%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU372+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 : n018.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 02:57:15 PM UTC 2026
% Result : Theorem 26.48s 9.32s
% Output : CNFRefutation 26.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 194 ( 12 unt; 2 def)
% Number of atoms : 869 ( 30 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1129 ( 478 ~; 498 |; 102 &)
% ( 15 <=>; 34 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 418 ( 0 sgn 391 !; 27 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( in(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( element(X4,powerset(the_carrier(X0)))
=> ~ ( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(f6,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f7,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f10,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(f11,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f13,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X2] :
( point_neighbourhood(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f21,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f37,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f40,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f41,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f44,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f48,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> ~ disjoint(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_6) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> ~ disjoint(X3,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f64,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f65,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ) ) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f67,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f10]) ).
fof(f71,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f73,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ point_neighbourhood(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f74,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ point_neighbourhood(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f78,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f77]) ).
fof(f82,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f84,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f90,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| point_neighbourhood(X1,X0,X2) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| point_neighbourhood(X1,X0,X2) ) ) ),
inference(flattening,[],[f91]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f94]) ).
fof(f97,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( ~ point_neighbourhood(X3,X0,X2)
| ~ disjoint(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f98,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( ~ point_neighbourhood(X3,X0,X2)
| ~ disjoint(X3,X1) ) ) ) ) ),
inference(flattening,[],[f97]) ).
fof(f104,plain,
! [X2,X1,X0] :
( ~ sP1(X2,X1,X0)
| ( ( topstr_closure(X0,X1) != X2
| sP0(X0,X1,X2) )
& ( ~ sP0(X0,X1,X2)
| X2 = topstr_closure(X0,X1) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ( ( topstr_closure(X2,X1) != X0
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| topstr_closure(X2,X1) = X0 ) ) ),
inference(rectify,[],[f104]) ).
fof(f110,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( ~ point_neighbourhood(X2,X0,X1)
| in(X1,interior(X0,X2)) )
& ( ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f127,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f128,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ point_neighbourhood(X3,X0,X2)
| ~ disjoint(X3,X1) ) )
& ( ~ in(X2,topstr_closure(X0,X1))
| ? [X3] :
( point_neighbourhood(X3,X0,X2)
& disjoint(X3,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f129,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ point_neighbourhood(X3,X0,X2)
| ~ disjoint(X3,X1) ) )
& ( ~ in(X2,topstr_closure(X0,X1))
| ? [X3] :
( point_neighbourhood(X3,X0,X2)
& disjoint(X3,X1) ) ) ) ) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ point_neighbourhood(X4,X0,X2)
| ~ disjoint(X4,X1) ) )
& ( ~ in(X2,topstr_closure(X0,X1))
| ? [X3] :
( point_neighbourhood(X3,X0,X2)
& disjoint(X3,X1) ) ) ) ) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
( top_str(sK21)
& topological_space(sK21)
& ~ empty_carrier(sK21)
& element(sK22,powerset(the_carrier(sK21)))
& element(sK23,the_carrier(sK21))
& ( in(sK23,topstr_closure(sK21,sK22))
| ! [X4] :
( ~ point_neighbourhood(X4,sK21,sK23)
| ~ disjoint(X4,sK22) ) )
& ( ~ in(sK23,topstr_closure(sK21,sK22))
| ( point_neighbourhood(sK24,sK21,sK23)
& disjoint(sK24,sK22) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24]),skolemize(X0,sK21),skolemize(X1,sK22),skolemize(X2,sK23),skolemize(X3,sK24)],[f130]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| topstr_closure(X2,X1) != X0
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1)
| in(X1,interior(X0,X2)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f153,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f69]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ point_neighbourhood(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f74]) ).
fof(f163,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f192,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f194,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f196,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f197,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f199,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| ~ in(X2,X1)
| ~ open_subset(X1,X0)
| point_neighbourhood(X1,X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f204,plain,
top_str(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
topological_space(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f206,plain,
~ empty_carrier(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f207,plain,
element(sK22,powerset(the_carrier(sK21))),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
element(sK23,the_carrier(sK21)),
inference(cnf_transformation,[],[f131]) ).
fof(f209,plain,
! [X4] :
( in(sK23,topstr_closure(sK21,sK22))
| ~ point_neighbourhood(X4,sK21,sK23)
| ~ disjoint(X4,sK22) ),
inference(cnf_transformation,[],[f131]) ).
fof(f210,plain,
( ~ in(sK23,topstr_closure(sK21,sK22))
| point_neighbourhood(sK24,sK21,sK23) ),
inference(cnf_transformation,[],[f131]) ).
fof(f211,plain,
( ~ in(sK23,topstr_closure(sK21,sK22))
| disjoint(sK24,sK22) ),
inference(cnf_transformation,[],[f131]) ).
fof(f214,plain,
! [X2,X1] :
( ~ sP1(topstr_closure(X2,X1),X1,X2)
| sP0(X2,X1,topstr_closure(X2,X1)) ),
inference(equality_resolution,[],[f137]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1,topstr_closure(X0,X1))
| ~ sP1(topstr_closure(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X0,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,interior(X1,X0))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( element(interior(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_69,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,[],[f154]) ).
tcf(c_70,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(X0,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_78,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( subset(interior(X1,X0),X0)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( open_subset(interior(X1,X0),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X0,X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_119,negated_conjecture,
( disjoint(sK24,sK22)
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_120,negated_conjecture,
( point_neighbourhood(sK24,sK21,sK23)
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_121,negated_conjecture,
! [X0: $i] :
( in(sK23,topstr_closure(sK21,sK22))
| ~ disjoint(X0,sK22)
| ~ point_neighbourhood(X0,sK21,sK23) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_122,negated_conjecture,
element(sK23,the_carrier(sK21)),
inference(cnf_transformation,[],[f208]) ).
tcf(c_123,negated_conjecture,
element(sK22,powerset(the_carrier(sK21))),
inference(cnf_transformation,[],[f207]) ).
tcf(c_124,negated_conjecture,
~ empty_carrier(sK21),
inference(cnf_transformation,[],[f206]) ).
tcf(c_125,negated_conjecture,
topological_space(sK21),
inference(cnf_transformation,[],[f205]) ).
tcf(c_126,negated_conjecture,
top_str(sK21),
inference(cnf_transformation,[],[f204]) ).
tcf(c_134,plain,
( one_sorted_str(sK21)
| ~ top_str(sK21) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_146,plain,
( empty_carrier(sK21)
| ~ one_sorted_str(sK21)
| ~ empty(the_carrier(sK21)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,interior(X1,X0))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_71,c_67]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(renaming,[status(thm)],[c_173]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1,topstr_closure(X0,X1))
| ~ sP1(topstr_closure(X0,X1),X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_215,plain,
( point_neighbourhood(sK24,sK21,sK23)
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(prop_impl_just,[status(thm)],[c_120]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_113,c_175]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X0,X1,topstr_closure(X0,X1))
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ element(X2,powerset(the_carrier(X3)))
| ( X1 != X4 )
| ( X0 != X3 )
| ( topstr_closure(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_199,c_65]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1,topstr_closure(X0,X1))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(unflattening,[status(thm)],[c_762]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_763,c_69]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| in(X2,interior(X0,X1))
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ point_neighbourhood(X1,X0,X2)
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_170,c_125]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK21)
| in(X1,interior(sK21,X0))
| ~ top_str(sK21)
| ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1) ),
inference(unflattening,[status(thm)],[c_885]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1)
| in(X1,interior(sK21,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_886,c_126,c_124,c_886]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i] :
( in(X1,interior(sK21,X0))
| ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1) ),
inference(renaming,[status(thm)],[c_888]) ).
tcf(c_900,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| point_neighbourhood(X1,X0,X2)
| ~ top_str(X0)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_115,c_125]) ).
tcf(c_901,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK21)
| point_neighbourhood(X0,sK21,X1)
| ~ top_str(sK21)
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK21))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_900]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i] :
( ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK21))
| ~ element(X0,powerset(the_carrier(sK21)))
| point_neighbourhood(X0,sK21,X1) ),
inference(global_subsumption_just,[status(thm)],[c_901,c_126,c_124,c_901]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X0,sK21,X1)
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK21))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(renaming,[status(thm)],[c_902]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i] :
( open_subset(interior(X0,X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_114,c_125]) ).
tcf(c_920,plain,
! [X0: $i] :
( open_subset(interior(sK21,X0),sK21)
| ~ top_str(sK21)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_919]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ point_neighbourhood(X1,X0,X2)
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_125]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK21)
| element(X0,powerset(the_carrier(sK21)))
| ~ top_str(sK21)
| ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1) ),
inference(unflattening,[status(thm)],[c_943]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1)
| element(X0,powerset(the_carrier(sK21))) ),
inference(global_subsumption_just,[status(thm)],[c_944,c_126,c_124,c_944]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(the_carrier(sK21)))
| ~ element(X1,the_carrier(sK21))
| ~ point_neighbourhood(X0,sK21,X1) ),
inference(renaming,[status(thm)],[c_946]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_773,c_126]) ).
tcf(c_1131,plain,
! [X0: $i] :
( sP0(sK21,X0,topstr_closure(sK21,X0))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_1130]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_112,c_126]) ).
tcf(c_1155,plain,
! [X0: $i] :
( subset(interior(sK21,X0),X0)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_1154]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_126]) ).
tcf(c_1173,plain,
! [X0: $i] :
( element(interior(sK21,X0),powerset(the_carrier(sK21)))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_1172]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X4,X3)
| ~ in(X4,X1)
| ~ element(X0,powerset(X2))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_174,c_353]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(unflattening,[status(thm)],[c_1241]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X0,sK21,X1)
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_903,c_1242]) ).
tcf(c_1396,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(the_carrier(sK21)))
| ~ element(X1,the_carrier(sK21))
| ~ in(sK23,topstr_closure(sK21,sK22))
| ( sK21 != sK21 )
| ( X1 != sK23 )
| ( X0 != sK24 ) ),
inference(resolution_lifted,[status(thm)],[c_215,c_947]) ).
tcf(c_1397,plain,
( element(sK24,powerset(the_carrier(sK21)))
| ~ element(sK23,the_carrier(sK21))
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(unflattening,[status(thm)],[c_1396]) ).
tcf(c_1406,plain,
! [X0: $i,X1: $i] :
( in(X1,interior(sK21,X0))
| ~ element(X1,the_carrier(sK21))
| ~ in(sK23,topstr_closure(sK21,sK22))
| ( sK21 != sK21 )
| ( X1 != sK23 )
| ( X0 != sK24 ) ),
inference(resolution_lifted,[status(thm)],[c_215,c_889]) ).
tcf(c_1407,plain,
( in(sK23,interior(sK21,sK24))
| ~ element(sK23,the_carrier(sK21))
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(unflattening,[status(thm)],[c_1406]) ).
tcf(c_1416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK23,topstr_closure(sK21,sK22))
| ~ disjoint(X0,sK22)
| ~ open_subset(X1,sK21)
| ~ in(X2,X1)
| ~ element(X1,powerset(the_carrier(sK21)))
| ( sK21 != sK21 )
| ( X2 != sK23 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_121,c_1345]) ).
tcf(c_1417,plain,
! [X0: $i] :
( in(sK23,topstr_closure(sK21,sK22))
| ~ disjoint(X0,sK22)
| ~ open_subset(X0,sK21)
| ~ in(sK23,X0)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(unflattening,[status(thm)],[c_1416]) ).
tcf(c_3245,plain,
! [X0: $i] :
( open_subset(interior(sK21,X0),sK21)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(prop_impl_just,[status(thm)],[c_126,c_920]) ).
tcf(c_3247,plain,
! [X0: $i] :
( sP0(sK21,X0,topstr_closure(sK21,X0))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(prop_impl_just,[status(thm)],[c_1131]) ).
tcf(c_3249,plain,
! [X0: $i] :
( subset(interior(sK21,X0),X0)
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(prop_impl_just,[status(thm)],[c_1155]) ).
tcf(c_3253,plain,
! [X0: $i] :
( element(interior(sK21,X0),powerset(the_carrier(sK21)))
| ~ element(X0,powerset(the_carrier(sK21))) ),
inference(prop_impl_just,[status(thm)],[c_1173]) ).
tcf(c_6863,plain,
( empty(the_carrier(sK21))
| in(sK23,the_carrier(sK21))
| ~ element(sK23,the_carrier(sK21)) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_6890,plain,
( sP0(sK21,sK22,topstr_closure(sK21,sK22))
| ~ element(sK22,powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_3247]) ).
tcf(c_10855,plain,
! [X0: $i] :
( disjoint(X0,sK22)
| ~ disjoint(sK24,sK22)
| ~ subset(X0,sK24) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_10949,plain,
( element(interior(sK21,sK24),powerset(the_carrier(sK21)))
| ~ element(sK24,powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_3253]) ).
tcf(c_10951,plain,
( open_subset(interior(sK21,sK24),sK21)
| ~ element(sK24,powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_3245]) ).
tcf(c_10952,plain,
( subset(interior(sK21,sK24),sK24)
| ~ element(sK24,powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_3249]) ).
tcf(c_11324,plain,
! [X0: $i] :
( disjoint(sK4(sK21,X0,sK23),X0)
| ~ disjoint(X0,sK4(sK21,X0,sK23)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_12226,plain,
( disjoint(sK4(sK21,sK22,sK23),sK22)
| ~ disjoint(sK22,sK4(sK21,sK22,sK23)) ),
inference(instantiation,[status(thm)],[c_11324]) ).
tcf(c_12333,plain,
( disjoint(interior(sK21,sK24),sK22)
| ~ disjoint(sK24,sK22)
| ~ subset(interior(sK21,sK24),sK24) ),
inference(instantiation,[status(thm)],[c_10855]) ).
tcf(c_15469,plain,
( in(sK23,topstr_closure(sK21,sK22))
| ~ disjoint(sK4(sK21,sK22,sK23),sK22)
| ~ open_subset(sK4(sK21,sK22,sK23),sK21)
| ~ in(sK23,sK4(sK21,sK22,sK23))
| ~ element(sK4(sK21,sK22,sK23),powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_1417]) ).
tcf(c_15695,plain,
( disjoint(sK22,interior(sK21,sK24))
| ~ disjoint(interior(sK21,sK24),sK22) ),
inference(instantiation,[status(thm)],[c_107]) ).
fof(f101,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f102,definition,
! [X2,X1,X0] :
( ~ sP1(X2,X1,X0)
| ( X2 = topstr_closure(X0,X1)
<=> sP0(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f103,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| sP1(X2,X1,X0) ) ) ),
inference(definition_folding,[],[f65,f102,f101]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP0(X0,X1,X2) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6] :
( ~ in(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ) )
& ( ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& disjoint(X1,X7)
& in(X6,X7)
& open_subset(X7,X0) )
| in(X6,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(X3,X5)
| ~ open_subset(X5,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6] :
( ~ in(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ) )
& ( ( element(sK4(X0,X1,X6),powerset(the_carrier(X0)))
& disjoint(X1,sK4(X0,X1,X6))
& in(X6,sK4(X0,X1,X6))
& open_subset(sK4(X0,X1,X6),X0) )
| in(X6,X2) ) ) ) )
& ( ( in(sK2(X0,X1,X2),the_carrier(X0))
& ( in(sK2(X0,X1,X2),X2)
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(sK2(X0,X1,X2),X5)
| ~ open_subset(X5,X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( element(sK3(X0,X1,X2),powerset(the_carrier(X0)))
& disjoint(X1,sK3(X0,X1,X2))
& in(sK2(X0,X1,X2),sK3(X0,X1,X2))
& open_subset(sK3(X0,X1,X2),X0) ) ) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2)),skolemize(X7,sK4(X0,X1,X6))],[f108]) ).
fof(f139,plain,
! [X2,X0,X1,X8,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| ~ in(X6,X2)
| ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f140,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| element(sK4(X0,X1,X6),powerset(the_carrier(X0)))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f141,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| disjoint(X1,sK4(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f142,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| in(X6,sK4(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f143,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| open_subset(sK4(X0,X1,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| open_subset(sK4(X0,X1,X3),X0)
| ~ in(X3,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X3,sK4(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| disjoint(X1,sK4(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| element(sK4(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ disjoint(X2,X0)
| ~ open_subset(X0,X1)
| ~ in(X4,X3)
| ~ in(X4,X0)
| ~ in(X4,the_carrier(X1))
| ~ sP0(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_7018,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| element(sK4(sK21,X0,sK23),powerset(the_carrier(sK21)))
| ~ in(sK23,the_carrier(sK21))
| ~ sP0(sK21,X0,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_7019,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| open_subset(sK4(sK21,X0,sK23),sK21)
| ~ in(sK23,the_carrier(sK21))
| ~ sP0(sK21,X0,X1) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_7020,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| in(sK23,sK4(sK21,X0,sK23))
| ~ in(sK23,the_carrier(sK21))
| ~ sP0(sK21,X0,X1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_7021,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| disjoint(X0,sK4(sK21,X0,sK23))
| ~ in(sK23,the_carrier(sK21))
| ~ sP0(sK21,X0,X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_7023,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| disjoint(X0,sK4(sK21,X0,sK23))
| ~ sP0(sK21,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_7021,c_126,c_124,c_122,c_134,c_146,c_6863,c_7021]) ).
tcf(c_7027,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| in(sK23,sK4(sK21,X0,sK23))
| ~ sP0(sK21,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_7020,c_126,c_124,c_122,c_134,c_146,c_6863,c_7020]) ).
tcf(c_7031,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| open_subset(sK4(sK21,X0,sK23),sK21)
| ~ sP0(sK21,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_7019,c_126,c_124,c_122,c_134,c_146,c_6863,c_7019]) ).
tcf(c_7035,plain,
! [X0: $i,X1: $i] :
( in(sK23,X1)
| element(sK4(sK21,X0,sK23),powerset(the_carrier(sK21)))
| ~ sP0(sK21,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_7018,c_126,c_124,c_122,c_134,c_146,c_6863,c_7018]) ).
tcf(c_7409,plain,
( in(sK23,topstr_closure(sK21,sK22))
| disjoint(sK22,sK4(sK21,sK22,sK23))
| ~ sP0(sK21,sK22,topstr_closure(sK21,sK22)) ),
inference(instantiation,[status(thm)],[c_7023]) ).
tcf(c_7416,plain,
( in(sK23,topstr_closure(sK21,sK22))
| in(sK23,sK4(sK21,sK22,sK23))
| ~ sP0(sK21,sK22,topstr_closure(sK21,sK22)) ),
inference(instantiation,[status(thm)],[c_7027]) ).
tcf(c_7423,plain,
( in(sK23,topstr_closure(sK21,sK22))
| open_subset(sK4(sK21,sK22,sK23),sK21)
| ~ sP0(sK21,sK22,topstr_closure(sK21,sK22)) ),
inference(instantiation,[status(thm)],[c_7031]) ).
tcf(c_7430,plain,
( in(sK23,topstr_closure(sK21,sK22))
| element(sK4(sK21,sK22,sK23),powerset(the_carrier(sK21)))
| ~ sP0(sK21,sK22,topstr_closure(sK21,sK22)) ),
inference(instantiation,[status(thm)],[c_7035]) ).
tcf(c_11725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(sK23,X3)
| ~ in(sK23,X0)
| ~ disjoint(X2,X0)
| ~ open_subset(X0,X1)
| ~ in(sK23,the_carrier(X1))
| ~ sP0(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_14029,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(sK22,X1)
| ~ in(sK23,X1)
| ~ open_subset(X1,X0)
| ~ in(sK23,the_carrier(X0))
| ~ in(sK23,topstr_closure(sK21,sK22))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ sP0(X0,sK22,topstr_closure(sK21,sK22)) ),
inference(instantiation,[status(thm)],[c_11725]) ).
tcf(c_15470,plain,
in(sK23,topstr_closure(sK21,sK22)),
inference(global_subsumption_just,[status(thm)],[c_15469,c_123,c_6890,c_7409,c_7416,c_7423,c_7430,c_12226,c_15469]) ).
tcf(c_18884,plain,
! [X0: $i] :
( ~ in(sK23,the_carrier(X0))
| ~ disjoint(sK22,interior(sK21,sK24))
| ~ in(sK23,interior(sK21,sK24))
| ~ in(sK23,topstr_closure(sK21,sK22))
| ~ open_subset(interior(sK21,sK24),X0)
| ~ sP0(X0,sK22,topstr_closure(sK21,sK22))
| ~ element(interior(sK21,sK24),powerset(the_carrier(X0))) ),
inference(instantiation,[status(thm)],[c_14029]) ).
tcf(c_18885,plain,
( ~ in(sK23,the_carrier(sK21))
| ~ disjoint(sK22,interior(sK21,sK24))
| ~ open_subset(interior(sK21,sK24),sK21)
| ~ in(sK23,interior(sK21,sK24))
| ~ in(sK23,topstr_closure(sK21,sK22))
| ~ sP0(sK21,sK22,topstr_closure(sK21,sK22))
| ~ element(interior(sK21,sK24),powerset(the_carrier(sK21))) ),
inference(instantiation,[status(thm)],[c_18884]) ).
tcf(c_18886,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18885,c_15695,c_15470,c_12333,c_10949,c_10951,c_10952,c_6890,c_6863,c_1407,c_1397,c_146,c_119,c_134,c_123,c_122,c_124,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU372+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.40 % Computer : n018.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Thu Sep 24 13:55:09 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 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
% 0.15/5.45
% 0.15/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.45
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 26.48/9.32 % SZS status Started for theBenchmark.p
% 26.48/9.32 % SZS status Theorem for theBenchmark.p
% 26.48/9.32
% 26.48/9.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.48/9.32
% 26.48/9.32 % ------ iProver source info
% 26.48/9.32
% 26.48/9.32 % git: date: 2026-07-19 20:42:38 +0200
% 26.48/9.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.48/9.32 % git: non_committed_changes: false
% 26.48/9.32
% 26.48/9.32 % ------ Parsing...
% 26.48/9.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.48/9.32
% 26.48/9.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 9 0s sf_e pe_s pe_e %
% 26.48/9.32
% 26.48/9.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.48/9.32
% 26.48/9.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.48/9.32 % ------ Proving...
% 26.48/9.32 % ------ Problem Properties
% 26.48/9.32
% 26.48/9.32 %
% 26.48/9.32 % clauses 68
% 26.48/9.32 % conjectures 3
% 26.48/9.32 % EPR 15
% 26.48/9.32 % Horn 56
% 26.48/9.32 % unary 17
% 26.48/9.32 % binary 31
% 26.48/9.32 % lits 156
% 26.48/9.32 % lits eq 10
% 26.48/9.32 % fd_pure 0
% 26.48/9.32 % fd_pseudo 0
% 26.48/9.32 % fd_cond 1
% 26.48/9.32 % fd_pseudo_cond 3
% 26.48/9.32 % AC symbols 0
% 26.48/9.32
% 26.48/9.32 % ------ Input Options Time Limit: Unbounded
% 26.48/9.32
% 26.48/9.32
% 26.48/9.32 % ------
% 26.48/9.32 % Current options:
% 26.48/9.32 % ------
% 26.48/9.32
% 26.48/9.32
% 26.48/9.32 %
% 26.48/9.32
% 26.48/9.32 % ------ Proving...
% 26.48/9.32 %
% 26.48/9.32
% 26.48/9.32 % SZS status Theorem for theBenchmark.p
% 26.48/9.32
% 26.48/9.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.48/9.32
% 26.48/9.32
%------------------------------------------------------------------------------