%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU318+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 : n011.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 02:20:09 PM UTC 2026
% Result : Theorem 81.06s 10.87s
% Output : CNFRefutation 70.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 134 ( 13 unt; 1 def)
% Number of atoms : 539 ( 70 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 669 ( 264 ~; 304 |; 66 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 224 ( 213 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,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(f40,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( in(C,B)
=> closed_subset(C,A) ) )
=> closed_subset(meet_of_subsets(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( in(C,the_carrier(A))
=> ( in(C,topstr_closure(A,B))
<=> ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( ( subset(B,D)
& closed_subset(D,A) )
=> in(C,D) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ? [C] :
( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C)
& ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ( subset(B,D)
& closed_subset(D,A) ) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( ( topstr_closure(A,B) = B
& topological_space(A) )
=> closed_subset(B,A) )
& ( closed_subset(B,A)
=> topstr_closure(A,B) = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( ( topstr_closure(A,B) = B
& topological_space(A) )
=> closed_subset(B,A) )
& ( closed_subset(B,A)
=> topstr_closure(A,B) = B ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f49,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f110,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f115,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,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)],[f22]) ).
fof(f122,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)],[f121]) ).
fof(f164,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f165,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f170,plain,
! [A] :
( ! [B] :
( closed_subset(meet_of_subsets(the_carrier(A),B),A)
| ? [C] :
( ~ closed_subset(C,A)
& in(C,B)
& element(C,powerset(the_carrier(A))) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f171,plain,
! [A] :
( ! [B] :
( closed_subset(meet_of_subsets(the_carrier(A),B),A)
| ( ~ closed_subset(sK8_skl(B,A),A)
& in(sK8_skl(B,A),B)
& element(sK8_skl(B,A),powerset(the_carrier(A))) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| element(sK8_skl(X1,X0),powerset(the_carrier(X0)))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0,X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| in(sK8_skl(X1,X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f174,plain,
! [X0,X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subset(sK8_skl(X1,X0),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( in(C,topstr_closure(A,B))
<=> ! [D] :
( in(C,D)
| ~ subset(B,D)
| ~ closed_subset(D,A)
| ~ element(D,powerset(the_carrier(A))) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f176,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ in(C,D)
& subset(B,D)
& closed_subset(D,A)
& element(D,powerset(the_carrier(A))) )
| in(C,topstr_closure(A,B)) )
& ( ! [D] :
( in(C,D)
| ~ subset(B,D)
| ~ closed_subset(D,A)
| ~ element(D,powerset(the_carrier(A))) )
| ~ in(C,topstr_closure(A,B)) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(NNF_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ in(C,sK9_skl(C,B,A))
& subset(B,sK9_skl(C,B,A))
& closed_subset(sK9_skl(C,B,A),A)
& element(sK9_skl(C,B,A),powerset(the_carrier(A))) )
| in(C,topstr_closure(A,B)) )
& ( ! [D] :
( in(C,D)
| ~ subset(B,D)
| ~ closed_subset(D,A)
| ~ element(D,powerset(the_carrier(A))) )
| ~ in(C,topstr_closure(A,B)) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f176]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X2,topstr_closure(X0,X1))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f183,plain,
! [A] :
( ! [B] :
( ? [C] :
( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C)
& ! [D] :
( ( in(D,C)
<=> ( subset(B,D)
& closed_subset(D,A) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f184,plain,
! [A] :
( ! [B] :
( ? [C] :
( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C)
& ! [D] :
( ( ( ~ subset(B,D)
| ~ closed_subset(D,A)
| in(D,C) )
& ( ( subset(B,D)
& closed_subset(D,A) )
| ~ in(D,C) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(NNF_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
! [A] :
( ! [B] :
( ( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),sK10_skl(B,A))
& ! [D] :
( ( ( ~ subset(B,D)
| ~ closed_subset(D,A)
| in(D,sK10_skl(B,A)) )
& ( ( subset(B,D)
& closed_subset(D,A) )
| ~ in(D,sK10_skl(B,A)) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(sK10_skl(B,A),powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f184]) ).
fof(f186,plain,
! [X0,X1] :
( element(sK10_skl(X1,X0),powerset(powerset(the_carrier(X0))))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [X0,X1,X2] :
( closed_subset(X2,X0)
| ~ in(X2,sK10_skl(X1,X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f190,plain,
! [X0,X1] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK10_skl(X1,X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f191,plain,
! [A] :
( ! [B] :
( subset(B,topstr_closure(A,B))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
! [X0,X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f193,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f194,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f195,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
? [A] :
( ? [B] :
( ( ( ~ closed_subset(B,A)
& topstr_closure(A,B) = B
& topological_space(A) )
| ( topstr_closure(A,B) != B
& closed_subset(B,A) ) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f197,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( topstr_closure(A,B) != B
& closed_subset(B,A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f198,plain,
? [A] :
( ? [B] :
( ( ( ~ closed_subset(B,A)
& topstr_closure(A,B) = B
& topological_space(A) )
| sP0_prd(B,A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(formula_renaming,[status(thm)],[f196,f197]) ).
fof(f199,plain,
( ( ( ~ closed_subset(sK12_skl,sK11_skl)
& topstr_closure(sK11_skl,sK12_skl) = sK12_skl
& topological_space(sK11_skl) )
| sP0_prd(sK12_skl,sK11_skl) )
& element(sK12_skl,powerset(the_carrier(sK11_skl)))
& top_str(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f198]) ).
fof(f200,plain,
top_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f201,plain,
element(sK12_skl,powerset(the_carrier(sK11_skl))),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f202,plain,
( topological_space(sK11_skl)
| sP0_prd(sK12_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f203,plain,
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| sP0_prd(sK12_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f204,plain,
( ~ closed_subset(sK12_skl,sK11_skl)
| sP0_prd(sK12_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f205,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f206,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f205]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f216,plain,
! [A,B] :
( ( topstr_closure(A,B) = B
| ~ closed_subset(B,A)
| sP0_prd(B,A) )
& ( ( topstr_closure(A,B) != B
& closed_subset(B,A) )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f197]) ).
fof(f217,plain,
( ! [A,B] :
( topstr_closure(A,B) = B
| ~ closed_subset(B,A)
| sP0_prd(B,A) )
& ! [A,B] :
( ( topstr_closure(A,B) != B
& closed_subset(B,A) )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f216]) ).
fof(f218,plain,
! [X0,X1] :
( closed_subset(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( topstr_closure(X1,X0) != X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f221,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f111]) ).
fof(f224,plain,
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| topological_space(sK11_skl) ),
inference(resolution,[status(thm)],[f202,f219]) ).
fof(f225,plain,
( closed_subset(sK12_skl,sK11_skl)
| topological_space(sK11_skl) ),
inference(resolution,[status(thm)],[f202,f218]) ).
fof(f229,plain,
( closed_subset(sK12_skl,sK11_skl)
| topstr_closure(sK11_skl,sK12_skl) = sK12_skl ),
inference(resolution,[status(thm)],[f203,f218]) ).
fof(f255,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X0),sK11_skl)
| in(sK8_skl(X0,sK11_skl),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl ),
inference(resolution,[status(thm)],[f224,f173]) ).
fof(f256,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X0),sK11_skl)
| element(sK8_skl(X0,sK11_skl),powerset(the_carrier(sK11_skl)))
| ~ element(X0,powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl ),
inference(resolution,[status(thm)],[f224,f172]) ).
fof(f257,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X0),sK11_skl)
| in(sK8_skl(X0,sK11_skl),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f200]) ).
fof(f258,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X0),sK11_skl)
| element(sK8_skl(X0,sK11_skl),powerset(the_carrier(sK11_skl)))
| ~ element(X0,powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f200]) ).
fof(f383,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2)
| in(X0,topstr_closure(X2,X1))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f118,f192]) ).
fof(f415,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(sK11_skl)))
| in(X0,topstr_closure(sK11_skl,X1))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f383,f200]) ).
fof(f420,plain,
! [X0] :
( in(X0,topstr_closure(sK11_skl,sK12_skl))
| ~ in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f415,f201]) ).
fof(f425,plain,
! [X0] :
( subset(sK12_skl,X0)
| in(sK0_skl(X0,sK12_skl),topstr_closure(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f420,f119]) ).
fof(f507,plain,
( subset(sK12_skl,topstr_closure(sK11_skl,sK12_skl))
| subset(sK12_skl,topstr_closure(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f425,f120]) ).
fof(f510,plain,
subset(sK12_skl,topstr_closure(sK11_skl,sK12_skl)),
inference(duplicate_literals_removal,[status(thm)],[f507]) ).
fof(f716,plain,
( ~ subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| topstr_closure(sK11_skl,sK12_skl) = sK12_skl ),
inference(resolution,[status(thm)],[f510,f113]) ).
fof(f1798,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ element(X0,powerset(the_carrier(sK11_skl)))
| ~ top_str(sK11_skl) ),
inference(resolution,[status(thm)],[f186,f224]) ).
fof(f1799,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1798,f200]) ).
fof(f2475,plain,
! [X0,X1] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(X1,sK11_skl)
| ~ in(X1,sK10_skl(X0,sK11_skl))
| ~ element(X1,powerset(the_carrier(sK11_skl)))
| ~ element(X0,powerset(the_carrier(sK11_skl)))
| ~ top_str(sK11_skl) ),
inference(resolution,[status(thm)],[f187,f224]) ).
fof(f2476,plain,
! [X0,X1] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(X1,sK11_skl)
| ~ in(X1,sK10_skl(X0,sK11_skl))
| ~ element(X1,powerset(the_carrier(sK11_skl)))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2475,f200]) ).
fof(f3361,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| in(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK10_skl(X0,sK11_skl))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f1799,f257]) ).
fof(f3367,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| in(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK10_skl(X0,sK11_skl))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f3361]) ).
fof(f3369,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| topstr_closure(sK11_skl,X0) = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl)))
| ~ top_str(sK11_skl) ),
inference(resolution,[status(thm)],[f190,f224]) ).
fof(f3370,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| topstr_closure(sK11_skl,X0) = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3369,f200]) ).
fof(f3407,plain,
! [X0,X1,X2] :
( in(X0,X2)
| empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f195,f165]) ).
fof(f3734,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3407,f207]) ).
fof(f3765,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| in(X0,the_carrier(X1))
| ~ in(X0,topstr_closure(X1,X2)) ),
inference(resolution,[status(thm)],[f3734,f122]) ).
fof(f4300,plain,
! [X0,X1] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X1),sK11_skl)
| ~ element(X1,powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(sK8_skl(X1,sK11_skl),sK11_skl)
| ~ in(sK8_skl(X1,sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f2476,f258]) ).
fof(f4313,plain,
! [X0,X1] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),X1),sK11_skl)
| ~ element(X1,powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(sK8_skl(X1,sK11_skl),sK11_skl)
| ~ in(sK8_skl(X1,sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f4300]) ).
fof(f4415,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| ~ element(X0,powerset(the_carrier(sK11_skl)))
| closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| ~ element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK11_skl)
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f4313,f3367]) ).
fof(f4417,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| ~ element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK11_skl)
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f4415]) ).
fof(f4418,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| topstr_closure(sK11_skl,sK12_skl) != sK12_skl
| closed_subset(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK11_skl)
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f4417,f1799]) ).
fof(f5320,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X2,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f178,f3765]) ).
fof(f5324,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ subset(X0,X2)
| ~ closed_subset(X2,sK11_skl)
| ~ element(X2,powerset(the_carrier(sK11_skl)))
| ~ in(X1,topstr_closure(sK11_skl,X0))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f5320,f200]) ).
fof(f5927,plain,
! [X0,X1] :
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| in(X1,sK12_skl)
| ~ subset(X0,sK12_skl)
| ~ element(sK12_skl,powerset(the_carrier(sK11_skl)))
| ~ in(X1,topstr_closure(sK11_skl,X0))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f5324,f229]) ).
fof(f5928,plain,
! [X0,X1] :
( topological_space(sK11_skl)
| in(X1,sK12_skl)
| ~ subset(X0,sK12_skl)
| ~ element(sK12_skl,powerset(the_carrier(sK11_skl)))
| ~ in(X1,topstr_closure(sK11_skl,X0))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f5324,f225]) ).
fof(f5936,plain,
! [X0,X1] :
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| in(X1,sK12_skl)
| ~ subset(X0,sK12_skl)
| ~ in(X1,topstr_closure(sK11_skl,X0))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f5927,f201]) ).
fof(f5937,plain,
! [X0,X1] :
( topological_space(sK11_skl)
| in(X1,sK12_skl)
| ~ subset(X0,sK12_skl)
| ~ in(X1,topstr_closure(sK11_skl,X0))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f5928,f201]) ).
fof(f6040,plain,
! [X0] :
( topological_space(sK11_skl)
| in(X0,sK12_skl)
| ~ in(X0,topstr_closure(sK11_skl,sK12_skl))
| ~ element(sK12_skl,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f5937,f221]) ).
fof(f6045,plain,
! [X0] :
( topological_space(sK11_skl)
| in(X0,sK12_skl)
| ~ in(X0,topstr_closure(sK11_skl,sK12_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6040,f201]) ).
fof(f6085,plain,
! [X0] :
( subset(topstr_closure(sK11_skl,sK12_skl),X0)
| topological_space(sK11_skl)
| in(sK0_skl(X0,topstr_closure(sK11_skl,sK12_skl)),sK12_skl) ),
inference(resolution,[status(thm)],[f6045,f119]) ).
fof(f6115,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| in(X0,sK12_skl)
| ~ in(X0,topstr_closure(sK11_skl,sK12_skl))
| ~ element(sK12_skl,powerset(the_carrier(sK11_skl))) ),
inference(resolution,[status(thm)],[f5936,f221]) ).
fof(f6120,plain,
! [X0] :
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| in(X0,sK12_skl)
| ~ in(X0,topstr_closure(sK11_skl,sK12_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6115,f201]) ).
fof(f6170,plain,
! [X0] :
( subset(topstr_closure(sK11_skl,sK12_skl),X0)
| topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| in(sK0_skl(X0,topstr_closure(sK11_skl,sK12_skl)),sK12_skl) ),
inference(resolution,[status(thm)],[f6120,f119]) ).
fof(f6254,plain,
( subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| topological_space(sK11_skl) ),
inference(resolution,[status(thm)],[f6085,f120]) ).
fof(f6263,plain,
( subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| topological_space(sK11_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f6254]) ).
fof(f6264,plain,
( topstr_closure(sK11_skl,sK12_skl) = sK12_skl
| topological_space(sK11_skl) ),
inference(resolution,[status(thm)],[f6263,f716]) ).
fof(f6271,plain,
topological_space(sK11_skl),
inference(forward_subsumption_resolution,[status(thm)],[f6264,f224]) ).
fof(f8114,plain,
( subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| topstr_closure(sK11_skl,sK12_skl) = sK12_skl ),
inference(resolution,[status(thm)],[f6170,f120]) ).
fof(f8123,plain,
( subset(topstr_closure(sK11_skl,sK12_skl),sK12_skl)
| topstr_closure(sK11_skl,sK12_skl) = sK12_skl ),
inference(duplicate_literals_removal,[status(thm)],[f8114]) ).
fof(f8124,plain,
topstr_closure(sK11_skl,sK12_skl) = sK12_skl,
inference(forward_subsumption_resolution,[status(thm)],[f8123,f716]) ).
fof(f8615,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| sK12_skl != sK12_skl
| closed_subset(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK11_skl)
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(backward_demodulation,[status(thm)],[f8124,f4418]) ).
fof(f8650,plain,
! [X0] :
( sK12_skl != sK12_skl
| topstr_closure(sK11_skl,X0) = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(backward_demodulation,[status(thm)],[f8124,f3370]) ).
fof(f8682,plain,
! [X0] :
( sK12_skl != sK12_skl
| element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(backward_demodulation,[status(thm)],[f8124,f1799]) ).
fof(f8843,plain,
! [X0] :
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl)),sK11_skl)
| closed_subset(sK8_skl(sK10_skl(X0,sK11_skl),sK11_skl),sK11_skl)
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(trivial_equality_resolution,[status(thm)],[f8615]) ).
fof(f8874,plain,
! [X0] :
( topstr_closure(sK11_skl,X0) = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(X0,sK11_skl))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(trivial_equality_resolution,[status(thm)],[f8650]) ).
fof(f8897,plain,
! [X0] :
( element(sK10_skl(X0,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ element(X0,powerset(the_carrier(sK11_skl))) ),
inference(trivial_equality_resolution,[status(thm)],[f8682]) ).
fof(f9042,plain,
topstr_closure(sK11_skl,sK12_skl) = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(sK12_skl,sK11_skl)),
inference(resolution,[status(thm)],[f8874,f201]) ).
fof(f9047,plain,
sK12_skl = meet_of_subsets(the_carrier(sK11_skl),sK10_skl(sK12_skl,sK11_skl)),
inference(forward_demodulation,[status(thm)],[f8124,f9042]) ).
fof(f11151,plain,
( closed_subset(sK12_skl,sK11_skl)
| closed_subset(sK8_skl(sK10_skl(sK12_skl,sK11_skl),sK11_skl),sK11_skl)
| ~ element(sK12_skl,powerset(the_carrier(sK11_skl))) ),
inference(paramodulation,[status(thm)],[f9047,f8843]) ).
fof(f11155,plain,
( closed_subset(sK12_skl,sK11_skl)
| closed_subset(sK8_skl(sK10_skl(sK12_skl,sK11_skl),sK11_skl),sK11_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11151,f201]) ).
fof(f11301,plain,
( closed_subset(meet_of_subsets(the_carrier(sK11_skl),sK10_skl(sK12_skl,sK11_skl)),sK11_skl)
| ~ element(sK10_skl(sK12_skl,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| ~ topological_space(sK11_skl)
| closed_subset(sK12_skl,sK11_skl) ),
inference(resolution,[status(thm)],[f11155,f174]) ).
fof(f11306,plain,
( closed_subset(sK12_skl,sK11_skl)
| ~ element(sK10_skl(sK12_skl,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| ~ topological_space(sK11_skl)
| closed_subset(sK12_skl,sK11_skl) ),
inference(forward_demodulation,[status(thm)],[f9047,f11301]) ).
fof(f11307,plain,
( ~ element(sK10_skl(sK12_skl,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| ~ topological_space(sK11_skl)
| closed_subset(sK12_skl,sK11_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f11306]) ).
fof(f11308,plain,
( ~ element(sK10_skl(sK12_skl,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| ~ top_str(sK11_skl)
| closed_subset(sK12_skl,sK11_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11307,f6271]) ).
fof(f12131,plain,
( ~ element(sK10_skl(sK12_skl,sK11_skl),powerset(powerset(the_carrier(sK11_skl))))
| closed_subset(sK12_skl,sK11_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f11308,f200]) ).
fof(f12132,plain,
( ~ element(sK12_skl,powerset(the_carrier(sK11_skl)))
| closed_subset(sK12_skl,sK11_skl) ),
inference(resolution,[status(thm)],[f12131,f8897]) ).
fof(f12135,plain,
closed_subset(sK12_skl,sK11_skl),
inference(forward_subsumption_resolution,[status(thm)],[f12132,f201]) ).
fof(f12136,plain,
sP0_prd(sK12_skl,sK11_skl),
inference(backward_subsumption_resolution,[status(thm)],[f204,f12135]) ).
fof(f12143,plain,
topstr_closure(sK11_skl,sK12_skl) != sK12_skl,
inference(resolution,[status(thm)],[f12136,f219]) ).
fof(f12145,plain,
sK12_skl != sK12_skl,
inference(forward_demodulation,[status(thm)],[f8124,f12143]) ).
fof(f12146,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f12145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU318+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n011.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 06:11:10 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 81.06/10.87 % Refutation found
% 81.06/10.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 81.06/10.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.72/10.98 % Elapsed time: 10.529717 seconds
% 17.72/10.98 % CPU time: 82.744748 seconds
% 17.72/10.98 % Total memory used: 428.214 MB
% 17.72/10.98 % Net memory used: 392.287 MB
%------------------------------------------------------------------------------