TSTP Solution File: SEU059+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU059+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n007.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 09:20:06 EDT 2024
% Result : Theorem 0.60s 0.76s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 106 ( 5 unt; 1 typ; 0 def)
% Number of atoms : 1596 ( 38 equ)
% Maximal formula atoms : 16 ( 15 avg)
% Number of connectives : 599 ( 251 ~; 262 |; 65 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1143 (1143 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 10 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 141 ( 123 !; 17 ?; 64 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_9,type,
sQ10_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f269,plain,
$false,
inference(avatar_sat_refutation,[],[f181,f207,f220,f225,f236,f243,f244,f254,f258,f268]) ).
tff(f268,plain,
( spl11_3
| ~ spl11_7
| spl11_10 ),
inference(avatar_contradiction_clause,[],[f267]) ).
tff(f267,plain,
( $false
| spl11_3
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f266,f73]) ).
tff(f73,plain,
relation(sK2),
inference(cnf_transformation,[],[f51]) ).
tff(f51,plain,
( ( relation_inverse_image(sK2,set_difference(sK0,sK1)) != set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)) )
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f40,f50]) ).
tff(f50,plain,
( ? [X0,X1,X2] :
( ( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
& function(X2)
& relation(X2) )
=> ( ( relation_inverse_image(sK2,set_difference(sK0,sK1)) != set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)) )
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
? [X0,X1,X2] :
( ( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f39]) ).
tff(f39,plain,
? [X0,X1,X2] :
( ( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
tff(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
inference(negated_conjecture,[],[f26]) ).
tff(f26,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.dklZCZGrQb/Vampire---4.8_14334',t138_funct_1) ).
tff(f266,plain,
( ~ relation(sK2)
| spl11_3
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f265,f74]) ).
tff(f74,plain,
function(sK2),
inference(cnf_transformation,[],[f51]) ).
tff(f265,plain,
( ~ function(sK2)
| ~ relation(sK2)
| spl11_3
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f264,f175]) ).
tff(f175,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| spl11_3 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f174,plain,
( spl11_3
<=> in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
tff(f264,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f263,f115]) ).
tff(f115,plain,
~ sQ10_eqProxy($i,relation_inverse_image(sK2,set_difference(sK0,sK1)),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),
inference(equality_proxy_replacement,[],[f75,f114]) ).
tff(f114,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ10_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ10_eqProxy])]) ).
tff(f75,plain,
relation_inverse_image(sK2,set_difference(sK0,sK1)) != set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)),
inference(cnf_transformation,[],[f51]) ).
tff(f263,plain,
( sQ10_eqProxy($i,relation_inverse_image(sK2,set_difference(sK0,sK1)),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_7
| spl11_10 ),
inference(resolution,[],[f262,f127]) ).
tff(f127,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(sK5(X0,X1,X2),relation_dom(X0))
| sQ10_eqProxy($i,relation_inverse_image(X0,X1),X2)
| in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f91,f114]) ).
tff(f91,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| in(sK5(X0,X1,X2),relation_dom(X0))
| in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_inverse_image(X0,X1) = X2 )
| ( ( ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK5(X0,X1,X2)),X1)
& in(sK5(X0,X1,X2),relation_dom(X0)) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| ( relation_inverse_image(X0,X1) != X2 ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f62,f63]) ).
tff(f63,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK5(X0,X1,X2)),X1)
& in(sK5(X0,X1,X2),relation_dom(X0)) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f62,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_inverse_image(X0,X1) = X2 )
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| ( relation_inverse_image(X0,X1) != X2 ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f61]) ).
tff(f61,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_inverse_image(X0,X1) = X2 )
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ( relation_inverse_image(X0,X1) != X2 ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f60]) ).
tff(f60,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_inverse_image(X0,X1) = X2 )
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ( relation_inverse_image(X0,X1) != X2 ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f44]) ).
tff(f44,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dklZCZGrQb/Vampire---4.8_14334',d13_funct_1) ).
tff(f262,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f261,f73]) ).
tff(f261,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ relation(sK2)
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f260,f74]) ).
tff(f260,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f259,f214]) ).
tff(f214,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0)
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f213]) ).
tff(f213,plain,
( spl11_7
<=> in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
tff(f259,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0)
| ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| spl11_10 ),
inference(resolution,[],[f249,f111]) ).
tff(f111,plain,
! [X0: $i,X1: $i,X4: $i] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f90]) ).
tff(f90,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| ( relation_inverse_image(X0,X1) != X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f249,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK0))
| spl11_10 ),
inference(avatar_component_clause,[],[f247]) ).
tff(f247,plain,
( spl11_10
<=> in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
tff(f258,plain,
( ~ spl11_11
| spl11_8 ),
inference(avatar_split_clause,[],[f257,f217,f251]) ).
tff(f251,plain,
( spl11_11
<=> in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
tff(f217,plain,
( spl11_8
<=> in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
tff(f257,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| spl11_8 ),
inference(subsumption_resolution,[],[f256,f73]) ).
tff(f256,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ relation(sK2)
| spl11_8 ),
inference(subsumption_resolution,[],[f255,f74]) ).
tff(f255,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ function(sK2)
| ~ relation(sK2)
| spl11_8 ),
inference(resolution,[],[f218,f112]) ).
tff(f112,plain,
! [X0: $i,X1: $i,X4: $i] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f89]) ).
tff(f89,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| ( relation_inverse_image(X0,X1) != X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f218,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| spl11_8 ),
inference(avatar_component_clause,[],[f217]) ).
tff(f254,plain,
( ~ spl11_10
| spl11_11
| spl11_3 ),
inference(avatar_split_clause,[],[f245,f174,f251,f247]) ).
tff(f245,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK0))
| spl11_3 ),
inference(resolution,[],[f175,f108]) ).
tff(f108,plain,
! [X0: $i,X1: $i,X4: $i] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f84]) ).
tff(f84,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| ( set_difference(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f59,plain,
! [X0,X1,X2] :
( ( ( set_difference(X0,X1) = X2 )
| ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| ( set_difference(X0,X1) != X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f57,f58]) ).
tff(f58,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f57,plain,
! [X0,X1,X2] :
( ( ( set_difference(X0,X1) = X2 )
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| ( set_difference(X0,X1) != X2 ) ) ),
inference(rectify,[],[f56]) ).
tff(f56,plain,
! [X0,X1,X2] :
( ( ( set_difference(X0,X1) = X2 )
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ( set_difference(X0,X1) != X2 ) ) ),
inference(flattening,[],[f55]) ).
tff(f55,plain,
! [X0,X1,X2] :
( ( ( set_difference(X0,X1) = X2 )
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ( set_difference(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dklZCZGrQb/Vampire---4.8_14334',d4_xboole_0) ).
tff(f244,plain,
( spl11_7
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f239,f178,f213]) ).
tff(f178,plain,
( spl11_4
<=> in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
tff(f239,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0)
| ~ spl11_4 ),
inference(resolution,[],[f180,f110]) ).
tff(f110,plain,
! [X0: $i,X1: $i,X4: $i] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f82]) ).
tff(f82,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,X0)
| ~ in(X4,X2)
| ( set_difference(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f180,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f178]) ).
tff(f243,plain,
( ~ spl11_8
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f240,f178,f217]) ).
tff(f240,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ spl11_4 ),
inference(resolution,[],[f180,f109]) ).
tff(f109,plain,
! [X0: $i,X1: $i,X4: $i] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f83]) ).
tff(f83,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| ( set_difference(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f236,plain,
( ~ spl11_3
| spl11_7 ),
inference(avatar_contradiction_clause,[],[f235]) ).
tff(f235,plain,
( $false
| ~ spl11_3
| spl11_7 ),
inference(subsumption_resolution,[],[f234,f73]) ).
tff(f234,plain,
( ~ relation(sK2)
| ~ spl11_3
| spl11_7 ),
inference(subsumption_resolution,[],[f233,f74]) ).
tff(f233,plain,
( ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3
| spl11_7 ),
inference(subsumption_resolution,[],[f232,f182]) ).
tff(f182,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK0))
| ~ spl11_3 ),
inference(resolution,[],[f176,f110]) ).
tff(f176,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f232,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK0))
| ~ function(sK2)
| ~ relation(sK2)
| spl11_7 ),
inference(resolution,[],[f215,f112]) ).
tff(f215,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0)
| spl11_7 ),
inference(avatar_component_clause,[],[f213]) ).
tff(f225,plain,
( ~ spl11_8
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f224,f174,f217]) ).
tff(f224,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f223,f73]) ).
tff(f223,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f222,f74]) ).
tff(f222,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f221,f201]) ).
tff(f201,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f200,f73]) ).
tff(f200,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f199,f74]) ).
tff(f199,plain,
( in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(resolution,[],[f182,f113]) ).
tff(f113,plain,
! [X0: $i,X1: $i,X4: $i] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f88]) ).
tff(f88,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| ( relation_inverse_image(X0,X1) != X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f221,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(resolution,[],[f183,f111]) ).
tff(f183,plain,
( ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ spl11_3 ),
inference(resolution,[],[f176,f109]) ).
tff(f220,plain,
( ~ spl11_7
| spl11_8
| spl11_4 ),
inference(avatar_split_clause,[],[f209,f178,f217,f213]) ).
tff(f209,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK1)
| ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),sK0)
| spl11_4 ),
inference(resolution,[],[f179,f108]) ).
tff(f179,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| spl11_4 ),
inference(avatar_component_clause,[],[f178]) ).
tff(f207,plain,
( ~ spl11_4
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f206,f174,f178]) ).
tff(f206,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f205,f73]) ).
tff(f205,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f204,f74]) ).
tff(f204,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f203,f176]) ).
tff(f203,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(subsumption_resolution,[],[f202,f115]) ).
tff(f202,plain,
( ~ in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| sQ10_eqProxy($i,relation_inverse_image(sK2,set_difference(sK0,sK1)),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl11_3 ),
inference(resolution,[],[f201,f125]) ).
tff(f125,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| sQ10_eqProxy($i,relation_inverse_image(X0,X1),X2)
| ~ in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f93,f114]) ).
tff(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f181,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f172,f178,f174]) ).
tff(f172,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))) ),
inference(subsumption_resolution,[],[f171,f73]) ).
tff(f171,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ relation(sK2) ),
inference(subsumption_resolution,[],[f170,f74]) ).
tff(f170,plain,
( in(apply(sK2,sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))),set_difference(sK0,sK1))
| in(sK5(sK2,set_difference(sK0,sK1),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))),set_difference(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolution,[],[f126,f115]) ).
tff(f126,plain,
! [X2: $i,X0: $i,X1: $i] :
( sQ10_eqProxy($i,relation_inverse_image(X0,X1),X2)
| in(apply(X0,sK5(X0,X1,X2)),X1)
| in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f92,f114]) ).
tff(f92,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| in(apply(X0,sK5(X0,X1,X2)),X1)
| in(sK5(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU059+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 10:49:20 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.dklZCZGrQb/Vampire---4.8_14334
% 0.60/0.75 % (14443)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)
% 0.60/0.75 % (14445)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.75 % (14447)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)
% 0.60/0.75 % (14448)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)
% 0.60/0.75 % (14444)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)
% 0.60/0.75 % (14446)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)
% 0.60/0.75 % (14449)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)
% 0.60/0.75 % (14450)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)
% 0.60/0.75 % (14448)Refutation not found, incomplete strategy% (14448)------------------------------
% 0.60/0.75 % (14448)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.75 % (14448)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.75
% 0.60/0.75 % (14448)Memory used [KB]: 1031
% 0.60/0.75 % (14448)Time elapsed: 0.002 s
% 0.60/0.75 % (14448)Instructions burned: 3 (million)
% 0.60/0.75 % (14448)------------------------------
% 0.60/0.75 % (14448)------------------------------
% 0.60/0.75 % (14450)Refutation not found, incomplete strategy% (14450)------------------------------
% 0.60/0.75 % (14450)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.75 % (14450)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.75
% 0.60/0.75 % (14450)Memory used [KB]: 1050
% 0.60/0.75 % (14450)Time elapsed: 0.004 s
% 0.60/0.75 % (14450)Instructions burned: 3 (million)
% 0.60/0.75 % (14450)------------------------------
% 0.60/0.75 % (14450)------------------------------
% 0.60/0.76 % (14451)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)
% 0.60/0.76 % (14443)First to succeed.
% 0.60/0.76 % (14443)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14442"
% 0.60/0.76 % (14452)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)
% 0.60/0.76 % (14447)Also succeeded, but the first one will report.
% 0.60/0.76 % (14443)Refutation found. Thanks to Tanya!
% 0.60/0.76 % SZS status Theorem for Vampire---4
% 0.60/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76 % (14443)------------------------------
% 0.60/0.76 % (14443)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76 % (14443)Termination reason: Refutation
% 0.60/0.76
% 0.60/0.76 % (14443)Memory used [KB]: 1112
% 0.60/0.76 % (14443)Time elapsed: 0.009 s
% 0.60/0.76 % (14443)Instructions burned: 13 (million)
% 0.60/0.76 % (14442)Success in time 0.394 s
% 0.60/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------