%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU318+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 : Fri Sep 25 02:56:47 PM UTC 2026
% Result : Theorem 36.32s 13.52s
% Output : CNFRefutation 36.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 148 ( 17 unt; 0 def)
% Number of atoms : 634 ( 65 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 820 ( 334 ~; 377 |; 74 &)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 261 ( 1 sgn 246 !; 15 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f18,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f22,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(f38,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f42,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( in(X2,X1)
=> closed_subset(X2,X0) ) )
=> closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
fof(f43,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f44,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(f45,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f47,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( ( topstr_closure(X0,X1) = X1
& topological_space(X0) )
=> closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f48,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( ( topstr_closure(X0,X1) = X1
& topological_space(X0) )
=> closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f38]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f83,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f22]) ).
fof(f84,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f83]) ).
fof(f93,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f94,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f96,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f102,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( ( topstr_closure(X0,X1) = X1
& topological_space(X0)
& ~ closed_subset(X1,X0) )
| ( closed_subset(X1,X0)
& topstr_closure(X0,X1) != X1 ) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f103,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( ( topstr_closure(X0,X1) = X1
& topological_space(X0)
& ~ closed_subset(X1,X0) )
| ( closed_subset(X1,X0)
& topstr_closure(X0,X1) != X1 ) ) ) ),
inference(flattening,[],[f102]) ).
fof(f108,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f109,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f111,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f111]) ).
fof(f119,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f120,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( element(sK7(X0,X1),powerset(the_carrier(X0)))
& in(sK7(X0,X1),X1)
& ~ closed_subset(sK7(X0,X1),X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f94]) ).
fof(f121,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f122,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ( element(sK8(X0,X1,X2),powerset(the_carrier(X0)))
& subset(X1,sK8(X0,X1,X2))
& closed_subset(sK8(X0,X1,X2),X0)
& ~ in(X2,sK8(X0,X1,X2)) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f122]) ).
fof(f124,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f125,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK9(X0,X1))
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,sK9(X0,X1))
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,sK9(X0,X1)) ) ) )
& element(sK9(X0,X1),powerset(powerset(the_carrier(X0)))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f125]) ).
fof(f127,plain,
( top_str(sK10)
& element(sK11,powerset(the_carrier(sK10)))
& ( ( sK11 = topstr_closure(sK10,sK11)
& topological_space(sK10)
& ~ closed_subset(sK11,sK10) )
| ( closed_subset(sK11,sK10)
& sK11 != topstr_closure(sK10,sK11) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f103]) ).
fof(f155,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f156,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f157,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f159,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f183,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f186,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f187,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f188,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| element(sK7(X0,X1),powerset(the_carrier(X0)))
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f189,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK7(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f190,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK7(X0,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f191,plain,
! [X2,X0,X1,X4] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,topstr_closure(X0,X1))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ),
inference(cnf_transformation,[],[f123]) ).
fof(f196,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK9(X0,X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f198,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK9(X0,X1))
| closed_subset(X3,X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| element(sK9(X0,X1),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f126]) ).
fof(f201,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f203,plain,
top_str(sK10),
inference(cnf_transformation,[],[f127]) ).
fof(f204,plain,
element(sK11,powerset(the_carrier(sK10))),
inference(cnf_transformation,[],[f127]) ).
fof(f205,plain,
( sK11 = topstr_closure(sK10,sK11)
| closed_subset(sK11,sK10) ),
inference(cnf_transformation,[],[f127]) ).
fof(f206,plain,
( topological_space(sK10)
| closed_subset(sK11,sK10) ),
inference(cnf_transformation,[],[f127]) ).
fof(f210,plain,
( ~ closed_subset(sK11,sK10)
| sK11 != topstr_closure(sK10,sK11) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_104,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f183]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ closed_subset(sK7(X1,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( in(sK7(X1,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| element(sK7(X1,X0),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ top_str(X1)
| ~ closed_subset(X3,X1)
| ~ subset(X2,X3)
| ~ in(X0,the_carrier(X1))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,topstr_closure(X1,X2)) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( element(sK9(X1,X0),powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X0,X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK9(X1,X2)) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(X1),sK9(X1,X0)) = topstr_closure(X1,X0) )
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( subset(X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_124,negated_conjecture,
( ~ closed_subset(sK11,sK10)
| ( topstr_closure(sK10,sK11) != sK11 ) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_126,negated_conjecture,
( topological_space(sK10)
| closed_subset(sK11,sK10) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_127,negated_conjecture,
( closed_subset(sK11,sK10)
| ( topstr_closure(sK10,sK11) = sK11 ) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_128,negated_conjecture,
element(sK11,powerset(the_carrier(sK10))),
inference(cnf_transformation,[],[f204]) ).
tcf(c_129,negated_conjecture,
top_str(sK10),
inference(cnf_transformation,[],[f203]) ).
tcf(c_134,plain,
subset(sK10,sK10),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_166,plain,
( ( sK10 = sK10 )
| ~ subset(sK10,sK10) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_252,plain,
( topological_space(sK10)
| closed_subset(sK11,sK10) ),
inference(prop_impl_just,[status(thm)],[c_126]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| ( meet_of_subsets(the_carrier(X0),sK9(X0,X1)) = topstr_closure(X0,X1) )
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_121,c_252]) ).
tcf(c_1229,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| ( meet_of_subsets(the_carrier(sK10),sK9(sK10,X0)) = topstr_closure(sK10,X0) )
| ~ top_str(sK10)
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(unflattening,[status(thm)],[c_1228]) ).
tcf(c_1231,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| ( meet_of_subsets(the_carrier(sK10),sK9(sK10,X0)) = topstr_closure(sK10,X0) )
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(global_subsumption_just,[status(thm)],[c_1229,c_129,c_1229]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK11,sK10)
| closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK9(X0,X2))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_119,c_252]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| closed_subset(X0,sK10)
| ~ top_str(sK10)
| ~ element(X1,powerset(the_carrier(sK10)))
| ~ element(X0,powerset(the_carrier(sK10)))
| ~ in(X0,sK9(sK10,X1)) ),
inference(unflattening,[status(thm)],[c_1262]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| closed_subset(X0,sK10)
| ~ in(X0,sK9(sK10,X1))
| ~ element(X0,powerset(the_carrier(sK10)))
| ~ element(X1,powerset(the_carrier(sK10))) ),
inference(global_subsumption_just,[status(thm)],[c_1263,c_129,c_1263]) ).
tcf(c_1266,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| closed_subset(X0,sK10)
| ~ element(X1,powerset(the_carrier(sK10)))
| ~ element(X0,powerset(the_carrier(sK10)))
| ~ in(X0,sK9(sK10,X1)) ),
inference(renaming,[status(thm)],[c_1265]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| element(sK9(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_117,c_252]) ).
tcf(c_1308,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| element(sK9(sK10,X0),powerset(powerset(the_carrier(sK10))))
| ~ top_str(sK10)
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(unflattening,[status(thm)],[c_1307]) ).
tcf(c_1310,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| element(sK9(sK10,X0),powerset(powerset(the_carrier(sK10))))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(global_subsumption_just,[status(thm)],[c_1308,c_129,c_1308]) ).
tcf(c_1322,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| element(sK7(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_111,c_252]) ).
tcf(c_1323,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| element(sK7(sK10,X0),powerset(the_carrier(sK10)))
| ~ top_str(sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(unflattening,[status(thm)],[c_1322]) ).
tcf(c_1325,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| element(sK7(sK10,X0),powerset(the_carrier(sK10)))
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(global_subsumption_just,[status(thm)],[c_1323,c_129,c_1323]) ).
tcf(c_1340,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| in(sK7(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_110,c_252]) ).
tcf(c_1341,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| in(sK7(sK10,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| ~ top_str(sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(unflattening,[status(thm)],[c_1340]) ).
tcf(c_1343,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| in(sK7(sK10,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(global_subsumption_just,[status(thm)],[c_1341,c_129,c_1341]) ).
tcf(c_1358,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ closed_subset(sK7(X0,X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_109,c_252]) ).
tcf(c_1359,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| ~ top_str(sK10)
| ~ closed_subset(sK7(sK10,X0),sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(unflattening,[status(thm)],[c_1358]) ).
tcf(c_1361,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10))))
| ~ closed_subset(sK7(sK10,X0),sK10) ),
inference(global_subsumption_just,[status(thm)],[c_1359,c_129,c_1359]) ).
tcf(c_1362,plain,
! [X0: $i] :
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),X0),sK10)
| ~ closed_subset(sK7(sK10,X0),sK10)
| ~ element(X0,powerset(powerset(the_carrier(sK10)))) ),
inference(renaming,[status(thm)],[c_1361]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_122,c_129]) ).
tcf(c_1537,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK10,X0))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(unflattening,[status(thm)],[c_1536]) ).
tcf(c_1545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X2,X3)
| ~ in(X1,the_carrier(X0))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,topstr_closure(X0,X2))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_116,c_129]) ).
tcf(c_1546,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK10)
| ~ subset(X1,X2)
| ~ in(X0,the_carrier(sK10))
| ~ element(X2,powerset(the_carrier(sK10)))
| ~ element(X1,powerset(the_carrier(sK10)))
| ~ in(X0,topstr_closure(sK10,X1)) ),
inference(unflattening,[status(thm)],[c_1545]) ).
tcf(c_1629,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_129]) ).
tcf(c_1630,plain,
! [X0: $i] :
( element(topstr_closure(sK10,X0),powerset(the_carrier(sK10)))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(unflattening,[status(thm)],[c_1629]) ).
tcf(c_1748,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK10,X0))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(prop_impl_just,[status(thm)],[c_1537]) ).
tcf(c_1750,plain,
! [X0: $i] :
( element(topstr_closure(sK10,X0),powerset(the_carrier(sK10)))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(prop_impl_just,[status(thm)],[c_1630]) ).
tcf(c_2433,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( closed_subset(X0,X2)
| ~ closed_subset(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3631,plain,
! [X0: $i] :
( element(X0,powerset(the_carrier(sK10)))
| ~ subset(X0,the_carrier(sK10)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_5502,plain,
( closed_subset(sK11,sK10)
| element(sK9(sK10,sK11),powerset(powerset(the_carrier(sK10))))
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(instantiation,[status(thm)],[c_1310]) ).
tcf(c_5803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK10)
| ~ subset(X1,X2)
| ~ subset(X1,the_carrier(sK10))
| ~ in(X0,the_carrier(sK10))
| ~ element(X2,powerset(the_carrier(sK10)))
| ~ in(X0,topstr_closure(sK10,X1)) ),
inference(superposition,[status(thm)],[c_107,c_1546]) ).
tcf(c_5883,plain,
! [X0: $i,X1: $i] :
( in(X0,sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X1,sK11)
| ~ subset(X1,the_carrier(sK10))
| ~ in(X0,the_carrier(sK10))
| ~ in(X0,topstr_closure(sK10,X1)) ),
inference(superposition,[status(thm)],[c_128,c_5803]) ).
tcf(c_5892,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK10,X0),X1)
| in(sK0(topstr_closure(sK10,X0),X1),sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X0,sK11)
| ~ subset(X0,the_carrier(sK10))
| ~ in(sK0(topstr_closure(sK10,X0),X1),the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_78,c_5883]) ).
tcf(c_6032,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_6156,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK11,sK10)
| ~ closed_subset(X0,X1)
| ( sK10 != X1 )
| ( sK11 != X0 ) ),
inference(instantiation,[status(thm)],[c_2445]) ).
tcf(c_6287,plain,
! [X0: $i] :
( subset(topstr_closure(sK10,X0),the_carrier(sK10))
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(superposition,[status(thm)],[c_1750,c_108]) ).
tcf(c_6892,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK10,X0),X1)
| in(sK0(topstr_closure(sK10,X0),X1),sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X0,sK11)
| ~ subset(X0,the_carrier(sK10))
| ~ subset(topstr_closure(sK10,X0),the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_6032,c_5892]) ).
tcf(c_7046,plain,
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)),sK10)
| in(sK7(sK10,sK9(sK10,sK11)),sK9(sK10,sK11))
| ~ element(sK9(sK10,sK11),powerset(powerset(the_carrier(sK10)))) ),
inference(instantiation,[status(thm)],[c_1343]) ).
tcf(c_7047,plain,
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)),sK10)
| element(sK7(sK10,sK9(sK10,sK11)),powerset(the_carrier(sK10)))
| ~ element(sK9(sK10,sK11),powerset(powerset(the_carrier(sK10)))) ),
inference(instantiation,[status(thm)],[c_1325]) ).
tcf(c_8591,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK10)
| ~ subset(X1,X2)
| ~ subset(X1,the_carrier(sK10))
| ~ in(X0,the_carrier(sK10))
| ~ element(X2,powerset(the_carrier(sK10)))
| ~ in(X0,topstr_closure(sK10,X1)) ),
inference(superposition,[status(thm)],[c_107,c_1546]) ).
tcf(c_8668,plain,
! [X0: $i,X1: $i] :
( in(X0,sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X1,sK11)
| ~ subset(X1,the_carrier(sK10))
| ~ in(X0,the_carrier(sK10))
| ~ in(X0,topstr_closure(sK10,X1)) ),
inference(superposition,[status(thm)],[c_128,c_8591]) ).
tcf(c_8677,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK10,X0),X1)
| in(sK0(topstr_closure(sK10,X0),X1),sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X0,sK11)
| ~ subset(X0,the_carrier(sK10))
| ~ in(sK0(topstr_closure(sK10,X0),X1),the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_78,c_8668]) ).
tcf(c_8690,plain,
subset(sK11,the_carrier(sK10)),
inference(superposition,[status(thm)],[c_128,c_108]) ).
tcf(c_8742,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK10,X0),X1)
| in(sK0(topstr_closure(sK10,X0),X1),sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X0,sK11)
| ~ subset(X0,the_carrier(sK10)) ),
inference(global_subsumption_just,[status(thm)],[c_8677,c_3631,c_6287,c_6892]) ).
tcf(c_8753,plain,
! [X0: $i] :
( subset(topstr_closure(sK10,X0),sK11)
| ~ closed_subset(sK11,sK10)
| ~ subset(X0,sK11)
| ~ subset(X0,the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_8742,c_77]) ).
tcf(c_8825,plain,
subset(sK11,topstr_closure(sK10,sK11)),
inference(superposition,[status(thm)],[c_128,c_1748]) ).
tcf(c_8842,plain,
( ( topstr_closure(sK10,sK11) = sK11 )
| ~ subset(topstr_closure(sK10,sK11),sK11) ),
inference(superposition,[status(thm)],[c_8825,c_74]) ).
tcf(c_9622,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2435,c_2433]) ).
tcf(c_10206,plain,
( ( topstr_closure(sK10,sK11) = sK11 )
| ~ closed_subset(sK11,sK10)
| ~ subset(sK11,sK11)
| ~ subset(sK11,the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_8753,c_8842]) ).
tcf(c_10209,plain,
( ( topstr_closure(sK10,sK11) = sK11 )
| ~ closed_subset(sK11,sK10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10206,c_104,c_8690]) ).
tcf(c_10463,plain,
topstr_closure(sK10,sK11) = sK11,
inference(global_subsumption_just,[status(thm)],[c_10209,c_127,c_10209]) ).
tcf(c_12627,plain,
( closed_subset(sK11,sK10)
| ( sK11 = topstr_closure(sK10,sK11) ) ),
inference(resolution,[status(thm)],[c_9622,c_127]) ).
tcf(c_12991,plain,
sK11 = topstr_closure(sK10,sK11),
inference(global_subsumption_just,[status(thm)],[c_12627,c_124,c_10463,c_12627]) ).
tcf(c_13024,plain,
( closed_subset(sK11,sK10)
| ~ closed_subset(meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)),sK10)
| ( sK10 != sK10 )
| ( sK11 != meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)) ) ),
inference(instantiation,[status(thm)],[c_6156]) ).
tcf(c_13053,plain,
topstr_closure(sK10,sK11) = sK11,
inference(resolution,[status(thm)],[c_12991,c_9622]) ).
tcf(c_13055,plain,
! [X0: $i] :
( ( sK11 = X0 )
| ( X0 != topstr_closure(sK10,sK11) ) ),
inference(resolution,[status(thm)],[c_12991,c_2435]) ).
tcf(c_13269,plain,
~ closed_subset(sK11,sK10),
inference(backward_subsumption_resolution,[status(thm)],[c_124,c_13053]) ).
tcf(c_13325,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK10),sK9(sK10,X0)) = topstr_closure(sK10,X0) )
| ~ element(X0,powerset(the_carrier(sK10))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1231,c_13269]) ).
tcf(c_19960,plain,
( ( sK11 = meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)) )
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(resolution,[status(thm)],[c_13325,c_13055]) ).
tcf(c_22005,plain,
( closed_subset(sK11,sK10)
| closed_subset(sK7(sK10,sK9(sK10,sK11)),sK10)
| ~ element(sK11,powerset(the_carrier(sK10)))
| ~ element(sK7(sK10,sK9(sK10,sK11)),powerset(the_carrier(sK10)))
| ~ in(sK7(sK10,sK9(sK10,sK11)),sK9(sK10,sK11)) ),
inference(instantiation,[status(thm)],[c_1266]) ).
tcf(c_34517,plain,
( closed_subset(sK11,sK10)
| closed_subset(meet_of_subsets(the_carrier(sK10),sK9(sK10,sK11)),sK10)
| ~ closed_subset(sK7(sK10,sK9(sK10,sK11)),sK10)
| ~ element(sK9(sK10,sK11),powerset(powerset(the_carrier(sK10)))) ),
inference(instantiation,[status(thm)],[c_1362]) ).
tcf(c_34518,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_34517,c_22005,c_19960,c_13024,c_10463,c_7046,c_7047,c_5502,c_166,c_124,c_128,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU318+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.54 % Computer : n010.cluster.edu
% 0.10/5.54 % Model : x86_64 x86_64
% 0.10/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.54 % Memory : 8046.5625MB
% 0.10/5.54 % OS : Linux 6.8.0-71-generic
% 0.10/5.54 % CPULimit : 300
% 0.10/5.54 % WCLimit : 300
% 0.10/5.54 % DateTime : Thu Sep 24 13:41:23 UTC 2026
% 0.10/5.54 % CPUTime :
% 0.10/5.54 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.58 Running first-order theorem proving
% 0.10/5.58 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59
% 0.10/5.59 % ======== iProver multi-core TPTP/SMT =========
% 0.10/5.59
% 0.10/5.59 % Detected problem language: tptp
% 0.15/5.60 % Proving...
% 36.32/13.52 % SZS status Started for theBenchmark.p
% 36.32/13.52 % SZS status Theorem for theBenchmark.p
% 36.32/13.52
% 36.32/13.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.32/13.52
% 36.32/13.52 % ------ iProver source info
% 36.32/13.52
% 36.32/13.52 % git: date: 2026-07-19 20:42:38 +0200
% 36.32/13.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.32/13.52 % git: non_committed_changes: false
% 36.32/13.52
% 36.32/13.52 % ------ Parsing...
% 36.32/13.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.32/13.52
% 36.32/13.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 36.32/13.52
% 36.32/13.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.32/13.52
% 36.32/13.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 36.32/13.52 % ------ Proving...
% 36.32/13.52 % ------ Problem Properties
% 36.32/13.52
% 36.32/13.52 %
% 36.32/13.52 % clauses 52
% 36.32/13.52 % conjectures 3
% 36.32/13.52 % EPR 13
% 36.32/13.52 % Horn 32
% 36.32/13.52 % unary 8
% 36.32/13.52 % binary 20
% 36.32/13.52 % lits 146
% 36.32/13.52 % lits eq 7
% 36.32/13.52 % fd_pure 0
% 36.32/13.52 % fd_pseudo 0
% 36.32/13.52 % fd_cond 1
% 36.32/13.52 % fd_pseudo_cond 2
% 36.32/13.52 % AC symbols 0
% 36.32/13.52
% 36.32/13.52 % ------ Input Options Time Limit: Unbounded
% 36.32/13.52
% 36.32/13.52
% 36.32/13.52 % ------
% 36.32/13.52 % Current options:
% 36.32/13.52 % ------
% 36.32/13.52
% 36.32/13.52
% 36.32/13.52 %
% 36.32/13.52
% 36.32/13.52 % ------ Proving...
% 36.32/13.52 %
% 36.32/13.52
% 36.32/13.52 % SZS status Theorem for theBenchmark.p
% 36.32/13.52
% 36.32/13.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.32/13.52
% 36.32/13.52
%------------------------------------------------------------------------------