TSTP Solution File: SEU323+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 31 12:36:42 EDT 2023
% Result : Theorem 0.15s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 12 unt; 0 def)
% Number of atoms : 143 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 141 ( 56 ~; 54 |; 14 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 37 (; 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& closed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( ( top_str(A)
& element(B,powerset(the_carrier(A))) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> closed_subset(topstr_closure(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
? [A] : top_str(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [A,B] :
( ~ topological_space(A)
| ~ top_str(A)
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| open_subset(subset_complement(the_carrier(A),B),A) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( ~ topological_space(X0)
| ~ top_str(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f35,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f36,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [A,B] :
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| element(topstr_closure(A,B),powerset(the_carrier(A))) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f38,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [A,B] :
( ~ topological_space(A)
| ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| closed_subset(topstr_closure(A,B),A) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f40,plain,
! [X0,X1] :
( ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f43,plain,
top_str(sk0_2),
inference(skolemization,[status(esa)],[f11]) ).
fof(f44,plain,
top_str(sk0_2),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f59,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f60,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
? [A] :
( topological_space(A)
& top_str(A)
& ? [B] :
( element(B,powerset(the_carrier(A)))
& ~ open_subset(interior(A,B),A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f62,plain,
( topological_space(sk0_5)
& top_str(sk0_5)
& element(sk0_6,powerset(the_carrier(sk0_5)))
& ~ open_subset(interior(sk0_5,sk0_6),sk0_5) ),
inference(skolemization,[status(esa)],[f61]) ).
fof(f63,plain,
topological_space(sk0_5),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f64,plain,
top_str(sk0_5),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f65,plain,
element(sk0_6,powerset(the_carrier(sk0_5))),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f66,plain,
~ open_subset(interior(sk0_5,sk0_6),sk0_5),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f67,plain,
( spl0_0
<=> top_str(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f69,plain,
( ~ top_str(sk0_5)
| spl0_0 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f75,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f64]) ).
fof(f76,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f87,plain,
( spl0_4
<=> topological_space(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f89,plain,
( ~ topological_space(sk0_5)
| spl0_4 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f148,plain,
( spl0_19
<=> interior(sk0_5,sk0_6) = subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6))) ),
introduced(split_symbol_definition) ).
fof(f149,plain,
( interior(sk0_5,sk0_6) = subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)))
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ top_str(sk0_5)
| interior(sk0_5,sk0_6) = subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6))) ),
inference(resolution,[status(thm)],[f60,f65]) ).
fof(f152,plain,
( ~ spl0_0
| spl0_19 ),
inference(split_clause,[status(thm)],[f151,f67,f148]) ).
fof(f196,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f63]) ).
fof(f197,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f252,plain,
element(subset_complement(the_carrier(sk0_5),sk0_6),powerset(the_carrier(sk0_5))),
inference(resolution,[status(thm)],[f36,f65]) ).
fof(f352,plain,
( spl0_58
<=> element(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),powerset(the_carrier(sk0_5))) ),
introduced(split_symbol_definition) ).
fof(f353,plain,
( element(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),powerset(the_carrier(sk0_5)))
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( ~ top_str(sk0_5)
| element(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),powerset(the_carrier(sk0_5))) ),
inference(resolution,[status(thm)],[f252,f38]) ).
fof(f356,plain,
( ~ spl0_0
| spl0_58 ),
inference(split_clause,[status(thm)],[f355,f67,f352]) ).
fof(f521,plain,
( spl0_89
<=> closed_subset(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f524,plain,
( ~ topological_space(sk0_5)
| ~ top_str(sk0_5)
| closed_subset(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),sk0_5) ),
inference(resolution,[status(thm)],[f40,f252]) ).
fof(f525,plain,
( ~ spl0_4
| ~ spl0_0
| spl0_89 ),
inference(split_clause,[status(thm)],[f524,f87,f67,f521]) ).
fof(f734,plain,
( spl0_121
<=> top_str(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f736,plain,
( ~ top_str(sk0_2)
| spl0_121 ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f776,plain,
( $false
| spl0_121 ),
inference(forward_subsumption_resolution,[status(thm)],[f736,f44]) ).
fof(f777,plain,
spl0_121,
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f1974,plain,
( spl0_358
<=> open_subset(subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6))),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f1975,plain,
( open_subset(subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6))),sk0_5)
| ~ spl0_358 ),
inference(component_clause,[status(thm)],[f1974]) ).
fof(f1977,plain,
( ~ topological_space(sk0_5)
| ~ top_str(sk0_5)
| ~ closed_subset(topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6)),sk0_5)
| open_subset(subset_complement(the_carrier(sk0_5),topstr_closure(sk0_5,subset_complement(the_carrier(sk0_5),sk0_6))),sk0_5)
| ~ spl0_58 ),
inference(resolution,[status(thm)],[f353,f24]) ).
fof(f1978,plain,
( ~ spl0_4
| ~ spl0_0
| ~ spl0_89
| spl0_358
| ~ spl0_58 ),
inference(split_clause,[status(thm)],[f1977,f87,f67,f521,f1974,f352]) ).
fof(f1989,plain,
( open_subset(interior(sk0_5,sk0_6),sk0_5)
| ~ spl0_19
| ~ spl0_358 ),
inference(forward_demodulation,[status(thm)],[f149,f1975]) ).
fof(f1990,plain,
( $false
| ~ spl0_19
| ~ spl0_358 ),
inference(forward_subsumption_resolution,[status(thm)],[f1989,f66]) ).
fof(f1991,plain,
( ~ spl0_19
| ~ spl0_358 ),
inference(contradiction_clause,[status(thm)],[f1990]) ).
fof(f1992,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f152,f197,f356,f525,f777,f1978,f1991]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n017.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 08:45:10 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.35 % Refutation found
% 0.15/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.58 % Elapsed time: 0.049131 seconds
% 0.23/0.58 % CPU time: 0.075786 seconds
% 0.23/0.58 % Memory used: 4.371 MB
%------------------------------------------------------------------------------