%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:20:10 PM UTC 2026
% Result : Theorem 0.13s 0.57s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 10 unt; 6 def)
% Number of atoms : 137 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 138 ( 55 ~; 53 |; 14 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& closed_subset(B,A)
& top_str(A)
& topological_space(A) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> closed_subset(topstr_closure(A,B),A) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(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] :
( open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ closed_subset(B,A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f24,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,[status(thm)],[f23]) ).
fof(f35,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
! [X0,X1] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [A,B] :
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [A,B] :
( closed_subset(topstr_closure(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
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(cnf_transformation,[status(thm)],[f39]) ).
fof(f59,plain,
! [A] :
( ! [B] :
( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f60,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(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
? [A] :
( ? [B] :
( ~ open_subset(interior(A,B),A)
& element(B,powerset(the_carrier(A))) )
& top_str(A)
& topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( ~ open_subset(interior(sK5_skl,sK6_skl),sK5_skl)
& element(sK6_skl,powerset(the_carrier(sK5_skl)))
& top_str(sK5_skl)
& topological_space(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f61]) ).
fof(f63,plain,
topological_space(sK5_skl),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
top_str(sK5_skl),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
element(sK6_skl,powerset(the_carrier(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
~ open_subset(interior(sK5_skl,sK6_skl),sK5_skl),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,plain,
! [X0] :
( interior(sK5_skl,X0) = subset_complement(the_carrier(sK5_skl),topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),X0)))
| ~ element(X0,powerset(the_carrier(sK5_skl))) ),
inference(resolution,[status(thm)],[f60,f64]) ).
fof(f69,plain,
interior(sK5_skl,sK6_skl) = subset_complement(the_carrier(sK5_skl),topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl))),
inference(resolution,[status(thm)],[f67,f65]) ).
fof(f73,definition,
( sQ1_spl
<=> top_str(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ1_spl
| ~ top_str(sK5_skl) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f79,definition,
( sQ2_spl
<=> topological_space(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ2_spl
| ~ topological_space(sK5_skl) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f86,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f64]) ).
fof(f87,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f63]) ).
fof(f89,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f101,definition,
( sQ5_spl
<=> element(subset_complement(the_carrier(sK5_skl),sK6_skl),powerset(the_carrier(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ5_spl
| ~ element(subset_complement(the_carrier(sK5_skl),sK6_skl),powerset(the_carrier(sK5_skl))) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f119,plain,
( open_subset(interior(sK5_skl,sK6_skl),sK5_skl)
| ~ element(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),powerset(the_carrier(sK5_skl)))
| ~ closed_subset(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),sK5_skl)
| ~ top_str(sK5_skl)
| ~ topological_space(sK5_skl) ),
inference(paramodulation,[status(thm)],[f69,f24]) ).
fof(f122,definition,
( sQ10_spl
<=> closed_subset(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( sQ10_spl
| ~ closed_subset(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ11_spl
<=> element(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),powerset(the_carrier(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ11_spl
| ~ element(topstr_closure(sK5_skl,subset_complement(the_carrier(sK5_skl),sK6_skl)),powerset(the_carrier(sK5_skl))) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ12_spl
<=> open_subset(interior(sK5_skl,sK6_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ12_spl
| open_subset(interior(sK5_skl,sK6_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f119,f79,f73,f122,f125,f128]) ).
fof(f155,plain,
( sQ5_spl
| ~ element(sK6_skl,powerset(the_carrier(sK5_skl))) ),
inference(resolution,[status(thm)],[f103,f36]) ).
fof(f156,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f65]) ).
fof(f157,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f223,plain,
! [X0] :
( element(topstr_closure(sK5_skl,X0),powerset(the_carrier(sK5_skl)))
| ~ element(X0,powerset(the_carrier(sK5_skl))) ),
inference(resolution,[status(thm)],[f38,f64]) ).
fof(f366,plain,
( sQ11_spl
| ~ element(subset_complement(the_carrier(sK5_skl),sK6_skl),powerset(the_carrier(sK5_skl))) ),
inference(resolution,[status(thm)],[f127,f223]) ).
fof(f367,plain,
( sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f366,f101,f125]) ).
fof(f422,plain,
( sQ10_spl
| ~ element(subset_complement(the_carrier(sK5_skl),sK6_skl),powerset(the_carrier(sK5_skl)))
| ~ top_str(sK5_skl)
| ~ topological_space(sK5_skl) ),
inference(resolution,[status(thm)],[f124,f40]) ).
fof(f423,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f422,f79,f73,f101,f122]) ).
fof(f424,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f66]) ).
fof(f425,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f426,plain,
$false,
inference(sat_refutation,[status(thm)],[f87,f89,f131,f157,f367,f423,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.53 % Computer : n004.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Mon Sep 21 06:11:36 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.54 % Drodi V4.1.1
% 0.13/0.57 % Refutation found
% 0.13/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.58 % Elapsed time: 0.050534 seconds
% 0.13/0.58 % CPU time: 0.196261 seconds
% 0.13/0.58 % Total memory used: 25.597 MB
% 0.13/0.58 % Net memory used: 25.486 MB
%------------------------------------------------------------------------------