TSTP Solution File: SEU323+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 : Tue Apr 30 15:28:51 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 34
% Syntax : Number of formulae : 180 ( 25 unt; 0 def)
% Number of atoms : 499 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 570 ( 251 ~; 240 |; 43 &)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 155 ( 135 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f292,plain,
$false,
inference(avatar_sat_refutation,[],[f127,f132,f139,f163,f172,f185,f189,f213,f231,f236,f243,f291]) ).
fof(f291,plain,
~ spl6_8,
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f290,plain,
( $false
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f289,f59]) ).
fof(f59,plain,
top_str(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
( ~ open_subset(interior(sK0,sK1),sK0)
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0)
& topological_space(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f48,f47]) ).
fof(f47,plain,
( ? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) )
=> ( ? [X1] :
( ~ open_subset(interior(sK0,X1),sK0)
& element(X1,powerset(the_carrier(sK0))) )
& top_str(sK0)
& topological_space(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
( ? [X1] :
( ~ open_subset(interior(sK0,X1),sK0)
& element(X1,powerset(the_carrier(sK0))) )
=> ( ~ open_subset(interior(sK0,sK1),sK0)
& element(sK1,powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
inference(negated_conjecture,[],[f21]) ).
fof(f21,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f289,plain,
( ~ top_str(sK0)
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f287,f179]) ).
fof(f179,plain,
( element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f178,plain,
( spl6_8
<=> element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f287,plain,
( ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ spl6_8 ),
inference(resolution,[],[f282,f74]) ).
fof(f74,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f282,plain,
( ~ element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f281,f58]) ).
fof(f58,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f281,plain,
( ~ element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ topological_space(sK0)
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f280,f59]) ).
fof(f280,plain,
( ~ element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0)
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f279,f203]) ).
fof(f203,plain,
( closed_subset(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f202,f58]) ).
fof(f202,plain,
( closed_subset(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ topological_space(sK0)
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f199,f59]) ).
fof(f199,plain,
( closed_subset(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0)
| ~ spl6_8 ),
inference(resolution,[],[f179,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(topstr_closure(X0,X1),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> closed_subset(topstr_closure(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f279,plain,
( ~ element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ closed_subset(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(subsumption_resolution,[],[f276,f61]) ).
fof(f61,plain,
~ open_subset(interior(sK0,sK1),sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f276,plain,
( open_subset(interior(sK0,sK1),sK0)
| ~ element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ closed_subset(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(superposition,[],[f72,f264]) ).
fof(f264,plain,
interior(sK0,sK1) = subset_complement(the_carrier(sK0),topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1))),
inference(subsumption_resolution,[],[f250,f59]) ).
fof(f250,plain,
( interior(sK0,sK1) = subset_complement(the_carrier(sK0),topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)))
| ~ top_str(sK0) ),
inference(resolution,[],[f62,f60]) ).
fof(f60,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f49]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f72,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& closed_subset(X1,X0)
& top_str(X0)
& topological_space(X0) )
=> open_subset(subset_complement(the_carrier(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(f243,plain,
( spl6_12
| ~ spl6_13 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| spl6_12
| ~ spl6_13 ),
inference(subsumption_resolution,[],[f240,f230]) ).
fof(f230,plain,
( element(sK3(sK0),powerset(the_carrier(sK0)))
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f228,plain,
( spl6_13
<=> element(sK3(sK0),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f240,plain,
( ~ element(sK3(sK0),powerset(the_carrier(sK0)))
| spl6_12 ),
inference(resolution,[],[f226,f69]) ).
fof(f69,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f226,plain,
( ~ element(subset_complement(the_carrier(sK0),sK3(sK0)),powerset(the_carrier(sK0)))
| spl6_12 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f224,plain,
( spl6_12
<=> element(subset_complement(the_carrier(sK0),sK3(sK0)),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f236,plain,
spl6_13,
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f235,plain,
( $false
| spl6_13 ),
inference(subsumption_resolution,[],[f234,f58]) ).
fof(f234,plain,
( ~ topological_space(sK0)
| spl6_13 ),
inference(subsumption_resolution,[],[f232,f59]) ).
fof(f232,plain,
( ~ top_str(sK0)
| ~ topological_space(sK0)
| spl6_13 ),
inference(resolution,[],[f229,f65]) ).
fof(f65,plain,
! [X0] :
( element(sK3(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ( closed_subset(sK3(X0),X0)
& element(sK3(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f33,f52]) ).
fof(f52,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK3(X0),X0)
& element(sK3(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f229,plain,
( ~ element(sK3(sK0),powerset(the_carrier(sK0)))
| spl6_13 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( ~ spl6_12
| spl6_13 ),
inference(avatar_split_clause,[],[f220,f228,f224]) ).
fof(f220,plain,
( element(sK3(sK0),powerset(the_carrier(sK0)))
| ~ element(subset_complement(the_carrier(sK0),sK3(sK0)),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f69,f217]) ).
fof(f217,plain,
sK3(sK0) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK3(sK0))),
inference(subsumption_resolution,[],[f215,f58]) ).
fof(f215,plain,
( sK3(sK0) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK3(sK0)))
| ~ topological_space(sK0) ),
inference(resolution,[],[f82,f59]) ).
fof(f82,plain,
! [X0] :
( ~ top_str(X0)
| sK3(X0) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),sK3(X0)))
| ~ topological_space(X0) ),
inference(resolution,[],[f70,f65]) ).
fof(f70,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f213,plain,
( ~ spl6_10
| spl6_11
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f198,f178,f210,f206]) ).
fof(f206,plain,
( spl6_10
<=> closed_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f210,plain,
( spl6_11
<=> open_subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f198,plain,
( open_subset(sK1,sK0)
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ spl6_8 ),
inference(global_subsumption,[],[f62,f58,f59,f77,f68,f60,f61,f67,f76,f64,f66,f63,f65,f69,f70,f82,f80,f78,f85,f86,f88,f83,f73,f91,f99,f96,f97,f95,f74,f102,f101,f90,f75,f105,f104,f79,f107,f108,f109,f111,f112,f106,f81,f117,f118,f71,f148,f149,f116,f151,f179,f72,f197]) ).
fof(f197,plain,
( open_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
inference(subsumption_resolution,[],[f196,f58]) ).
fof(f196,plain,
( open_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ topological_space(sK0) ),
inference(subsumption_resolution,[],[f192,f59]) ).
fof(f192,plain,
( open_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(superposition,[],[f72,f80]) ).
fof(f151,plain,
( closed_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
inference(subsumption_resolution,[],[f150,f58]) ).
fof(f150,plain,
( closed_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ topological_space(sK0) ),
inference(subsumption_resolution,[],[f146,f59]) ).
fof(f146,plain,
( closed_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(superposition,[],[f71,f80]) ).
fof(f116,plain,
( sK2(sK5) = subset_complement(the_carrier(sK5),subset_complement(the_carrier(sK5),sK2(sK5)))
| ~ topological_space(sK5) ),
inference(resolution,[],[f81,f77]) ).
fof(f149,plain,
! [X0] :
( closed_subset(sK4(powerset(the_carrier(X0))),X0)
| ~ element(subset_complement(the_carrier(X0),sK4(powerset(the_carrier(X0)))),powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),sK4(powerset(the_carrier(X0)))),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(superposition,[],[f71,f83]) ).
fof(f148,plain,
! [X0] :
( closed_subset(the_carrier(X0),X0)
| ~ element(subset_complement(the_carrier(X0),the_carrier(X0)),powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),the_carrier(X0)),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(superposition,[],[f71,f85]) ).
fof(f71,plain,
! [X0,X1] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& open_subset(X1,X0)
& top_str(X0)
& topological_space(X0) )
=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
fof(f118,plain,
( element(sK2(sK0),powerset(the_carrier(sK0)))
| ~ element(subset_complement(the_carrier(sK0),sK2(sK0)),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f69,f117]) ).
fof(f117,plain,
sK2(sK0) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK2(sK0))),
inference(subsumption_resolution,[],[f115,f58]) ).
fof(f115,plain,
( sK2(sK0) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK2(sK0)))
| ~ topological_space(sK0) ),
inference(resolution,[],[f81,f59]) ).
fof(f81,plain,
! [X0] :
( ~ top_str(X0)
| sK2(X0) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),sK2(X0)))
| ~ topological_space(X0) ),
inference(resolution,[],[f70,f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| subset_complement(X0,X1) = subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))) ),
inference(resolution,[],[f79,f76]) ).
fof(f112,plain,
! [X0] :
( subset_complement(the_carrier(X0),sK3(X0)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),sK3(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f79,f65]) ).
fof(f111,plain,
! [X0] :
( subset_complement(the_carrier(X0),sK2(X0)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),sK2(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f79,f63]) ).
fof(f109,plain,
! [X0,X1] :
( subset_complement(the_carrier(X0),interior(X0,X1)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),interior(X0,X1))))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(resolution,[],[f79,f75]) ).
fof(f108,plain,
! [X0,X1] :
( subset_complement(the_carrier(X0),topstr_closure(X0,X1)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),topstr_closure(X0,X1))))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(resolution,[],[f79,f74]) ).
fof(f107,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = subset_complement(X0,subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))))
| ~ element(X1,powerset(X0)) ),
inference(resolution,[],[f79,f69]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))) ),
inference(resolution,[],[f70,f69]) ).
fof(f104,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| interior(X1,X0) = subset_complement(the_carrier(X1),subset_complement(the_carrier(X1),interior(X1,X0))) ),
inference(resolution,[],[f75,f70]) ).
fof(f105,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| closed_subset(topstr_closure(X1,interior(X1,X0)),X1)
| ~ topological_space(X1) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| closed_subset(topstr_closure(X1,interior(X1,X0)),X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(resolution,[],[f75,f73]) ).
fof(f75,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f90,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ subset(X1,the_carrier(X0)) ),
inference(resolution,[],[f73,f76]) ).
fof(f101,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| topstr_closure(X1,X0) = subset_complement(the_carrier(X1),subset_complement(the_carrier(X1),topstr_closure(X1,X0))) ),
inference(resolution,[],[f74,f70]) ).
fof(f102,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| closed_subset(topstr_closure(X1,topstr_closure(X1,X0)),X1)
| ~ topological_space(X1) ),
inference(duplicate_literal_removal,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| closed_subset(topstr_closure(X1,topstr_closure(X1,X0)),X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(resolution,[],[f74,f73]) ).
fof(f95,plain,
! [X0] :
( closed_subset(topstr_closure(X0,sK4(powerset(the_carrier(X0)))),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f73,f67]) ).
fof(f97,plain,
! [X0] :
( closed_subset(topstr_closure(X0,sK2(X0)),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(duplicate_literal_removal,[],[f93]) ).
fof(f93,plain,
! [X0] :
( closed_subset(topstr_closure(X0,sK2(X0)),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f73,f63]) ).
fof(f96,plain,
! [X0] :
( closed_subset(topstr_closure(X0,sK3(X0)),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(duplicate_literal_removal,[],[f94]) ).
fof(f94,plain,
! [X0] :
( closed_subset(topstr_closure(X0,sK3(X0)),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f73,f65]) ).
fof(f99,plain,
closed_subset(topstr_closure(sK0,sK1),sK0),
inference(subsumption_resolution,[],[f98,f58]) ).
fof(f98,plain,
( closed_subset(topstr_closure(sK0,sK1),sK0)
| ~ topological_space(sK0) ),
inference(subsumption_resolution,[],[f92,f59]) ).
fof(f92,plain,
( closed_subset(topstr_closure(sK0,sK1),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(resolution,[],[f73,f60]) ).
fof(f91,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,subset_complement(the_carrier(X0),X1)),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(resolution,[],[f73,f69]) ).
fof(f83,plain,
! [X0] : sK4(powerset(X0)) = subset_complement(X0,subset_complement(X0,sK4(powerset(X0)))),
inference(resolution,[],[f70,f67]) ).
fof(f88,plain,
! [X0] :
( ~ subset(subset_complement(X0,X0),X0)
| element(X0,powerset(X0)) ),
inference(resolution,[],[f86,f76]) ).
fof(f86,plain,
! [X0] :
( ~ element(subset_complement(X0,X0),powerset(X0))
| element(X0,powerset(X0)) ),
inference(superposition,[],[f69,f85]) ).
fof(f85,plain,
! [X0] : subset_complement(X0,subset_complement(X0,X0)) = X0,
inference(resolution,[],[f78,f68]) ).
fof(f78,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(resolution,[],[f70,f76]) ).
fof(f80,plain,
sK1 = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)),
inference(resolution,[],[f70,f60]) ).
fof(f63,plain,
! [X0] :
( element(sK2(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ( open_subset(sK2(X0),X0)
& element(sK2(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f50]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( open_subset(sK2(X0),X0)
& element(sK2(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
fof(f66,plain,
! [X0] :
( closed_subset(sK3(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f64,plain,
! [X0] :
( open_subset(sK2(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f67,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f12,f54]) ).
fof(f54,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f12,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f68,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f77,plain,
top_str(sK5),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
top_str(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f11,f56]) ).
fof(f56,plain,
( ? [X0] : top_str(X0)
=> top_str(sK5) ),
introduced(choice_axiom,[]) ).
fof(f11,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f189,plain,
spl6_8,
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| spl6_8 ),
inference(subsumption_resolution,[],[f186,f60]) ).
fof(f186,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| spl6_8 ),
inference(resolution,[],[f180,f69]) ).
fof(f180,plain,
( ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| spl6_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f185,plain,
( ~ spl6_7
| ~ spl6_8
| spl6_9 ),
inference(avatar_split_clause,[],[f151,f182,f178,f174]) ).
fof(f174,plain,
( spl6_7
<=> open_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f182,plain,
( spl6_9
<=> closed_subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f172,plain,
( ~ spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f116,f169,f165]) ).
fof(f165,plain,
( spl6_5
<=> topological_space(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f169,plain,
( spl6_6
<=> sK2(sK5) = subset_complement(the_carrier(sK5),subset_complement(the_carrier(sK5),sK2(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f163,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f154,f120,f160,f156]) ).
fof(f156,plain,
( spl6_3
<=> open_subset(subset_complement(the_carrier(sK0),sK2(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f160,plain,
( spl6_4
<=> closed_subset(sK2(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f120,plain,
( spl6_1
<=> element(subset_complement(the_carrier(sK0),sK2(sK0)),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f154,plain,
( closed_subset(sK2(sK0),sK0)
| ~ open_subset(subset_complement(the_carrier(sK0),sK2(sK0)),sK0)
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f153,f58]) ).
fof(f153,plain,
( closed_subset(sK2(sK0),sK0)
| ~ open_subset(subset_complement(the_carrier(sK0),sK2(sK0)),sK0)
| ~ topological_space(sK0)
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f152,f59]) ).
fof(f152,plain,
( closed_subset(sK2(sK0),sK0)
| ~ open_subset(subset_complement(the_carrier(sK0),sK2(sK0)),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0)
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f147,f121]) ).
fof(f121,plain,
( element(subset_complement(the_carrier(sK0),sK2(sK0)),powerset(the_carrier(sK0)))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f147,plain,
( closed_subset(sK2(sK0),sK0)
| ~ element(subset_complement(the_carrier(sK0),sK2(sK0)),powerset(the_carrier(sK0)))
| ~ open_subset(subset_complement(the_carrier(sK0),sK2(sK0)),sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(superposition,[],[f71,f117]) ).
fof(f139,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f138]) ).
fof(f138,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f136,f126]) ).
fof(f126,plain,
( element(sK2(sK0),powerset(the_carrier(sK0)))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl6_2
<=> element(sK2(sK0),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f136,plain,
( ~ element(sK2(sK0),powerset(the_carrier(sK0)))
| spl6_1 ),
inference(resolution,[],[f122,f69]) ).
fof(f122,plain,
( ~ element(subset_complement(the_carrier(sK0),sK2(sK0)),powerset(the_carrier(sK0)))
| spl6_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f132,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f131]) ).
fof(f131,plain,
( $false
| spl6_2 ),
inference(subsumption_resolution,[],[f130,f58]) ).
fof(f130,plain,
( ~ topological_space(sK0)
| spl6_2 ),
inference(subsumption_resolution,[],[f128,f59]) ).
fof(f128,plain,
( ~ top_str(sK0)
| ~ topological_space(sK0)
| spl6_2 ),
inference(resolution,[],[f125,f63]) ).
fof(f125,plain,
( ~ element(sK2(sK0),powerset(the_carrier(sK0)))
| spl6_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f118,f124,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:18:25 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (32688)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (32693)WARNING: value z3 for option sas not known
% 0.14/0.37 % (32692)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (32691)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (32694)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (32693)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (32695)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (32696)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (32697)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 % (32693)First to succeed.
% 0.20/0.38 TRYING [4]
% 0.20/0.38 % (32693)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (32693)------------------------------
% 0.20/0.38 % (32693)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.38 % (32693)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (32693)Memory used [KB]: 909
% 0.20/0.38 % (32693)Time elapsed: 0.014 s
% 0.20/0.38 % (32693)Instructions burned: 17 (million)
% 0.20/0.38 % (32693)------------------------------
% 0.20/0.38 % (32693)------------------------------
% 0.20/0.38 % (32688)Success in time 0.03 s
%------------------------------------------------------------------------------