TSTP Solution File: SEU058+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU058+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : n002.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 18:26:30 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 103 ( 8 unt; 0 def)
% Number of atoms : 436 ( 40 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 557 ( 224 ~; 238 |; 67 &)
% ( 21 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 146 ( 129 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f551,plain,
$false,
inference(avatar_sat_refutation,[],[f219,f268,f271,f325,f332,f356,f362,f382,f387,f400,f401,f508,f513,f532,f533,f536,f550]) ).
fof(f550,plain,
( ~ spl13_8
| ~ spl13_7
| ~ spl13_33
| ~ spl13_5
| spl13_23 ),
inference(avatar_split_clause,[],[f539,f296,f200,f384,f208,f212]) ).
fof(f212,plain,
( spl13_8
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f208,plain,
( spl13_7
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f384,plain,
( spl13_33
<=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f200,plain,
( spl13_5
<=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f296,plain,
( spl13_23
<=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f539,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
| ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
| ~ function(sK9)
| ~ relation(sK9)
| spl13_23 ),
inference(resolution,[],[f298,f159]) ).
fof(f159,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f132]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK5(X0,X1,X2)),X1) )
& ( in(sK5(X0,X1,X2),X2)
| ( in(sK5(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK5(X0,X1,X2)),X1) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) )
& ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f90,f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( in(X3,X2)
| ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
=> ( ( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK5(X0,X1,X2)),X1) )
& ( in(sK5(X0,X1,X2),X2)
| ( in(sK5(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK5(X0,X1,X2)),X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( in(X3,X2)
| ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) )
& ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( in(X3,X2)
| ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( in(X3,X2)
| ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
<=> in(X3,X2) ) ) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
<=> in(X3,X2) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
<=> in(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f298,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
| spl13_23 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f536,plain,
( ~ spl13_23
| ~ spl13_24
| spl13_9 ),
inference(avatar_split_clause,[],[f534,f216,f300,f296]) ).
fof(f300,plain,
( spl13_24
<=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f216,plain,
( spl13_9
<=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f534,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
| ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
| spl13_9 ),
inference(resolution,[],[f218,f156]) ).
fof(f156,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK3(X0,X1,X2),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) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f81,f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X2)
| ( in(X3,X1)
& in(X3,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)
| ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& in(X3,X2) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& in(X3,X2) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( set_intersection2(X2,X0) = X1
<=> ! [X3] :
( ( in(X3,X0)
& in(X3,X2) )
<=> in(X3,X1) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X2,X0] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f218,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| spl13_9 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f533,plain,
( spl13_33
| ~ spl13_6 ),
inference(avatar_split_clause,[],[f525,f204,f384]) ).
fof(f204,plain,
( spl13_6
<=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f525,plain,
( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
| ~ spl13_6 ),
inference(resolution,[],[f205,f154]) ).
fof(f154,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f121]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f205,plain,
( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f532,plain,
( spl13_28
| ~ spl13_6 ),
inference(avatar_split_clause,[],[f526,f204,f322]) ).
fof(f322,plain,
( spl13_28
<=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f526,plain,
( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
| ~ spl13_6 ),
inference(resolution,[],[f205,f155]) ).
fof(f155,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f513,plain,
( ~ spl13_23
| ~ spl13_8
| ~ spl13_7
| spl13_33 ),
inference(avatar_split_clause,[],[f511,f384,f208,f212,f296]) ).
fof(f511,plain,
( ~ function(sK9)
| ~ relation(sK9)
| ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
| spl13_33 ),
inference(resolution,[],[f386,f158]) ).
fof(f158,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f133]) ).
fof(f133,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f386,plain,
( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
| spl13_33 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f508,plain,
( ~ spl13_7
| ~ spl13_8
| ~ spl13_24
| spl13_28 ),
inference(avatar_split_clause,[],[f501,f322,f300,f212,f208]) ).
fof(f501,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
| ~ relation(sK9)
| ~ function(sK9)
| spl13_28 ),
inference(resolution,[],[f324,f158]) ).
fof(f324,plain,
( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
| spl13_28 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f401,plain,
( spl13_23
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f394,f216,f296]) ).
fof(f394,plain,
( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
| ~ spl13_9 ),
inference(resolution,[],[f217,f154]) ).
fof(f217,plain,
( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f400,plain,
( spl13_24
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f395,f216,f300]) ).
fof(f395,plain,
( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
| ~ spl13_9 ),
inference(resolution,[],[f217,f155]) ).
fof(f387,plain,
( ~ spl13_33
| ~ spl13_28
| spl13_6 ),
inference(avatar_split_clause,[],[f371,f204,f322,f384]) ).
fof(f371,plain,
( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
| ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
| spl13_6 ),
inference(resolution,[],[f206,f156]) ).
fof(f206,plain,
( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
| spl13_6 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f382,plain,
( spl13_29
| ~ spl13_7
| spl13_9
| ~ spl13_8
| spl13_6 ),
inference(avatar_split_clause,[],[f370,f204,f212,f216,f208,f329]) ).
fof(f329,plain,
( spl13_29
<=> sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f370,plain,
( ~ relation(sK9)
| in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| ~ function(sK9)
| sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| spl13_6 ),
inference(resolution,[],[f206,f169]) ).
fof(f169,plain,
! [X2,X0,X1] :
( in(apply(X0,sK5(X0,X1,X2)),X1)
| sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
| ~ function(X0)
| ~ relation(X0)
| in(sK5(X0,X1,X2),X2) ),
inference(equality_proxy_replacement,[],[f135,f160]) ).
fof(f160,plain,
! [X0,X1] :
( sQ12_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(sK5(X0,X1,X2),X2)
| in(apply(X0,sK5(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f362,plain,
~ spl13_29,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f361,plain,
( $false
| ~ spl13_29 ),
inference(resolution,[],[f331,f171]) ).
fof(f171,plain,
~ sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),
inference(equality_proxy_replacement,[],[f148,f160]) ).
fof(f148,plain,
relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( relation(sK9)
& function(sK9)
& relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f53,f98]) ).
fof(f98,plain,
( ? [X0,X1,X2] :
( relation(X1)
& function(X1)
& relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) )
=> ( relation(sK9)
& function(sK9)
& relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
? [X0,X1,X2] :
( relation(X1)
& function(X1)
& relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
? [X1,X2,X0] :
( relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
~ ! [X1,X2,X0] :
( ( relation(X1)
& function(X1) )
=> relation_inverse_image(X1,set_intersection2(X0,X2)) = set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) ),
inference(rectify,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0,X2,X1] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0,X2,X1] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).
fof(f331,plain,
( sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f356,plain,
( spl13_5
| ~ spl13_8
| ~ spl13_7
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f351,f296,f208,f212,f200]) ).
fof(f351,plain,
( ~ function(sK9)
| ~ relation(sK9)
| in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
| ~ spl13_23 ),
inference(resolution,[],[f297,f157]) ).
fof(f157,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f134,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f297,plain,
( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f332,plain,
( spl13_9
| ~ spl13_8
| ~ spl13_7
| spl13_29
| spl13_5 ),
inference(avatar_split_clause,[],[f326,f200,f329,f208,f212,f216]) ).
fof(f326,plain,
( sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| ~ function(sK9)
| ~ relation(sK9)
| in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| spl13_5 ),
inference(resolution,[],[f202,f168]) ).
fof(f168,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),relation_dom(X0))
| in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f136,f160]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),relation_dom(X0)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f202,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
| spl13_5 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f325,plain,
( ~ spl13_7
| ~ spl13_5
| ~ spl13_8
| ~ spl13_28
| spl13_24 ),
inference(avatar_split_clause,[],[f314,f300,f322,f212,f200,f208]) ).
fof(f314,plain,
( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
| ~ relation(sK9)
| ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
| ~ function(sK9)
| spl13_24 ),
inference(resolution,[],[f302,f159]) ).
fof(f302,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
| spl13_24 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f271,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| spl13_8 ),
inference(resolution,[],[f214,f150]) ).
fof(f150,plain,
relation(sK9),
inference(cnf_transformation,[],[f99]) ).
fof(f214,plain,
( ~ relation(sK9)
| spl13_8 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f268,plain,
spl13_7,
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f266,plain,
( $false
| spl13_7 ),
inference(resolution,[],[f210,f149]) ).
fof(f149,plain,
function(sK9),
inference(cnf_transformation,[],[f99]) ).
fof(f210,plain,
( ~ function(sK9)
| spl13_7 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f219,plain,
( ~ spl13_5
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f177,f216,f212,f208,f204,f200]) ).
fof(f177,plain,
( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
| ~ relation(sK9)
| ~ function(sK9)
| ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
| ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9)) ),
inference(resolution,[],[f171,f167]) ).
fof(f167,plain,
! [X2,X0,X1] :
( sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
| ~ relation(X0)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(sK5(X0,X1,X2),X2)
| ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| ~ function(X0) ),
inference(equality_proxy_replacement,[],[f137,f160]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK5(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU058+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:47:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % (872)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50 % (891)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.50 % (867)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)
% 0.19/0.50 % (869)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)
% 0.19/0.50 % (893)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.51 % (883)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.51 % (891)Instruction limit reached!
% 0.19/0.51 % (891)------------------------------
% 0.19/0.51 % (891)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (887)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)
% 0.19/0.51 % (882)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.52 % (888)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.52 % (882)First to succeed.
% 0.19/0.52 % (891)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (891)Termination reason: Unknown
% 0.19/0.52 % (891)Termination phase: Saturation
% 0.19/0.52
% 0.19/0.52 % (891)Memory used [KB]: 6140
% 0.19/0.52 % (891)Time elapsed: 0.100 s
% 0.19/0.52 % (891)Instructions burned: 9 (million)
% 0.19/0.52 % (891)------------------------------
% 0.19/0.52 % (891)------------------------------
% 0.19/0.52 % (873)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)
% 0.19/0.52 % (864)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.52 % (866)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)
% 0.19/0.52 % (864)Refutation not found, incomplete strategy% (864)------------------------------
% 0.19/0.52 % (864)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (864)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (864)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52
% 0.19/0.52 % (864)Memory used [KB]: 6012
% 0.19/0.52 % (864)Time elapsed: 0.114 s
% 0.19/0.52 % (864)Instructions burned: 3 (million)
% 0.19/0.52 % (864)------------------------------
% 0.19/0.52 % (864)------------------------------
% 0.19/0.52 % (878)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (871)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)
% 0.19/0.53 % (882)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (882)------------------------------
% 0.19/0.53 % (882)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (882)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (882)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (882)Memory used [KB]: 6268
% 0.19/0.53 % (882)Time elapsed: 0.125 s
% 0.19/0.53 % (882)Instructions burned: 8 (million)
% 0.19/0.53 % (882)------------------------------
% 0.19/0.53 % (882)------------------------------
% 0.19/0.53 % (862)Success in time 0.177 s
%------------------------------------------------------------------------------