f723,f106,f98,f86,f119,f110]) ).
fof(f723,plain,
( ! [X0,X1] :
( ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) )
| spl11_1
| spl11_3
| ~ spl11_5 ),
inference(subsumption_resolution,[],[f722,f108]) ).
fof(f722,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) )
| spl11_1
| spl11_3 ),
inference(resolution,[],[f555,f88]) ).
fof(f555,plain,
( ! [X2,X0,X1] :
( sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),X0)
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),X0),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),X0)),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ sQ10_eqProxy(ordered_pair(X1,X2),sK8(X0))
| ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),X0),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),X0)),X0) )
| spl11_3 ),
inference(resolution,[],[f99,f77]) ).
fof(f77,plain,
! [X0,X1,X6,X5] :
( in(sK9(X0),X0)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ~ sQ10_eqProxy(ordered_pair(X5,X6),sK8(X1))
| sQ10_eqProxy(X0,X1) ),
inference(equality_proxy_replacement,[],[f62,f68,f68]) ).
fof(f62,plain,
! [X0,X1,X6,X5] :
( X0 = X1
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| ~ in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ordered_pair(X5,X6) != sK8(X1)
| in(sK9(X0),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f99,plain,
( ~ in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_3 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f719,plain,
( ~ spl11_70
| ~ spl11_49
| spl11_63 ),
inference(avatar_split_clause,[],[f718,f564,f475,f704]) ).
fof(f704,plain,
( spl11_70
<=> in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).
fof(f718,plain,
( ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl11_49
| spl11_63 ),
inference(subsumption_resolution,[],[f716,f476]) ).
fof(f476,plain,
( in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl11_49 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f716,plain,
( ~ in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| spl11_63 ),
inference(resolution,[],[f565,f55]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f565,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| spl11_63 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f707,plain,
( spl11_69
| spl11_70
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f700,f471,f704,f633]) ).
fof(f633,plain,
( spl11_69
<=> in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).
fof(f700,plain,
( in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ spl11_48 ),
inference(resolution,[],[f472,f67]) ).
fof(f67,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f472,plain,
( in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(sK0,sK1))
| ~ spl11_48 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f683,plain,
( spl11_9
| spl11_14
| spl11_2
| spl11_12
| spl11_11 ),
inference(avatar_split_clause,[],[f644,f134,f138,f90,f147,f126]) ).
fof(f126,plain,
( spl11_9
<=> in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f147,plain,
( spl11_14
<=> ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f90,plain,
( spl11_2
<=> sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f138,plain,
( spl11_12
<=> in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f134,plain,
( spl11_11
<=> in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f644,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1))) )
| spl11_11 ),
inference(resolution,[],[f135,f81]) ).
fof(f81,plain,
! [X0,X1,X6,X5] :
( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| sQ10_eqProxy(X0,X1)
| ~ sQ10_eqProxy(ordered_pair(X5,X6),sK8(X1))
| in(sK9(X0),X0) ),
inference(equality_proxy_replacement,[],[f58,f68,f68]) ).
fof(f58,plain,
! [X0,X1,X6,X5] :
( X0 = X1
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ordered_pair(X5,X6) != sK8(X1)
| in(sK9(X0),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f135,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| spl11_11 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f682,plain,
( spl11_13
| spl11_14
| spl11_2
| spl11_12
| spl11_11 ),
inference(avatar_split_clause,[],[f645,f134,f138,f90,f147,f144]) ).
fof(f144,plain,
( spl11_13
<=> ! [X2,X3] : ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f645,plain,
( ! [X2,X3,X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_11 ),
inference(resolution,[],[f135,f80]) ).
fof(f80,plain,
! [X0,X1,X8,X6,X9,X5] :
( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| sQ10_eqProxy(X0,X1)
| ~ sQ10_eqProxy(ordered_pair(X5,X6),sK8(X1))
| ~ sQ10_eqProxy(ordered_pair(X8,X9),sK9(X0)) ),
inference(equality_proxy_replacement,[],[f59,f68,f68,f68]) ).
fof(f59,plain,
! [X0,X1,X8,X6,X9,X5] :
( X0 = X1
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| ordered_pair(X5,X6) != sK8(X1)
| ordered_pair(X8,X9) != sK9(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f681,plain,
( spl11_15
| ~ spl11_18 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f680,plain,
( $false
| spl11_15
| ~ spl11_18 ),
inference(subsumption_resolution,[],[f676,f160]) ).
fof(f160,plain,
( ~ in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl11_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f158,plain,
( spl11_15
<=> in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f676,plain,
( in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl11_18 ),
inference(resolution,[],[f191,f53]) ).
fof(f191,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f189,plain,
( spl11_18
<=> in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f671,plain,
( spl11_17
| spl11_18
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f659,f138,f189,f185]) ).
fof(f185,plain,
( spl11_17
<=> in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f659,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| ~ spl11_12 ),
inference(resolution,[],[f140,f67]) ).
fof(f140,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f670,plain,
( spl11_15
| ~ spl11_17 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f669,plain,
( $false
| spl11_15
| ~ spl11_17 ),
inference(subsumption_resolution,[],[f665,f160]) ).
fof(f665,plain,
( in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl11_17 ),
inference(resolution,[],[f187,f53]) ).
fof(f187,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f654,plain,
( ~ spl11_15
| ~ spl11_16
| spl11_11 ),
inference(avatar_split_clause,[],[f641,f134,f162,f158]) ).
fof(f162,plain,
( spl11_16
<=> in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f641,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(sK0,sK1))
| ~ in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl11_11 ),
inference(resolution,[],[f135,f55]) ).
fof(f636,plain,
( ~ spl11_69
| ~ spl11_49
| spl11_62 ),
inference(avatar_split_clause,[],[f618,f560,f475,f633]) ).
fof(f618,plain,
( ~ in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| spl11_62 ),
inference(resolution,[],[f561,f55]) ).
fof(f561,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| spl11_62 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f631,plain,
( ~ spl11_32
| ~ spl11_15
| spl11_18 ),
inference(avatar_split_clause,[],[f630,f189,f158,f278]) ).
fof(f278,plain,
( spl11_32
<=> in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
fof(f630,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ spl11_15
| spl11_18 ),
inference(subsumption_resolution,[],[f437,f159]) ).
fof(f159,plain,
( in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f437,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl11_18 ),
inference(resolution,[],[f190,f55]) ).
fof(f190,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| spl11_18 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f629,plain,
( spl11_31
| spl11_32
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f405,f162,f278,f274]) ).
fof(f274,plain,
( spl11_31
<=> in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
fof(f405,plain,
( in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ spl11_16 ),
inference(resolution,[],[f163,f67]) ).
fof(f163,plain,
( in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(sK0,sK1))
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f628,plain,
( spl11_7
| spl11_8
| spl11_1
| spl11_6
| spl11_5 ),
inference(avatar_split_clause,[],[f469,f106,f110,f86,f119,f116]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_5 ),
inference(resolution,[],[f107,f80]) ).
fof(f107,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f625,plain,
( spl11_48
| ~ spl11_63 ),
inference(avatar_contradiction_clause,[],[f624]) ).
fof(f624,plain,
( $false
| spl11_48
| ~ spl11_63 ),
inference(subsumption_resolution,[],[f620,f614]) ).
fof(f614,plain,
( ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| spl11_48 ),
inference(resolution,[],[f473,f66]) ).
fof(f473,plain,
( ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(sK0,sK1))
| spl11_48 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f620,plain,
( in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK0)
| ~ spl11_63 ),
inference(resolution,[],[f566,f53]) ).
fof(f566,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| ~ spl11_63 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f617,plain,
( spl11_48
| ~ spl11_62 ),
inference(avatar_contradiction_clause,[],[f616]) ).
fof(f616,plain,
( $false
| spl11_48
| ~ spl11_62 ),
inference(subsumption_resolution,[],[f615,f605]) ).
fof(f605,plain,
( in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| ~ spl11_62 ),
inference(resolution,[],[f562,f53]) ).
fof(f562,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| ~ spl11_62 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f615,plain,
( ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK1)
| spl11_48 ),
inference(resolution,[],[f473,f65]) ).
fof(f611,plain,
( spl11_49
| ~ spl11_62 ),
inference(avatar_split_clause,[],[f606,f560,f475]) ).
fof(f606,plain,
( in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl11_62 ),
inference(resolution,[],[f562,f54]) ).
fof(f602,plain,
( spl11_49
| ~ spl11_63 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f601,plain,
( $false
| spl11_49
| ~ spl11_63 ),
inference(subsumption_resolution,[],[f598,f477]) ).
fof(f477,plain,
( ~ in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| spl11_49 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f598,plain,
( in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ spl11_63 ),
inference(resolution,[],[f566,f54]) ).
fof(f567,plain,
( spl11_62
| spl11_63
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f556,f110,f564,f560]) ).
fof(f556,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK0,sK2))
| in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(sK1,sK2))
| ~ spl11_6 ),
inference(resolution,[],[f112,f67]) ).
fof(f112,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f543,plain,
( ~ spl11_4
| ~ spl11_8 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f542,plain,
( $false
| ~ spl11_4
| ~ spl11_8 ),
inference(subsumption_resolution,[],[f541,f515]) ).
fof(f515,plain,
( ! [X0,X1] : ~ in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),cartesian_product2(X0,X1))
| ~ spl11_8 ),
inference(resolution,[],[f120,f75]) ).
fof(f75,plain,
! [X2,X0,X1] :
( sQ10_eqProxy(ordered_pair(sK4(X0),sK5(X0)),X0)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_proxy_replacement,[],[f52,f68]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ordered_pair(sK4(X0),sK5(X0)) = X0
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ordered_pair(sK4(X0),sK5(X0)) = X0
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f22,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X3,X4] : ordered_pair(X3,X4) = X0
=> ordered_pair(sK4(X0),sK5(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X0
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815',t102_zfmisc_1) ).
fof(f120,plain,
( ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f541,plain,
( in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),cartesian_product2(sK1,sK2))
| ~ spl11_4
| ~ spl11_8 ),
inference(subsumption_resolution,[],[f538,f515]) ).
fof(f538,plain,
( in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),cartesian_product2(sK0,sK2))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),cartesian_product2(sK1,sK2))
| ~ spl11_4 ),
inference(resolution,[],[f104,f67]) ).
fof(f104,plain,
( in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f514,plain,
( spl11_4
| spl11_6
| spl11_1
| spl11_5
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f513,f116,f106,f86,f110,f102]) ).
fof(f513,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| spl11_1
| spl11_5
| ~ spl11_7 ),
inference(subsumption_resolution,[],[f512,f483]) ).
fof(f483,plain,
( ! [X0,X1] : ~ in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(X0,X1))
| ~ spl11_7 ),
inference(resolution,[],[f117,f75]) ).
fof(f117,plain,
( ! [X2,X3] : ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(set_union2(sK0,sK1),sK2)))
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f512,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_1
| spl11_5 ),
inference(subsumption_resolution,[],[f462,f107]) ).
fof(f462,plain,
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),cartesian_product2(set_union2(sK0,sK1),sK2))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| spl11_1 ),
inference(resolution,[],[f88,f83]) ).
fof(f83,plain,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| in(sK9(X0),X0) ),
inference(equality_proxy_replacement,[],[f56,f68]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| in(sK9(X0),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f511,plain,
( spl11_8
| spl11_6
| spl11_1
| spl11_5
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f510,f116,f106,f86,f110,f119]) ).
fof(f510,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))) )
| spl11_1
| spl11_5
| ~ spl11_7 ),
inference(subsumption_resolution,[],[f509,f483]) ).
fof(f509,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2)) )
| spl11_1
| spl11_5 ),
inference(subsumption_resolution,[],[f468,f88]) ).
fof(f468,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))))
| in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2)) )
| spl11_5 ),
inference(resolution,[],[f107,f81]) ).
fof(f508,plain,
( ~ spl11_3
| ~ spl11_7 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f506,plain,
( $false
| ~ spl11_3
| ~ spl11_7 ),
inference(resolution,[],[f483,f100]) ).
fof(f100,plain,
( in(sK9(cartesian_product2(set_union2(sK0,sK1),sK2)),cartesian_product2(set_union2(sK0,sK1),sK2))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f480,plain,
( spl11_7
| spl11_4
| spl11_6
| spl11_1
| spl11_5 ),
inference(avatar_split_clause,[],[f479,f106,f86,f110,f102,f116]) ).
fof(f479,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_1
| spl11_5 ),
inference(subsumption_resolution,[],[f467,f88]) ).
fof(f467,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| in(sK8(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(set_union2(sK0,sK1),sK2))) )
| spl11_5 ),
inference(resolution,[],[f107,f82]) ).
fof(f82,plain,
! [X0,X1,X8,X9] :
( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| sQ10_eqProxy(X0,X1)
| in(sK8(X1),X1)
| ~ sQ10_eqProxy(ordered_pair(X8,X9),sK9(X0)) ),
inference(equality_proxy_replacement,[],[f57,f68,f68]) ).
fof(f57,plain,
! [X0,X1,X8,X9] :
( X0 = X1
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X1)
| in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK8(X1),X1)
| ordered_pair(X8,X9) != sK9(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f478,plain,
( ~ spl11_48
| ~ spl11_49
| spl11_5 ),
inference(avatar_split_clause,[],[f465,f106,f475,f471]) ).
fof(f465,plain,
( ~ in(sK7(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK2)
| ~ in(sK6(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),set_union2(sK0,sK1))
| spl11_5 ),
inference(resolution,[],[f107,f55]) ).
fof(f459,plain,
( spl11_14
| spl11_2
| spl11_9
| ~ spl11_11
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f458,f138,f134,f126,f90,f147]) ).
fof(f458,plain,
( ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| spl11_2
| spl11_9
| ~ spl11_11
| ~ spl11_12 ),
inference(subsumption_resolution,[],[f457,f140]) ).
fof(f457,plain,
( ! [X0,X1] :
( ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) )
| spl11_2
| spl11_9
| ~ spl11_11 ),
inference(subsumption_resolution,[],[f456,f136]) ).
fof(f136,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f456,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) )
| spl11_2
| spl11_9 ),
inference(resolution,[],[f449,f92]) ).
fof(f92,plain,
( ~ sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| spl11_2 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f449,plain,
( ! [X2,X0,X1] :
( sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),X0)
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),X0),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),X0)),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X1,X2),sK8(X0))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),X0),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),X0)),X0) )
| spl11_9 ),
inference(resolution,[],[f127,f77]) ).
fof(f127,plain,
( ~ in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| spl11_9 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f444,plain,
( spl11_13
| spl11_2
| spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f443,f138,f134,f130,f90,f144]) ).
fof(f130,plain,
( spl11_10
<=> in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f443,plain,
( ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1))))
| spl11_2
| spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(subsumption_resolution,[],[f442,f140]) ).
fof(f442,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_2
| spl11_10
| ~ spl11_11 ),
inference(subsumption_resolution,[],[f441,f136]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_2
| spl11_10 ),
inference(resolution,[],[f370,f92]) ).
fof(f370,plain,
( ! [X2,X0,X1] :
( sQ10_eqProxy(X0,set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ in(ordered_pair(sK6(X0,set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(X0,set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),X0)
| ~ in(ordered_pair(sK6(X0,set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(X0,set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X1,X2),sK9(X0)) )
| spl11_10 ),
inference(resolution,[],[f131,f78]) ).
fof(f131,plain,
( ~ in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| spl11_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f365,plain,
( ~ spl11_31
| ~ spl11_15
| spl11_17 ),
inference(avatar_split_clause,[],[f364,f185,f158,f274]) ).
fof(f364,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ spl11_15
| spl11_17 ),
inference(subsumption_resolution,[],[f301,f159]) ).
fof(f301,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| spl11_17 ),
inference(resolution,[],[f186,f55]) ).
fof(f186,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| spl11_17 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f361,plain,
( ~ spl11_10
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f360,plain,
( $false
| ~ spl11_10
| ~ spl11_14 ),
inference(subsumption_resolution,[],[f359,f323]) ).
fof(f323,plain,
( ! [X0,X1] : ~ in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),cartesian_product2(X0,X1))
| ~ spl11_14 ),
inference(resolution,[],[f148,f75]) ).
fof(f148,plain,
( ! [X0,X1] : ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f359,plain,
( in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),cartesian_product2(sK2,sK1))
| ~ spl11_10
| ~ spl11_14 ),
inference(subsumption_resolution,[],[f350,f323]) ).
fof(f350,plain,
( in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),cartesian_product2(sK2,sK0))
| in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),cartesian_product2(sK2,sK1))
| ~ spl11_10 ),
inference(resolution,[],[f132,f67]) ).
fof(f132,plain,
( in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f322,plain,
( spl11_13
| spl11_10
| spl11_2
| spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f321,f138,f134,f90,f130,f144]) ).
fof(f321,plain,
( ! [X0,X1] :
( in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_2
| spl11_11
| spl11_12 ),
inference(subsumption_resolution,[],[f311,f139]) ).
fof(f139,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| spl11_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f311,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_2
| spl11_11 ),
inference(subsumption_resolution,[],[f284,f92]) ).
fof(f284,plain,
( ! [X0,X1] :
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_11 ),
inference(resolution,[],[f135,f82]) ).
fof(f320,plain,
( ~ spl11_9
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f318,plain,
( $false
| ~ spl11_9
| ~ spl11_13 ),
inference(resolution,[],[f314,f128]) ).
fof(f128,plain,
( in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f314,plain,
( ! [X0,X1] : ~ in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(X0,X1))
| ~ spl11_13 ),
inference(resolution,[],[f145,f75]) ).
fof(f145,plain,
( ! [X2,X3] : ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(sK2,set_union2(sK0,sK1))))
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f308,plain,
( ~ spl11_18
| spl11_32 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f307,plain,
( $false
| ~ spl11_18
| spl11_32 ),
inference(subsumption_resolution,[],[f304,f279]) ).
fof(f279,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| spl11_32 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f304,plain,
( in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| ~ spl11_18 ),
inference(resolution,[],[f191,f54]) ).
fof(f299,plain,
( ~ spl11_17
| spl11_31 ),
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f298,plain,
( $false
| ~ spl11_17
| spl11_31 ),
inference(subsumption_resolution,[],[f295,f275]) ).
fof(f275,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| spl11_31 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f295,plain,
( in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| ~ spl11_17 ),
inference(resolution,[],[f187,f54]) ).
fof(f290,plain,
( ~ spl11_31
| spl11_16 ),
inference(avatar_split_clause,[],[f288,f162,f274]) ).
fof(f288,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK1)
| spl11_16 ),
inference(resolution,[],[f164,f65]) ).
fof(f164,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(sK0,sK1))
| spl11_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f289,plain,
( ~ spl11_32
| spl11_16 ),
inference(avatar_split_clause,[],[f287,f162,f278]) ).
fof(f287,plain,
( ~ in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK0)
| spl11_16 ),
inference(resolution,[],[f164,f66]) ).
fof(f269,plain,
( ~ spl11_17
| spl11_12 ),
inference(avatar_split_clause,[],[f267,f138,f185]) ).
fof(f267,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK1))
| spl11_12 ),
inference(resolution,[],[f139,f65]) ).
fof(f268,plain,
( ~ spl11_18
| spl11_12 ),
inference(avatar_split_clause,[],[f266,f138,f189]) ).
fof(f266,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,sK0))
| spl11_12 ),
inference(resolution,[],[f139,f66]) ).
fof(f175,plain,
( spl11_16
| ~ spl11_11 ),
inference(avatar_split_clause,[],[f171,f134,f162]) ).
fof(f171,plain,
( in(sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(sK0,sK1))
| ~ spl11_11 ),
inference(resolution,[],[f136,f54]) ).
fof(f174,plain,
( spl11_15
| ~ spl11_11 ),
inference(avatar_split_clause,[],[f170,f134,f158]) ).
fof(f170,plain,
( in(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK2)
| ~ spl11_11 ),
inference(resolution,[],[f136,f53]) ).
fof(f149,plain,
( spl11_13
| spl11_14
| ~ spl11_11
| ~ spl11_12
| spl11_2 ),
inference(avatar_split_clause,[],[f124,f90,f138,f134,f147,f144]) ).
fof(f124,plain,
( ! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| ~ sQ10_eqProxy(ordered_pair(X0,X1),sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))))
| ~ sQ10_eqProxy(ordered_pair(X2,X3),sK9(cartesian_product2(sK2,set_union2(sK0,sK1)))) )
| spl11_2 ),
inference(resolution,[],[f92,f76]) ).
fof(f142,plain,
( spl11_9
| spl11_10
| ~ spl11_11
| ~ spl11_12
| spl11_2 ),
inference(avatar_split_clause,[],[f123,f90,f138,f134,f130,f126]) ).
fof(f123,plain,
( ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| spl11_2 ),
inference(resolution,[],[f92,f79]) ).
fof(f141,plain,
( spl11_9
| spl11_10
| spl11_11
| spl11_12
| spl11_2 ),
inference(avatar_split_clause,[],[f122,f90,f138,f134,f130,f126]) ).
fof(f122,plain,
( in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(ordered_pair(sK6(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| in(sK8(set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| in(sK9(cartesian_product2(sK2,set_union2(sK0,sK1))),cartesian_product2(sK2,set_union2(sK0,sK1)))
| spl11_2 ),
inference(resolution,[],[f92,f83]) ).
fof(f93,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f69,f90,f86]) ).
fof(f69,plain,
( ~ sQ10_eqProxy(cartesian_product2(sK2,set_union2(sK0,sK1)),set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))
| ~ sQ10_eqProxy(cartesian_product2(set_union2(sK0,sK1),sK2),set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))) ),
inference(equality_proxy_replacement,[],[f42,f68,f68]) ).
fof(f42,plain,
( cartesian_product2(sK2,set_union2(sK0,sK1)) != set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_union2(sK0,sK1),sK2) != set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( cartesian_product2(sK2,set_union2(sK0,sK1)) != set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_union2(sK0,sK1),sK2) != set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f26]) ).
fof(f26,plain,
( ? [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) != set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| cartesian_product2(set_union2(X0,X1),X2) != set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
=> ( cartesian_product2(sK2,set_union2(sK0,sK1)) != set_union2(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| cartesian_product2(set_union2(sK0,sK1),sK2) != set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) != set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| cartesian_product2(set_union2(X0,X1),X2) != set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f16]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815',t120_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET967+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 3 16:35:23 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.4B70ixuwa5/Vampire---4.8_8815
% 0.57/0.77 % (8996)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)
% 0.57/0.78 % (8998)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.78 % (8999)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)
% 0.57/0.78 % (8997)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)
% 0.57/0.78 % (9001)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)
% 0.57/0.78 % (9000)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)
% 0.57/0.78 % (9002)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)
% 0.57/0.78 % (9003)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)
% 0.63/0.78 % (9001)Refutation not found, incomplete strategy% (9001)------------------------------
% 0.63/0.78 % (9001)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.78 % (9001)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.78
% 0.63/0.78 % (9001)Memory used [KB]: 1029
% 0.63/0.78 % (9001)Time elapsed: 0.004 s
% 0.63/0.78 % (9001)Instructions burned: 3 (million)
% 0.63/0.78 % (9001)------------------------------
% 0.63/0.78 % (9001)------------------------------
% 0.63/0.78 % (9002)Refutation not found, incomplete strategy% (9002)------------------------------
% 0.63/0.78 % (9002)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.78 % (9002)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.78
% 0.63/0.78 % (9002)Memory used [KB]: 1033
% 0.63/0.78 % (9002)Time elapsed: 0.004 s
% 0.63/0.78 % (9002)Instructions burned: 4 (million)
% 0.63/0.78 % (9002)------------------------------
% 0.63/0.78 % (9002)------------------------------
% 0.63/0.78 % (9005)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)
% 0.63/0.78 % (9004)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)
% 0.63/0.78 % (9005)Refutation not found, incomplete strategy% (9005)------------------------------
% 0.63/0.78 % (9005)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.78 % (9005)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.78
% 0.63/0.78 % (9005)Memory used [KB]: 1040
% 0.63/0.78 % (9005)Time elapsed: 0.004 s
% 0.63/0.78 % (9005)Instructions burned: 4 (million)
% 0.63/0.78 % (9005)------------------------------
% 0.63/0.78 % (9005)------------------------------
% 0.63/0.79 % (8996)Instruction limit reached!
% 0.63/0.79 % (8996)------------------------------
% 0.63/0.79 % (8996)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.79 % (8996)Termination reason: Unknown
% 0.63/0.79 % (8996)Termination phase: Saturation
% 0.63/0.79
% 0.63/0.79 % (8996)Memory used [KB]: 1225
% 0.63/0.79 % (8996)Time elapsed: 0.013 s
% 0.63/0.79 % (8996)Instructions burned: 35 (million)
% 0.63/0.79 % (8996)------------------------------
% 0.63/0.79 % (8996)------------------------------
% 0.63/0.79 % (9006)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 (2995ds/208Mi)
% 0.63/0.79 % (9003)First to succeed.
% 0.63/0.79 % (8999)Instruction limit reached!
% 0.63/0.79 % (8999)------------------------------
% 0.63/0.79 % (8999)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.79 % (9007)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)
% 0.63/0.79 % (8999)Termination reason: Unknown
% 0.63/0.79 % (8999)Termination phase: Saturation
% 0.63/0.79
% 0.63/0.79 % (8999)Memory used [KB]: 1152
% 0.63/0.79 % (8999)Time elapsed: 0.019 s
% 0.63/0.79 % (8999)Instructions burned: 33 (million)
% 0.63/0.79 % (8999)------------------------------
% 0.63/0.79 % (8999)------------------------------
% 0.63/0.79 % (9000)Instruction limit reached!
% 0.63/0.79 % (9000)------------------------------
% 0.63/0.79 % (9000)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.79 % (9000)Termination reason: Unknown
% 0.63/0.79 % (9000)Termination phase: Saturation
% 0.63/0.79
% 0.63/0.79 % (9000)Memory used [KB]: 1492
% 0.63/0.79 % (9000)Time elapsed: 0.021 s
% 0.63/0.79 % (9000)Instructions burned: 34 (million)
% 0.63/0.79 % (9000)------------------------------
% 0.63/0.79 % (9000)------------------------------
% 0.63/0.80 % (9009)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.63/0.80 % (9003)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8994"
% 0.63/0.80 % (9003)Refutation found. Thanks to Tanya!
% 0.63/0.80 % SZS status Theorem for Vampire---4
% 0.63/0.80 % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.80 % (9003)------------------------------
% 0.63/0.80 % (9003)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.80 % (9003)Termination reason: Refutation
% 0.63/0.80
% 0.63/0.80 % (9003)Memory used [KB]: 1283
% 0.63/0.80 % (9003)Time elapsed: 0.025 s
% 0.63/0.80 % (9003)Instructions burned: 39 (million)
% 0.63/0.80 % (8994)Success in time 0.416 s
% 0.63/0.80 % Vampire---4.8 exiting
%------------------------------------------------------------------------------