TSTP Solution File: SEU314+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU314+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 : n011.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 May 1 03:51:48 EDT 2024
% Result : Theorem 0.66s 0.81s
% Output : Refutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 137 ( 5 unt; 0 def)
% Number of atoms : 944 ( 130 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 1243 ( 436 ~; 523 |; 254 &)
% ( 12 <=>; 16 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 6 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 300 ( 203 !; 97 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f273,plain,
$false,
inference(avatar_sat_refutation,[],[f180,f194,f216,f244,f257,f270]) ).
fof(f270,plain,
( ~ spl15_1
| spl15_2
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| ~ spl15_1
| spl15_2
| ~ spl15_3 ),
inference(subsumption_resolution,[],[f268,f178]) ).
fof(f178,plain,
( ~ sP1(sK3,sK2)
| spl15_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f177,plain,
( spl15_2
<=> sP1(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f268,plain,
( sP1(sK3,sK2)
| ~ spl15_1
| ~ spl15_3 ),
inference(subsumption_resolution,[],[f264,f70]) ).
fof(f70,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
( ! [X2] :
( ( ! [X4] :
( ~ subset(sK3,sK4(X2))
| ~ closed_subset(X4,sK2)
| sK4(X2) != X4
| ~ element(X4,powerset(the_carrier(sK2))) )
| ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ in(sK4(X2),X2) )
& ( ( subset(sK3,sK4(X2))
& closed_subset(sK5(X2),sK2)
& sK4(X2) = sK5(X2)
& element(sK5(X2),powerset(the_carrier(sK2)))
& in(sK4(X2),powerset(the_carrier(sK2))) )
| in(sK4(X2),X2) ) )
& element(sK3,powerset(the_carrier(sK2)))
& top_str(sK2)
& topological_space(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f46,f49,f48,f47]) ).
fof(f47,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(sK3,X3)
| ~ closed_subset(X4,sK2)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK2))) )
| ~ in(X3,powerset(the_carrier(sK2)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(sK3,X3)
& closed_subset(X5,sK2)
& X3 = X5
& element(X5,powerset(the_carrier(sK2))) )
& in(X3,powerset(the_carrier(sK2))) )
| in(X3,X2) ) )
& element(sK3,powerset(the_carrier(sK2)))
& top_str(sK2)
& topological_space(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(sK3,X3)
| ~ closed_subset(X4,sK2)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK2))) )
| ~ in(X3,powerset(the_carrier(sK2)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(sK3,X3)
& closed_subset(X5,sK2)
& X3 = X5
& element(X5,powerset(the_carrier(sK2))) )
& in(X3,powerset(the_carrier(sK2))) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ subset(sK3,sK4(X2))
| ~ closed_subset(X4,sK2)
| sK4(X2) != X4
| ~ element(X4,powerset(the_carrier(sK2))) )
| ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ in(sK4(X2),X2) )
& ( ( ? [X5] :
( subset(sK3,sK4(X2))
& closed_subset(X5,sK2)
& sK4(X2) = X5
& element(X5,powerset(the_carrier(sK2))) )
& in(sK4(X2),powerset(the_carrier(sK2))) )
| in(sK4(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X2] :
( ? [X5] :
( subset(sK3,sK4(X2))
& closed_subset(X5,sK2)
& sK4(X2) = X5
& element(X5,powerset(the_carrier(sK2))) )
=> ( subset(sK3,sK4(X2))
& closed_subset(sK5(X2),sK2)
& sK4(X2) = sK5(X2)
& element(sK5(X2),powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MUWuGFYsjU/Vampire---4.8_18380',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f264,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| sP1(sK3,sK2)
| ~ spl15_1
| ~ spl15_3 ),
inference(resolution,[],[f207,f175]) ).
fof(f175,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f173,plain,
( spl15_1
<=> in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f207,plain,
( ! [X0] :
( ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f206,plain,
( spl15_3
<=> ! [X0] :
( ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f257,plain,
( ~ spl15_1
| spl15_2
| spl15_5 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f256,plain,
( $false
| ~ spl15_1
| spl15_2
| spl15_5 ),
inference(subsumption_resolution,[],[f255,f68]) ).
fof(f68,plain,
topological_space(sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f255,plain,
( ~ topological_space(sK2)
| ~ spl15_1
| spl15_2
| spl15_5 ),
inference(subsumption_resolution,[],[f254,f175]) ).
fof(f254,plain,
( ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ topological_space(sK2)
| spl15_2
| spl15_5 ),
inference(subsumption_resolution,[],[f253,f70]) ).
fof(f253,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ topological_space(sK2)
| spl15_2
| spl15_5 ),
inference(subsumption_resolution,[],[f252,f178]) ).
fof(f252,plain,
( sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ topological_space(sK2)
| spl15_5 ),
inference(resolution,[],[f246,f69]) ).
fof(f69,plain,
top_str(sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f246,plain,
( ! [X0] :
( ~ top_str(X0)
| sP1(sK3,X0)
| ~ element(sK3,powerset(the_carrier(X0)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(X0,sK3))
| ~ topological_space(X0) )
| spl15_5 ),
inference(resolution,[],[f215,f94]) ).
fof(f94,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ( subset(X1,X3)
& closed_subset(sK13(X0,X1,X3),X0)
& sK13(X0,X1,X3) = X3
& element(sK13(X0,X1,X3),powerset(the_carrier(X0)))
& sK12(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),powerset(the_carrier(X0))) )
| ~ in(X3,sK11(X0,X1)) ) )
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f61,f64,f63,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X6] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X6
& in(X6,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X6] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X6
& in(X6,powerset(the_carrier(X0))) )
| ~ in(X3,sK11(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1,X3] :
( ? [X6] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X6
& in(X6,powerset(the_carrier(X0))) )
=> ( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& sK12(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1,X3] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
=> ( subset(X1,X3)
& closed_subset(sK13(X0,X1,X3),X0)
& sK13(X0,X1,X3) = X3
& element(sK13(X0,X1,X3),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) ) )
& ( ? [X6] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X6
& in(X6,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ! [X10] :
( ~ subset(X1,X8)
| ~ closed_subset(X10,X0)
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
| X8 != X9
| ~ in(X9,powerset(the_carrier(X0))) ) )
& ( ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) )
| ~ in(X8,X7) ) )
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f37,f42,f41]) ).
fof(f41,plain,
! [X3,X1,X0] :
( ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
| ~ sP0(X3,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f42,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& sP0(X3,X1,X0)
& X2 = X3 )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X4 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X4
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MUWuGFYsjU/Vampire---4.8_18380',s1_tarski__e1_40__pre_topc__1) ).
fof(f215,plain,
( ~ subset(sK3,sK4(sK11(sK2,sK3)))
| spl15_5 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f213,plain,
( spl15_5
<=> subset(sK3,sK4(sK11(sK2,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f244,plain,
( spl15_4
| ~ spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f243,f177,f173,f209]) ).
fof(f209,plain,
( spl15_4
<=> in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f243,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f242,f68]) ).
fof(f242,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ topological_space(sK2)
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f241,f69]) ).
fof(f241,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f240,f70]) ).
fof(f240,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ element(sK3,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f239,f178]) ).
fof(f239,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f231,f175]) ).
fof(f231,plain,
( in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| ~ spl15_1
| spl15_2 ),
inference(superposition,[],[f225,f90]) ).
fof(f90,plain,
! [X3,X0,X1] :
( sK12(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f225,plain,
( in(sK12(sK2,sK3,sK4(sK11(sK2,sK3))),powerset(the_carrier(sK2)))
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f224,f70]) ).
fof(f224,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| in(sK12(sK2,sK3,sK4(sK11(sK2,sK3))),powerset(the_carrier(sK2)))
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f199,f178]) ).
fof(f199,plain,
( sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| in(sK12(sK2,sK3,sK4(sK11(sK2,sK3))),powerset(the_carrier(sK2)))
| ~ spl15_1 ),
inference(resolution,[],[f175,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ in(X0,sK11(sK2,X1))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| in(sK12(sK2,X1,X0),powerset(the_carrier(sK2))) ),
inference(subsumption_resolution,[],[f109,f68]) ).
fof(f109,plain,
! [X0,X1] :
( ~ in(X0,sK11(sK2,X1))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| in(sK12(sK2,X1,X0),powerset(the_carrier(sK2)))
| ~ topological_space(sK2) ),
inference(resolution,[],[f89,f69]) ).
fof(f89,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f216,plain,
( spl15_3
| ~ spl15_4
| ~ spl15_5
| ~ spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f204,f177,f173,f213,f209,f206]) ).
fof(f204,plain,
( ! [X0] :
( ~ subset(sK3,sK4(sK11(sK2,sK3)))
| ~ in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) )
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f203,f175]) ).
fof(f203,plain,
( ! [X0] :
( ~ subset(sK3,sK4(sK11(sK2,sK3)))
| ~ in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) )
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f202,f178]) ).
fof(f202,plain,
( ! [X0] :
( ~ subset(sK3,sK4(sK11(sK2,sK3)))
| sP1(sK3,sK2)
| ~ in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) )
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f197,f70]) ).
fof(f197,plain,
( ! [X0] :
( ~ element(sK3,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,sK3)))
| sP1(sK3,sK2)
| ~ in(sK4(sK11(sK2,sK3)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ in(sK4(sK11(sK2,sK3)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) )
| ~ spl15_1 ),
inference(resolution,[],[f175,f141]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(sK4(X1),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(X1))
| sP1(X0,sK2)
| ~ in(sK4(X1),powerset(the_carrier(sK2)))
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),sK11(sK2,X2))
| sP1(X2,sK2)
| ~ element(X2,powerset(the_carrier(sK2))) ),
inference(subsumption_resolution,[],[f140,f68]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(sK4(X1),sK11(sK2,X0))
| ~ subset(sK3,sK4(X1))
| sP1(X0,sK2)
| ~ in(sK4(X1),powerset(the_carrier(sK2)))
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),sK11(sK2,X2))
| sP1(X2,sK2)
| ~ element(X2,powerset(the_carrier(sK2)))
| ~ topological_space(sK2) ),
inference(subsumption_resolution,[],[f139,f69]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(sK4(X1),sK11(sK2,X0))
| ~ subset(sK3,sK4(X1))
| sP1(X0,sK2)
| ~ in(sK4(X1),powerset(the_carrier(sK2)))
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),sK11(sK2,X2))
| sP1(X2,sK2)
| ~ element(X2,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2) ),
inference(resolution,[],[f117,f116]) ).
fof(f116,plain,
! [X2,X0,X1] :
( element(X2,powerset(the_carrier(X0)))
| ~ in(X2,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(duplicate_literal_removal,[],[f115]) ).
fof(f115,plain,
! [X2,X0,X1] :
( element(X2,powerset(the_carrier(X0)))
| ~ in(X2,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X2,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(superposition,[],[f91,f92]) ).
fof(f92,plain,
! [X3,X0,X1] :
( sK13(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
! [X3,X0,X1] :
( element(sK13(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f117,plain,
! [X0,X1] :
( ~ element(sK4(X1),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(sK4(X1),sK11(sK2,X0))
| ~ subset(sK3,sK4(X1))
| sP1(X0,sK2)
| ~ in(sK4(X1),powerset(the_carrier(sK2)))
| ~ in(sK4(X1),X1) ),
inference(resolution,[],[f114,f100]) ).
fof(f100,plain,
! [X2] :
( ~ closed_subset(sK4(X2),sK2)
| ~ subset(sK3,sK4(X2))
| ~ element(sK4(X2),powerset(the_carrier(sK2)))
| ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f76]) ).
fof(f76,plain,
! [X2,X4] :
( ~ subset(sK3,sK4(X2))
| ~ closed_subset(X4,sK2)
| sK4(X2) != X4
| ~ element(X4,powerset(the_carrier(sK2)))
| ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f114,plain,
! [X0,X1] :
( closed_subset(X1,sK2)
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(X1,sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f113,f68]) ).
fof(f113,plain,
! [X0,X1] :
( closed_subset(X1,sK2)
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(X1,sK11(sK2,X0))
| ~ topological_space(sK2) ),
inference(subsumption_resolution,[],[f112,f69]) ).
fof(f112,plain,
! [X0,X1] :
( closed_subset(X1,sK2)
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(X1,sK11(sK2,X0))
| ~ top_str(sK2)
| ~ topological_space(sK2) ),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( closed_subset(X1,sK2)
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ in(X1,sK11(sK2,X0))
| ~ in(X1,sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2) ),
inference(superposition,[],[f108,f92]) ).
fof(f108,plain,
! [X0,X1] :
( closed_subset(sK13(sK2,X1,X0),sK2)
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ in(X0,sK11(sK2,X1)) ),
inference(subsumption_resolution,[],[f107,f68]) ).
fof(f107,plain,
! [X0,X1] :
( ~ in(X0,sK11(sK2,X1))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| closed_subset(sK13(sK2,X1,X0),sK2)
| ~ topological_space(sK2) ),
inference(resolution,[],[f93,f69]) ).
fof(f93,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK11(X0,X1))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(sK13(X0,X1,X3),X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f194,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f192,f179]) ).
fof(f179,plain,
( sP1(sK3,sK2)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f192,plain,
( ~ sP1(sK3,sK2)
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f190,f183]) ).
fof(f183,plain,
( sK6(sK3,sK2) = sK7(sK3,sK2)
| ~ spl15_2 ),
inference(resolution,[],[f179,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sK6(X0,X1) = sK7(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( sK7(X0,X1) != sK8(X0,X1)
& subset(X0,sK8(X0,X1))
& closed_subset(sK9(X0,X1),X1)
& sK8(X0,X1) = sK9(X0,X1)
& element(sK9(X0,X1),powerset(the_carrier(X1)))
& sK6(X0,X1) = sK8(X0,X1)
& sP0(sK7(X0,X1),X0,X1)
& sK6(X0,X1) = sK7(X0,X1) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f52,f54,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X0,X4)
& closed_subset(X5,X1)
& X4 = X5
& element(X5,powerset(the_carrier(X1))) )
& X2 = X4
& sP0(X3,X0,X1)
& X2 = X3 )
=> ( sK7(X0,X1) != sK8(X0,X1)
& ? [X5] :
( subset(X0,sK8(X0,X1))
& closed_subset(X5,X1)
& sK8(X0,X1) = X5
& element(X5,powerset(the_carrier(X1))) )
& sK6(X0,X1) = sK8(X0,X1)
& sP0(sK7(X0,X1),X0,X1)
& sK6(X0,X1) = sK7(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X5] :
( subset(X0,sK8(X0,X1))
& closed_subset(X5,X1)
& sK8(X0,X1) = X5
& element(X5,powerset(the_carrier(X1))) )
=> ( subset(X0,sK8(X0,X1))
& closed_subset(sK9(X0,X1),X1)
& sK8(X0,X1) = sK9(X0,X1)
& element(sK9(X0,X1),powerset(the_carrier(X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X0,X4)
& closed_subset(X5,X1)
& X4 = X5
& element(X5,powerset(the_carrier(X1))) )
& X2 = X4
& sP0(X3,X0,X1)
& X2 = X3 )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& sP0(X3,X1,X0)
& X2 = X3 )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f190,plain,
( sK6(sK3,sK2) != sK7(sK3,sK2)
| ~ sP1(sK3,sK2)
| ~ spl15_2 ),
inference(superposition,[],[f84,f182]) ).
fof(f182,plain,
( sK8(sK3,sK2) = sK6(sK3,sK2)
| ~ spl15_2 ),
inference(resolution,[],[f179,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sK6(X0,X1) = sK8(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X0,X1] :
( sK7(X0,X1) != sK8(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f180,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f171,f177,f173]) ).
fof(f171,plain,
( sP1(sK3,sK2)
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
inference(subsumption_resolution,[],[f170,f70]) ).
fof(f170,plain,
( sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
inference(duplicate_literal_removal,[],[f167]) ).
fof(f167,plain,
( sP1(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
inference(resolution,[],[f166,f75]) ).
fof(f75,plain,
! [X2] :
( subset(sK3,sK4(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f166,plain,
! [X0] :
( ~ subset(X0,sK4(sK11(sK2,X0)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f165,f153]) ).
fof(f153,plain,
! [X0] :
( element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(subsumption_resolution,[],[f151,f75]) ).
fof(f151,plain,
! [X0] :
( element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(superposition,[],[f72,f150]) ).
fof(f150,plain,
! [X0] :
( sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ~ subset(sK3,sK4(sK11(sK2,X0)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(resolution,[],[f146,f73]) ).
fof(f73,plain,
! [X2] :
( in(sK4(X2),X2)
| sK4(X2) = sK5(X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f145,f129]) ).
fof(f129,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f128,f73]) ).
fof(f128,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f127,f68]) ).
fof(f127,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ topological_space(sK2) ),
inference(subsumption_resolution,[],[f126,f69]) ).
fof(f126,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ top_str(sK2)
| ~ topological_space(sK2) ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f125,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ topological_space(sK2) ),
inference(superposition,[],[f120,f90]) ).
fof(f120,plain,
! [X0] :
( in(sK12(sK2,X0,sK4(sK11(sK2,X0))),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(resolution,[],[f110,f73]) ).
fof(f145,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| sP1(X0,sK2)
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f142,f73]) ).
fof(f142,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| sP1(X0,sK2)
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| sP1(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| sK4(sK11(sK2,X0)) = sK5(sK11(sK2,X0)) ),
inference(resolution,[],[f141,f73]) ).
fof(f72,plain,
! [X2] :
( element(sK5(X2),powerset(the_carrier(sK2)))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f165,plain,
! [X0] :
( ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(subsumption_resolution,[],[f163,f75]) ).
fof(f163,plain,
! [X0] :
( ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(resolution,[],[f161,f71]) ).
fof(f71,plain,
! [X2] :
( in(sK4(X2),powerset(the_carrier(sK2)))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f161,plain,
! [X0] :
( ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ subset(X0,sK4(sK11(sK2,X0))) ),
inference(subsumption_resolution,[],[f160,f154]) ).
fof(f154,plain,
! [X0] :
( closed_subset(sK4(sK11(sK2,X0)),sK2)
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(subsumption_resolution,[],[f152,f114]) ).
fof(f152,plain,
! [X0] :
( closed_subset(sK4(sK11(sK2,X0)),sK2)
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(superposition,[],[f74,f150]) ).
fof(f74,plain,
! [X2] :
( closed_subset(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f160,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0))) ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK4(sK11(sK2,X0))) ),
inference(resolution,[],[f156,f119]) ).
fof(f119,plain,
! [X0,X1] :
( in(X1,sK11(sK2,X0))
| ~ closed_subset(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ in(X1,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f118,f68]) ).
fof(f118,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ closed_subset(X1,sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ in(X1,powerset(the_carrier(sK2)))
| sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| in(X1,sK11(sK2,X0))
| ~ topological_space(sK2) ),
inference(resolution,[],[f102,f69]) ).
fof(f102,plain,
! [X0,X1,X5] :
( ~ top_str(X0)
| ~ subset(X1,X5)
| ~ closed_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0)))
| ~ in(X5,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| in(X5,sK11(X0,X1))
| ~ topological_space(X0) ),
inference(equality_resolution,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X4,X5] :
( in(X5,sK11(X0,X1))
| ~ subset(X1,X5)
| ~ closed_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0)))
| X4 != X5
| ~ in(X4,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f95,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK11(X0,X1))
| ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f156,plain,
! [X0] :
( ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| sP1(X0,sK2) ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f155,plain,
! [X0] :
( sP1(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(resolution,[],[f154,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU314+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14 % 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 16:20:16 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35 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.MUWuGFYsjU/Vampire---4.8_18380
% 0.61/0.80 % (18490)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)
% 0.61/0.80 % (18492)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.61/0.80 % (18493)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)
% 0.61/0.80 % (18494)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)
% 0.61/0.80 % (18495)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)
% 0.61/0.80 % (18496)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)
% 0.61/0.80 % (18497)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)
% 0.61/0.80 % (18497)Refutation not found, incomplete strategy% (18497)------------------------------
% 0.61/0.80 % (18497)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (18495)Refutation not found, incomplete strategy% (18495)------------------------------
% 0.61/0.80 % (18495)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (18495)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (18495)Memory used [KB]: 1067
% 0.61/0.80 % (18495)Time elapsed: 0.004 s
% 0.61/0.80 % (18495)Instructions burned: 4 (million)
% 0.61/0.80 % (18495)------------------------------
% 0.61/0.80 % (18495)------------------------------
% 0.61/0.80 % (18497)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (18497)Memory used [KB]: 1073
% 0.61/0.80 % (18497)Time elapsed: 0.004 s
% 0.61/0.80 % (18497)Instructions burned: 4 (million)
% 0.61/0.80 % (18497)------------------------------
% 0.61/0.80 % (18497)------------------------------
% 0.61/0.80 % (18491)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)
% 0.61/0.80 % (18490)Refutation not found, incomplete strategy% (18490)------------------------------
% 0.61/0.80 % (18490)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (18490)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (18490)Memory used [KB]: 1137
% 0.61/0.80 % (18490)Time elapsed: 0.005 s
% 0.61/0.80 % (18490)Instructions burned: 8 (million)
% 0.61/0.80 % (18490)------------------------------
% 0.61/0.80 % (18490)------------------------------
% 0.61/0.80 % (18493)Refutation not found, incomplete strategy% (18493)------------------------------
% 0.61/0.80 % (18493)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (18493)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (18493)Memory used [KB]: 1122
% 0.61/0.80 % (18493)Time elapsed: 0.006 s
% 0.61/0.80 % (18493)Instructions burned: 6 (million)
% 0.61/0.80 % (18493)------------------------------
% 0.61/0.80 % (18493)------------------------------
% 0.61/0.81 % (18494)Refutation not found, incomplete strategy% (18494)------------------------------
% 0.61/0.81 % (18494)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.81 % (18494)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.81
% 0.61/0.81 % (18494)Memory used [KB]: 1194
% 0.61/0.81 % (18494)Time elapsed: 0.008 s
% 0.61/0.81 % (18494)Instructions burned: 12 (million)
% 0.61/0.81 % (18494)------------------------------
% 0.61/0.81 % (18494)------------------------------
% 0.61/0.81 % (18498)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)
% 0.61/0.81 % (18499)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 (2995ds/50Mi)
% 0.61/0.81 % (18500)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.66/0.81 % (18492)First to succeed.
% 0.66/0.81 % (18501)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.66/0.81 % (18502)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.66/0.81 % (18491)Also succeeded, but the first one will report.
% 0.66/0.81 % (18492)Refutation found. Thanks to Tanya!
% 0.66/0.81 % SZS status Theorem for Vampire---4
% 0.66/0.81 % SZS output start Proof for Vampire---4
% See solution above
% 0.66/0.81 % (18492)------------------------------
% 0.66/0.81 % (18492)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.66/0.81 % (18492)Termination reason: Refutation
% 0.66/0.81
% 0.66/0.81 % (18492)Memory used [KB]: 1183
% 0.66/0.81 % (18492)Time elapsed: 0.014 s
% 0.66/0.81 % (18492)Instructions burned: 23 (million)
% 0.66/0.81 % (18492)------------------------------
% 0.66/0.81 % (18492)------------------------------
% 0.66/0.81 % (18487)Success in time 0.46 s
% 0.66/0.81 % Vampire---4.8 exiting
%------------------------------------------------------------------------------