TSTP Solution File: SET972+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET972+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n015.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 : Wed Aug 31 18:22:54 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 186 ( 17 unt; 0 def)
% Number of atoms : 548 ( 47 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 629 ( 267 ~; 281 |; 46 &)
% ( 28 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 263 ( 240 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f394,plain,
$false,
inference(avatar_sat_refutation,[],[f100,f196,f197,f226,f228,f247,f249,f250,f267,f271,f281,f283,f285,f294,f296,f312,f323,f334,f336,f350,f355,f359,f364,f368,f378,f382,f392,f393]) ).
fof(f393,plain,
( spl9_23
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f365,f304,f343]) ).
fof(f343,plain,
( spl9_23
<=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f304,plain,
( spl9_22
<=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f365,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
| ~ spl9_22 ),
inference(resolution,[],[f305,f80]) ).
fof(f80,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) )
& ( in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) ) ) )
& ( ! [X4] :
( ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) )
& ( in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) ) ) )
& ( ! [X4] :
( ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X0,X2,X1] :
( ( set_difference(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X1)
| ( ~ in(X3,X2)
& in(X3,X0) ) ) ) )
& ( ! [X3] :
( ( ( ~ in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) ) )
| set_difference(X0,X2) != X1 ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X2,X1] :
( ( set_difference(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X1)
| ( ~ in(X3,X2)
& in(X3,X0) ) ) ) )
& ( ! [X3] :
( ( ( ~ in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) ) )
| set_difference(X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X2,X1] :
( set_difference(X0,X2) = X1
<=> ! [X3] :
( ( ~ in(X3,X2)
& in(X3,X0) )
<=> in(X3,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X2,X1] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X0)
& ~ in(X3,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f305,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f392,plain,
( spl9_24
| ~ spl9_26 ),
inference(avatar_contradiction_clause,[],[f391]) ).
fof(f391,plain,
( $false
| spl9_24
| ~ spl9_26 ),
inference(subsumption_resolution,[],[f389,f348]) ).
fof(f348,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| spl9_24 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f347,plain,
( spl9_24
<=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f389,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| ~ spl9_26 ),
inference(resolution,[],[f377,f73]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
| in(X1,X2) ),
inference(definition_unfolding,[],[f59,f66]) ).
fof(f66,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
| ~ in(X1,X2)
| ~ in(X3,X0) )
& ( ( in(X1,X2)
& in(X3,X0) )
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X2,X0,X3] :
( ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
| ~ in(X2,X0)
| ~ in(X3,X1) )
& ( ( in(X2,X0)
& in(X3,X1) )
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X1,X2,X0,X3] :
( ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
| ~ in(X2,X0)
| ~ in(X3,X1) )
& ( ( in(X2,X0)
& in(X3,X1) )
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X2,X0,X3] :
( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
<=> ( in(X2,X0)
& in(X3,X1) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ( in(X1,X3)
& in(X0,X2) )
<=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f377,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f375,plain,
( spl9_26
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f382,plain,
( ~ spl9_21
| ~ spl9_23
| spl9_25 ),
inference(avatar_contradiction_clause,[],[f381]) ).
fof(f381,plain,
( $false
| ~ spl9_21
| ~ spl9_23
| spl9_25 ),
inference(subsumption_resolution,[],[f380,f301]) ).
fof(f301,plain,
( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ spl9_21 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f300,plain,
( spl9_21
<=> in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f380,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ spl9_23
| spl9_25 ),
inference(subsumption_resolution,[],[f379,f344]) ).
fof(f344,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f379,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
| ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| spl9_25 ),
inference(resolution,[],[f373,f72]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
| ~ in(X3,X0)
| ~ in(X1,X2) ),
inference(definition_unfolding,[],[f60,f66]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
| ~ in(X1,X2)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f373,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
| spl9_25 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f371,plain,
( spl9_25
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f378,plain,
( ~ spl9_25
| spl9_26
| spl9_13 ),
inference(avatar_split_clause,[],[f369,f171,f375,f371]) ).
fof(f171,plain,
( spl9_13
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f369,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
| ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
| spl9_13 ),
inference(resolution,[],[f173,f81]) ).
fof(f81,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f173,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
| spl9_13 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f368,plain,
( ~ spl9_24
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f366,f304,f347]) ).
fof(f366,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| ~ spl9_22 ),
inference(resolution,[],[f305,f79]) ).
fof(f79,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f364,plain,
( spl9_22
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f362,f167,f304]) ).
fof(f167,plain,
( spl9_12
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f362,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
| ~ spl9_12 ),
inference(resolution,[],[f168,f73]) ).
fof(f168,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f359,plain,
( ~ spl9_24
| ~ spl9_13
| ~ spl9_21 ),
inference(avatar_split_clause,[],[f358,f300,f171,f347]) ).
fof(f358,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| ~ spl9_13
| ~ spl9_21 ),
inference(subsumption_resolution,[],[f357,f301]) ).
fof(f357,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| ~ spl9_13 ),
inference(resolution,[],[f338,f72]) ).
fof(f338,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
| ~ spl9_13 ),
inference(resolution,[],[f172,f79]) ).
fof(f172,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f355,plain,
( spl9_23
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f353,f171,f343]) ).
fof(f353,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
| ~ spl9_13 ),
inference(resolution,[],[f337,f73]) ).
fof(f337,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
| ~ spl9_13 ),
inference(resolution,[],[f172,f80]) ).
fof(f350,plain,
( ~ spl9_23
| spl9_24
| spl9_22 ),
inference(avatar_split_clause,[],[f341,f304,f347,f343]) ).
fof(f341,plain,
( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
| ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
| spl9_22 ),
inference(resolution,[],[f306,f81]) ).
fof(f306,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
| spl9_22 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f336,plain,
( ~ spl9_22
| ~ spl9_21
| spl9_12 ),
inference(avatar_split_clause,[],[f335,f167,f300,f304]) ).
fof(f335,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
| spl9_12 ),
inference(resolution,[],[f169,f72]) ).
fof(f169,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
| spl9_12 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f334,plain,
( ~ spl9_12
| spl9_21 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f333,plain,
( $false
| ~ spl9_12
| spl9_21 ),
inference(subsumption_resolution,[],[f329,f302]) ).
fof(f302,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| spl9_21 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f329,plain,
( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ spl9_12 ),
inference(resolution,[],[f168,f74]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
| in(X3,X0) ),
inference(definition_unfolding,[],[f58,f66]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f323,plain,
( ~ spl9_13
| spl9_21 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f322,plain,
( $false
| ~ spl9_13
| spl9_21 ),
inference(subsumption_resolution,[],[f319,f302]) ).
fof(f319,plain,
( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
| ~ spl9_13 ),
inference(resolution,[],[f313,f74]) ).
fof(f313,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
| ~ spl9_13 ),
inference(resolution,[],[f172,f80]) ).
fof(f312,plain,
( ~ spl9_18
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f310,f146,f210]) ).
fof(f210,plain,
( spl9_18
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f146,plain,
( spl9_9
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f310,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
| ~ spl9_9 ),
inference(resolution,[],[f147,f79]) ).
fof(f147,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f296,plain,
( spl9_11
| spl9_10
| ~ spl9_12
| ~ spl9_13
| spl9_2 ),
inference(avatar_split_clause,[],[f291,f97,f171,f167,f161,f164]) ).
fof(f164,plain,
( spl9_11
<=> ! [X4,X5] : ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f161,plain,
( spl9_10
<=> ! [X6,X7] : ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f97,plain,
( spl9_2
<=> sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f291,plain,
( ! [X6,X7,X4,X5] :
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
| ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
| ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7))
| ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5)) )
| spl9_2 ),
inference(resolution,[],[f99,f88]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ8_eqProxy(X0,X3)
| ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
| ~ subset(X3,cartesian_product2(X5,X2))
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3) ),
inference(equality_proxy_replacement,[],[f76,f82]) ).
fof(f82,plain,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ8_eqProxy])]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
| ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(definition_unfolding,[],[f69,f66,f66]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3)
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) )
& ( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) ) )
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f47,f48]) ).
fof(f48,plain,
! [X0,X3] :
( ? [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X0)
| in(ordered_pair(X6,X7),X3) ) )
=> ( ( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) )
& ( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X0)
| in(ordered_pair(X6,X7),X3) ) )
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
! [X4,X3,X0,X1,X5,X2] :
( ? [X7,X6] :
( ( ~ in(ordered_pair(X7,X6),X4)
| ~ in(ordered_pair(X7,X6),X1) )
& ( in(ordered_pair(X7,X6),X4)
| in(ordered_pair(X7,X6),X1) ) )
| X1 = X4
| ~ subset(X4,cartesian_product2(X3,X5))
| ~ subset(X1,cartesian_product2(X2,X0)) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X4,X3,X0,X1,X5,X2] :
( ? [X7,X6] :
( in(ordered_pair(X7,X6),X1)
<~> in(ordered_pair(X7,X6),X4) )
| X1 = X4
| ~ subset(X4,cartesian_product2(X3,X5))
| ~ subset(X1,cartesian_product2(X2,X0)) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X2,X5,X1,X3,X0,X4] :
( X1 = X4
| ~ subset(X1,cartesian_product2(X2,X0))
| ? [X7,X6] :
( in(ordered_pair(X7,X6),X1)
<~> in(ordered_pair(X7,X6),X4) )
| ~ subset(X4,cartesian_product2(X3,X5)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X2,X5,X1,X3,X0,X4] :
( ( subset(X1,cartesian_product2(X2,X0))
& ! [X6,X7] :
( in(ordered_pair(X7,X6),X4)
<=> in(ordered_pair(X7,X6),X1) )
& subset(X4,cartesian_product2(X3,X5)) )
=> X1 = X4 ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X2,X0,X1,X4,X3,X5] :
( ( subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2))
& ! [X7,X6] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) )
=> X0 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(f99,plain,
( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))
| spl9_2 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f294,plain,
( spl9_13
| spl9_11
| spl9_12
| spl9_10
| spl9_2 ),
inference(avatar_split_clause,[],[f290,f97,f161,f167,f164,f171]) ).
fof(f290,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X2,X3))
| in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
| ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4))) )
| spl9_2 ),
inference(resolution,[],[f99,f89]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ8_eqProxy(X0,X3)
| in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
| in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
| ~ subset(X3,cartesian_product2(X5,X2))
| ~ subset(X0,cartesian_product2(X1,X4)) ),
inference(equality_proxy_replacement,[],[f77,f82]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
| in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(definition_unfolding,[],[f68,f66,f66]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X4,X5] :
( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
| in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3)
| X0 = X3
| ~ subset(X0,cartesian_product2(X1,X4))
| ~ subset(X3,cartesian_product2(X5,X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f285,plain,
~ spl9_10,
inference(avatar_contradiction_clause,[],[f284]) ).
fof(f284,plain,
( $false
| ~ spl9_10 ),
inference(resolution,[],[f162,f64]) ).
fof(f64,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] : subset(set_difference(X1,X0),X1),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X1,X0] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f162,plain,
( ! [X6,X7] : ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7))
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f283,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f282,plain,
( $false
| ~ spl9_11 ),
inference(resolution,[],[f165,f71]) ).
fof(f71,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1] : subset(X1,X1),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f165,plain,
( ! [X4,X5] : ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f281,plain,
( ~ spl9_18
| spl9_19 ),
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f280,plain,
( $false
| ~ spl9_18
| spl9_19 ),
inference(subsumption_resolution,[],[f277,f254]) ).
fof(f254,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| spl9_19 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl9_19
<=> in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f277,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| ~ spl9_18 ),
inference(resolution,[],[f212,f74]) ).
fof(f212,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f271,plain,
( ~ spl9_19
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f269,f136,f252]) ).
fof(f136,plain,
( spl9_6
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f269,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| ~ spl9_6 ),
inference(resolution,[],[f261,f79]) ).
fof(f261,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
| ~ spl9_6 ),
inference(resolution,[],[f137,f74]) ).
fof(f137,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f267,plain,
( spl9_18
| ~ spl9_17
| spl9_9 ),
inference(avatar_split_clause,[],[f266,f146,f206,f210]) ).
fof(f206,plain,
( spl9_17
<=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f266,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
| in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
| spl9_9 ),
inference(resolution,[],[f148,f81]) ).
fof(f148,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
| spl9_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f250,plain,
( spl9_17
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f237,f146,f206]) ).
fof(f237,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
| ~ spl9_9 ),
inference(resolution,[],[f147,f80]) ).
fof(f249,plain,
~ spl9_7,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f248,plain,
( $false
| ~ spl9_7 ),
inference(resolution,[],[f141,f64]) ).
fof(f141,plain,
( ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3))
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl9_7
<=> ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f247,plain,
( spl9_6
| ~ spl9_17
| spl9_18 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f246,plain,
( $false
| spl9_6
| ~ spl9_17
| spl9_18 ),
inference(subsumption_resolution,[],[f245,f242]) ).
fof(f242,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| spl9_6
| ~ spl9_17 ),
inference(subsumption_resolution,[],[f241,f230]) ).
fof(f230,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
| ~ spl9_17 ),
inference(resolution,[],[f207,f74]) ).
fof(f207,plain,
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f241,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
| in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| spl9_6
| ~ spl9_17 ),
inference(resolution,[],[f236,f81]) ).
fof(f236,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
| spl9_6
| ~ spl9_17 ),
inference(subsumption_resolution,[],[f235,f231]) ).
fof(f231,plain,
( in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
| ~ spl9_17 ),
inference(resolution,[],[f207,f73]) ).
fof(f235,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
| ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
| spl9_6 ),
inference(resolution,[],[f138,f72]) ).
fof(f138,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
| spl9_6 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f245,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| ~ spl9_17
| spl9_18 ),
inference(subsumption_resolution,[],[f244,f231]) ).
fof(f244,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
| ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
| spl9_18 ),
inference(resolution,[],[f211,f72]) ).
fof(f211,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
| spl9_18 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f228,plain,
~ spl9_8,
inference(avatar_contradiction_clause,[],[f227]) ).
fof(f227,plain,
( $false
| ~ spl9_8 ),
inference(resolution,[],[f144,f71]) ).
fof(f144,plain,
( ! [X0,X1] : ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1))
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f143,plain,
( spl9_8
<=> ! [X0,X1] : ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f226,plain,
( ~ spl9_6
| spl9_17 ),
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f225,plain,
( $false
| ~ spl9_6
| spl9_17 ),
inference(subsumption_resolution,[],[f219,f215]) ).
fof(f215,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
| ~ spl9_6 ),
inference(resolution,[],[f200,f80]) ).
fof(f200,plain,
( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
| ~ spl9_6 ),
inference(resolution,[],[f137,f74]) ).
fof(f219,plain,
( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
| ~ spl9_6
| spl9_17 ),
inference(subsumption_resolution,[],[f218,f201]) ).
fof(f201,plain,
( in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
| ~ spl9_6 ),
inference(resolution,[],[f137,f73]) ).
fof(f218,plain,
( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
| ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
| spl9_17 ),
inference(resolution,[],[f208,f72]) ).
fof(f208,plain,
( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
| spl9_17 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f197,plain,
( ~ spl9_9
| ~ spl9_6
| spl9_8
| spl9_7
| spl9_1 ),
inference(avatar_split_clause,[],[f195,f93,f140,f143,f136,f146]) ).
fof(f93,plain,
( spl9_1
<=> sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f195,plain,
( ! [X6,X7,X4,X5] :
( ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X6,X7))
| ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X4,X5))
| ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
| ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5))) )
| spl9_1 ),
inference(resolution,[],[f95,f88]) ).
fof(f95,plain,
( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))
| spl9_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f196,plain,
( spl9_8
| spl9_7
| spl9_6
| spl9_9
| spl9_1 ),
inference(avatar_split_clause,[],[f194,f93,f146,f136,f140,f143]) ).
fof(f194,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
| in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
| ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3))
| ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1)) )
| spl9_1 ),
inference(resolution,[],[f95,f89]) ).
fof(f100,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f87,f97,f93]) ).
fof(f87,plain,
( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))
| ~ sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
inference(equality_proxy_replacement,[],[f63,f82,f82]) ).
fof(f63,plain,
( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
| set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
| set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f40,f41]) ).
fof(f41,plain,
( ? [X0,X1,X2] :
( set_difference(cartesian_product2(X1,X0),cartesian_product2(X1,X2)) != cartesian_product2(X1,set_difference(X0,X2))
| cartesian_product2(set_difference(X0,X2),X1) != set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) )
=> ( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
| set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0,X1,X2] :
( set_difference(cartesian_product2(X1,X0),cartesian_product2(X1,X2)) != cartesian_product2(X1,set_difference(X0,X2))
| cartesian_product2(set_difference(X0,X2),X1) != set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X2,X1,X0] :
( cartesian_product2(X1,set_difference(X2,X0)) != set_difference(cartesian_product2(X1,X2),cartesian_product2(X1,X0))
| cartesian_product2(set_difference(X2,X0),X1) != set_difference(cartesian_product2(X2,X1),cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X2,X1] :
( cartesian_product2(set_difference(X2,X0),X1) = set_difference(cartesian_product2(X2,X1),cartesian_product2(X0,X1))
& cartesian_product2(X1,set_difference(X2,X0)) = set_difference(cartesian_product2(X1,X2),cartesian_product2(X1,X0)) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X1,X2,X0] :
( 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,
! [X1,X2,X0] :
( 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/benchmark/theBenchmark.p',t125_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET972+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 14:44:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.46 % (31715)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.47 % (31725)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.48 % (31712)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.48 % (31712)Refutation not found, incomplete strategy% (31712)------------------------------
% 0.21/0.48 % (31712)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.48 % (31712)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.48 % (31712)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48
% 0.21/0.48 % (31712)Memory used [KB]: 1407
% 0.21/0.48 % (31712)Time elapsed: 0.091 s
% 0.21/0.48 % (31712)Instructions burned: 2 (million)
% 0.21/0.48 % (31712)------------------------------
% 0.21/0.48 % (31712)------------------------------
% 0.21/0.48 % (31715)Refutation not found, incomplete strategy% (31715)------------------------------
% 0.21/0.48 % (31715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.48 % (31715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.48 % (31715)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48
% 0.21/0.48 % (31715)Memory used [KB]: 5884
% 0.21/0.48 % (31715)Time elapsed: 0.092 s
% 0.21/0.48 % (31715)Instructions burned: 3 (million)
% 0.21/0.48 % (31715)------------------------------
% 0.21/0.48 % (31715)------------------------------
% 0.21/0.49 % (31725)Instruction limit reached!
% 0.21/0.49 % (31725)------------------------------
% 0.21/0.49 % (31725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (31717)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.21/0.49 % (31725)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (31725)Termination reason: Unknown
% 0.21/0.49 % (31725)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (31725)Memory used [KB]: 1407
% 0.21/0.49 % (31725)Time elapsed: 0.006 s
% 0.21/0.49 % (31725)Instructions burned: 2 (million)
% 0.21/0.49 % (31725)------------------------------
% 0.21/0.49 % (31725)------------------------------
% 0.21/0.49 % (31723)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.49 % (31723)Refutation not found, incomplete strategy% (31723)------------------------------
% 0.21/0.49 % (31723)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (31723)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (31723)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49 % (31723)Memory used [KB]: 6012
% 0.21/0.49 % (31723)Time elapsed: 0.099 s
% 0.21/0.49 % (31723)Instructions burned: 3 (million)
% 0.21/0.49 % (31723)------------------------------
% 0.21/0.49 % (31723)------------------------------
% 0.21/0.49 % (31731)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.50 % (31731)First to succeed.
% 0.21/0.51 % (31717)Instruction limit reached!
% 0.21/0.51 % (31717)------------------------------
% 0.21/0.51 % (31717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (31717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (31717)Termination reason: Unknown
% 0.21/0.51 % (31717)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (31717)Memory used [KB]: 6140
% 0.21/0.51 % (31717)Time elapsed: 0.082 s
% 0.21/0.51 % (31717)Instructions burned: 12 (million)
% 0.21/0.51 % (31717)------------------------------
% 0.21/0.51 % (31717)------------------------------
% 0.21/0.51 % (31711)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.51 % (31721)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.51 % (31710)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (31721)Instruction limit reached!
% 0.21/0.51 % (31721)------------------------------
% 0.21/0.51 % (31721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (31721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (31721)Termination reason: Unknown
% 0.21/0.51 % (31721)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (31721)Memory used [KB]: 5884
% 0.21/0.51 % (31721)Time elapsed: 0.002 s
% 0.21/0.51 % (31721)Instructions burned: 3 (million)
% 0.21/0.51 % (31721)------------------------------
% 0.21/0.51 % (31721)------------------------------
% 0.21/0.52 % (31713)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.53 % (31731)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (31731)------------------------------
% 0.21/0.53 % (31731)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (31731)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (31731)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (31731)Memory used [KB]: 6140
% 0.21/0.53 % (31731)Time elapsed: 0.108 s
% 0.21/0.53 % (31731)Instructions burned: 12 (million)
% 0.21/0.53 % (31731)------------------------------
% 0.21/0.53 % (31731)------------------------------
% 0.21/0.53 % (31706)Success in time 0.17 s
%------------------------------------------------------------------------------