TSTP Solution File: SEU205+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU205+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n018.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 09:20:59 EDT 2024
% Result : Theorem 0.62s 0.79s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 89 ( 5 unt; 1 typ; 0 def)
% Number of atoms : 1140 ( 34 equ)
% Maximal formula atoms : 15 ( 12 avg)
% Number of connectives : 489 ( 190 ~; 197 |; 75 &)
% ( 14 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 753 ( 753 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 7 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 187 ( 157 !; 29 ?; 61 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_5,type,
sQ10_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f316,plain,
$false,
inference(avatar_sat_refutation,[],[f241,f271,f295,f305,f315]) ).
tff(f315,plain,
( ~ spl11_7
| spl11_10 ),
inference(avatar_contradiction_clause,[],[f314]) ).
tff(f314,plain,
( $false
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f313,f77]) ).
tff(f77,plain,
relation(sK1),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
( ( relation_image(sK1,sK0) != relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)) )
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f53]) ).
tff(f53,plain,
( ? [X0,X1] :
( ( relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0)) )
& relation(X1) )
=> ( ( relation_image(sK1,sK0) != relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)) )
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0,X1] :
( ( relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0)) )
& relation(X1) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ) ),
inference(negated_conjecture,[],[f31]) ).
tff(f31,conjecture,
! [X0,X1] :
( relation(X1)
=> ( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057',t145_relat_1) ).
tff(f313,plain,
( ~ relation(sK1)
| ~ spl11_7
| spl11_10 ),
inference(subsumption_resolution,[],[f312,f236]) ).
tff(f236,plain,
( in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f235]) ).
tff(f235,plain,
( spl11_7
<=> in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
tff(f312,plain,
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| ~ relation(sK1)
| spl11_10 ),
inference(resolution,[],[f294,f95]) ).
tff(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(sK4(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK4(X0,X1,X2),X0),X2)
& in(sK4(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f64,f65]) ).
tff(f65,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK4(X0,X1,X2),X0),X2)
& in(sK4(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f64,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f63]) ).
tff(f63,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f30]) ).
tff(f30,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057',t143_relat_1) ).
tff(f294,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),sK0)
| spl11_10 ),
inference(avatar_component_clause,[],[f292]) ).
tff(f292,plain,
( spl11_10
<=> in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
tff(f305,plain,
( ~ spl11_7
| spl11_9 ),
inference(avatar_contradiction_clause,[],[f304]) ).
tff(f304,plain,
( $false
| ~ spl11_7
| spl11_9 ),
inference(subsumption_resolution,[],[f303,f77]) ).
tff(f303,plain,
( ~ relation(sK1)
| ~ spl11_7
| spl11_9 ),
inference(subsumption_resolution,[],[f302,f236]) ).
tff(f302,plain,
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| ~ relation(sK1)
| spl11_9 ),
inference(resolution,[],[f290,f93]) ).
tff(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(sK4(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f66]) ).
tff(f290,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),relation_dom(sK1))
| spl11_9 ),
inference(avatar_component_clause,[],[f288]) ).
tff(f288,plain,
( spl11_9
<=> in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),relation_dom(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
tff(f295,plain,
( ~ spl11_9
| ~ spl11_10
| ~ spl11_7
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f286,f239,f235,f292,f288]) ).
tff(f239,plain,
( spl11_8
<=> ! [X0] :
( ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ in(X0,set_intersection2(relation_dom(sK1),sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
tff(f286,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),sK0)
| ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),relation_dom(sK1))
| ~ spl11_7
| ~ spl11_8 ),
inference(resolution,[],[f278,f113]) ).
tff(f113,plain,
! [X0: $i,X1: $i,X4: $i] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f87]) ).
tff(f87,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| ( set_intersection2(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0,X1,X2] :
( ( ( set_intersection2(X0,X1) = X2 )
| ( ( ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| ( set_intersection2(X0,X1) != X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f60,f61]) ).
tff(f61,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) )
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f60,plain,
! [X0,X1,X2] :
( ( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ) ),
inference(rectify,[],[f59]) ).
tff(f59,plain,
! [X0,X1,X2] :
( ( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ) ),
inference(flattening,[],[f58]) ).
tff(f58,plain,
! [X0,X1,X2] :
( ( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057',d3_xboole_0) ).
tff(f278,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),sK0,sK1),set_intersection2(relation_dom(sK1),sK0))
| ~ spl11_7
| ~ spl11_8 ),
inference(resolution,[],[f276,f236]) ).
tff(f276,plain,
( ! [X0: $i] :
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,X0))
| ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),X0,sK1),set_intersection2(relation_dom(sK1),sK0)) )
| ~ spl11_8 ),
inference(subsumption_resolution,[],[f274,f77]) ).
tff(f274,plain,
( ! [X0: $i] :
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),X0,sK1),set_intersection2(relation_dom(sK1),sK0))
| ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,X0))
| ~ relation(sK1) )
| ~ spl11_8 ),
inference(resolution,[],[f240,f94]) ).
tff(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(ordered_pair(sK4(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f66]) ).
tff(f240,plain,
( ! [X0: $i] :
( ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ in(X0,set_intersection2(relation_dom(sK1),sK0)) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f239]) ).
tff(f271,plain,
spl11_7,
inference(avatar_contradiction_clause,[],[f270]) ).
tff(f270,plain,
( $false
| spl11_7 ),
inference(subsumption_resolution,[],[f269,f237]) ).
tff(f237,plain,
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| spl11_7 ),
inference(avatar_component_clause,[],[f235]) ).
tff(f269,plain,
( in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| spl11_7 ),
inference(subsumption_resolution,[],[f267,f120]) ).
tff(f120,plain,
~ sQ10_eqProxy($i,relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),
inference(equality_proxy_replacement,[],[f78,f119]) ).
tff(f119,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ10_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ10_eqProxy])]) ).
tff(f78,plain,
relation_image(sK1,sK0) != relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)),
inference(cnf_transformation,[],[f54]) ).
tff(f267,plain,
( sQ10_eqProxy($i,relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))
| in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| spl11_7 ),
inference(resolution,[],[f262,f124]) ).
tff(f124,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| sQ10_eqProxy($i,X0,X1)
| in(sK2(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f81,f119]) ).
tff(f81,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,plain,
! [X0,X1] :
( ( X0 = X1 )
| ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f55,f56]) ).
tff(f56,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f55,plain,
! [X0,X1] :
( ( X0 = X1 )
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0,X1] :
( ( X0 = X1 )
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f36,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057',t2_tarski) ).
tff(f262,plain,
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))
| spl11_7 ),
inference(subsumption_resolution,[],[f261,f77]) ).
tff(f261,plain,
( ~ relation(sK1)
| ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))
| spl11_7 ),
inference(resolution,[],[f255,f152]) ).
tff(f152,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( in(sK4(X0,set_intersection2(X2,X3),X1),X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(resolution,[],[f95,f114]) ).
tff(f114,plain,
! [X0: $i,X1: $i,X4: $i] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f86]) ).
tff(f86,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( in(X4,X1)
| ~ in(X4,X2)
| ( set_intersection2(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f62]) ).
tff(f255,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),set_intersection2(relation_dom(sK1),sK0),sK1),sK0)
| spl11_7 ),
inference(subsumption_resolution,[],[f254,f237]) ).
tff(f254,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),set_intersection2(relation_dom(sK1),sK0),sK1),sK0)
| in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| spl11_7 ),
inference(subsumption_resolution,[],[f252,f120]) ).
tff(f252,plain,
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),set_intersection2(relation_dom(sK1),sK0),sK1),sK0)
| sQ10_eqProxy($i,relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))
| in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0))
| spl11_7 ),
inference(resolution,[],[f246,f124]) ).
tff(f246,plain,
( ! [X0: $i] :
( ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,X0))
| ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),X0,sK1),sK0) )
| spl11_7 ),
inference(subsumption_resolution,[],[f244,f77]) ).
tff(f244,plain,
( ! [X0: $i] :
( ~ in(sK4(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),X0,sK1),sK0)
| ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,X0))
| ~ relation(sK1) )
| spl11_7 ),
inference(resolution,[],[f243,f94]) ).
tff(f243,plain,
( ! [X0: $i] :
( ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ in(X0,sK0) )
| spl11_7 ),
inference(subsumption_resolution,[],[f242,f77]) ).
tff(f242,plain,
( ! [X0: $i] :
( ~ in(X0,sK0)
| ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ relation(sK1) )
| spl11_7 ),
inference(resolution,[],[f237,f116]) ).
tff(f116,plain,
! [X0: $i,X1: $i,X6: $i,X7: $i] :
( in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f99]) ).
tff(f99,plain,
! [X2: $i,X0: $i,X1: $i,X6: $i,X7: $i] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| ( relation_image(X0,X1) != X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f72,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_image(X0,X1) = X2 )
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK5(X0,X1,X2)),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK6(X0,X1,X2),X1)
& in(ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),X0) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ( in(sK7(X0,X1,X6),X1)
& in(ordered_pair(sK7(X0,X1,X6),X6),X0) )
| ~ in(X6,X2) ) )
| ( relation_image(X0,X1) != X2 ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f68,f71,f70,f69]) ).
tff(f69,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK5(X0,X1,X2)),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK5(X0,X1,X2)),X0) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f70,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK5(X0,X1,X2)),X0) )
=> ( in(sK6(X0,X1,X2),X1)
& in(ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f71,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
=> ( in(sK7(X0,X1,X6),X1)
& in(ordered_pair(sK7(X0,X1,X6),X6),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f68,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_image(X0,X1) = X2 )
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| ~ in(X6,X2) ) )
| ( relation_image(X0,X1) != X2 ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f67]) ).
tff(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_image(X0,X1) = X2 )
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| ( relation_image(X0,X1) != X2 ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( ( relation_image(X0,X1) = X2 )
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057',d13_relat_1) ).
tff(f241,plain,
( ~ spl11_7
| spl11_8 ),
inference(avatar_split_clause,[],[f233,f239,f235]) ).
tff(f233,plain,
! [X0: $i] :
( ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ in(X0,set_intersection2(relation_dom(sK1),sK0))
| ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0)) ),
inference(subsumption_resolution,[],[f232,f77]) ).
tff(f232,plain,
! [X0: $i] :
( ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0)))),sK1)
| ~ relation(sK1)
| ~ in(X0,set_intersection2(relation_dom(sK1),sK0))
| ~ in(sK2(relation_image(sK1,sK0),relation_image(sK1,set_intersection2(relation_dom(sK1),sK0))),relation_image(sK1,sK0)) ),
inference(resolution,[],[f163,f120]) ).
tff(f163,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( sQ10_eqProxy($i,X2,relation_image(X3,X1))
| ~ in(ordered_pair(X0,sK2(X2,relation_image(X3,X1))),X3)
| ~ relation(X3)
| ~ in(X0,X1)
| ~ in(sK2(X2,relation_image(X3,X1)),X2) ),
inference(resolution,[],[f116,f123]) ).
tff(f123,plain,
! [X0: $i,X1: $i] :
( ~ in(sK2(X0,X1),X1)
| sQ10_eqProxy($i,X0,X1)
| ~ in(sK2(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f82,f119]) ).
tff(f82,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU205+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 11:34:01 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.32 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.jlR8yd5jl0/Vampire---4.8_26057
% 0.62/0.78 % (26168)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 (2995ds/34Mi)
% 0.62/0.78 % (26171)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.78 % (26169)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 (2995ds/51Mi)
% 0.62/0.78 % (26172)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 (2995ds/34Mi)
% 0.62/0.78 % (26173)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.78 % (26170)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.78 % (26174)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 (2995ds/83Mi)
% 0.62/0.78 % (26175)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 (2995ds/56Mi)
% 0.62/0.79 % (26173)Refutation not found, incomplete strategy% (26173)------------------------------
% 0.62/0.79 % (26173)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (26173)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (26173)Memory used [KB]: 1036
% 0.62/0.79 % (26173)Time elapsed: 0.003 s
% 0.62/0.79 % (26173)Instructions burned: 3 (million)
% 0.62/0.79 % (26173)------------------------------
% 0.62/0.79 % (26173)------------------------------
% 0.62/0.79 % (26176)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 (2995ds/55Mi)
% 0.62/0.79 % (26168)First to succeed.
% 0.62/0.79 % (26168)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26166"
% 0.62/0.79 % (26168)Refutation found. Thanks to Tanya!
% 0.62/0.79 % SZS status Theorem for Vampire---4
% 0.62/0.79 % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.79 % (26168)------------------------------
% 0.62/0.79 % (26168)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (26168)Termination reason: Refutation
% 0.62/0.79
% 0.62/0.79 % (26168)Memory used [KB]: 1112
% 0.62/0.79 % (26168)Time elapsed: 0.010 s
% 0.62/0.79 % (26168)Instructions burned: 16 (million)
% 0.62/0.79 % (26166)Success in time 0.466 s
% 0.62/0.79 % Vampire---4.8 exiting
%------------------------------------------------------------------------------