%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU389+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:57:19 PM UTC 2026
% Result : Theorem 53.20s 12.97s
% Output : CNFRefutation 53.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 253 ( 35 unt; 0 def)
% Number of atoms : 1024 ( 61 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1325 ( 554 ~; 614 |; 103 &)
% ( 20 <=>; 32 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 487 ( 0 sgn 462 !; 25 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
fof(f27,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/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f28,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow19) ).
fof(f29,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f30,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( in(X2,X3)
& open_subset(X3,X0) )
=> in(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_waybel_7) ).
fof(f32,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f40,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f42,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/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f73,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f79,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( X0 = X3
& point_neighbourhood(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(f118,axiom,
! [X0,X1] :
( element(X1,powerset(the_carrier(boole_POSet(X0))))
=> ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X0)
& subset(X2,X3) )
=> in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_waybel_7) ).
fof(f119,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f123,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f124,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow19) ).
fof(f125,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f127,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0))) )
=> ( is_a_convergence_point_of_set(X0,X2,X1)
<=> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow19) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0))) )
=> ( is_a_convergence_point_of_set(X0,X2,X1)
<=> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
fof(f129,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/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f251,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,[],[f27]) ).
fof(f252,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,[],[f251]) ).
fof(f253,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f254,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ) ),
inference(flattening,[],[f253]) ).
fof(f255,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f256,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| in(X3,X1) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f257,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| in(X3,X1) ) ) ),
inference(flattening,[],[f256]) ).
fof(f259,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f32]) ).
fof(f260,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f259]) ).
fof(f265,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f266,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,[],[f42]) ).
fof(f267,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,[],[f266]) ).
fof(f299,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(interior(X0,X1),X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f300,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(interior(X0,X1),X0) ),
inference(flattening,[],[f299]) ).
fof(f303,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( X0 = X3
& point_neighbourhood(X3,X1,X2) ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f304,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( X0 = X3
& point_neighbourhood(X3,X1,X2) ) ) ),
inference(flattening,[],[f303]) ).
fof(f339,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( ~ in(X2,X1)
| ~ subset(X3,X0)
| ~ subset(X2,X3)
| in(X3,X1) ) ) ),
inference(ennf_transformation,[],[f118]) ).
fof(f340,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( ~ in(X2,X1)
| ~ subset(X3,X0)
| ~ subset(X2,X3)
| in(X3,X1) ) ) ),
inference(flattening,[],[f339]) ).
fof(f341,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f346,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
inference(ennf_transformation,[],[f124]) ).
fof(f347,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
inference(flattening,[],[f346]) ).
fof(f348,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ) ),
inference(ennf_transformation,[],[f125]) ).
fof(f351,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& ( is_a_convergence_point_of_set(X0,X2,X1)
<~> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(ennf_transformation,[],[f128]) ).
fof(f352,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& ( is_a_convergence_point_of_set(X0,X2,X1)
<~> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(flattening,[],[f351]) ).
fof(f353,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,[],[f129]) ).
fof(f354,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,[],[f353]) ).
fof(f364,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,[],[f252]) ).
fof(f365,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,[],[f255]) ).
fof(f366,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,[],[f365]) ).
fof(f367,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f366]) ).
fof(f368,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1,X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X2,X3)
| ~ open_subset(X3,X0)
| in(X3,X1) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& in(X2,X3)
& open_subset(X3,X0)
& ~ in(X3,X1) )
| is_a_convergence_point_of_set(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f257]) ).
fof(f369,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1,X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| in(X4,X1) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& in(X2,X3)
& open_subset(X3,X0)
& ~ in(X3,X1) )
| is_a_convergence_point_of_set(X0,X1,X2) ) ) ),
inference(rectify,[],[f368]) ).
fof(f370,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1,X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| in(X4,X1) ) )
& ( ( element(sK3(X0,X1,X2),powerset(the_carrier(X0)))
& in(X2,sK3(X0,X1,X2))
& open_subset(sK3(X0,X1,X2),X0)
& ~ in(sK3(X0,X1,X2),X1) )
| is_a_convergence_point_of_set(X0,X1,X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f369]) ).
fof(f379,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_2_0_yellow19(X1,X2))
| ? [X3] :
( X0 = X3
& point_neighbourhood(X3,X1,X2) ) )
& ( ! [X3] :
( X0 != X3
| ~ point_neighbourhood(X3,X1,X2) )
| in(X0,a_2_0_yellow19(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f304]) ).
fof(f380,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_2_0_yellow19(X1,X2))
| ? [X4] :
( X0 = X4
& point_neighbourhood(X4,X1,X2) ) )
& ( ! [X3] :
( X0 != X3
| ~ point_neighbourhood(X3,X1,X2) )
| in(X0,a_2_0_yellow19(X1,X2)) ) ) ),
inference(rectify,[],[f379]) ).
fof(f381,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_2_0_yellow19(X1,X2))
| ( sK11(X0,X1,X2) = X0
& point_neighbourhood(sK11(X0,X1,X2),X1,X2) ) )
& ( ! [X3] :
( X0 != X3
| ~ point_neighbourhood(X3,X1,X2) )
| in(X0,a_2_0_yellow19(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2))],[f380]) ).
fof(f417,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ( ( ~ upper_relstr_subset(X1,boole_POSet(X0))
| ! [X2,X3] :
( ~ in(X2,X1)
| ~ subset(X3,X0)
| ~ subset(X2,X3)
| in(X3,X1) ) )
& ( ? [X2,X3] :
( in(X2,X1)
& subset(X3,X0)
& subset(X2,X3)
& ~ in(X3,X1) )
| upper_relstr_subset(X1,boole_POSet(X0)) ) ) ),
inference(nnf_transformation,[],[f340]) ).
fof(f418,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ( ( ~ upper_relstr_subset(X1,boole_POSet(X0))
| ! [X4,X5] :
( ~ in(X4,X1)
| ~ subset(X5,X0)
| ~ subset(X4,X5)
| in(X5,X1) ) )
& ( ? [X2,X3] :
( in(X2,X1)
& subset(X3,X0)
& subset(X2,X3)
& ~ in(X3,X1) )
| upper_relstr_subset(X1,boole_POSet(X0)) ) ) ),
inference(rectify,[],[f417]) ).
fof(f419,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ( ( ~ upper_relstr_subset(X1,boole_POSet(X0))
| ! [X4,X5] :
( ~ in(X4,X1)
| ~ subset(X5,X0)
| ~ subset(X4,X5)
| in(X5,X1) ) )
& ( ( in(sK46(X0,X1),X1)
& subset(sK47(X0,X1),X0)
& subset(sK46(X0,X1),sK47(X0,X1))
& ~ in(sK47(X0,X1),X1) )
| upper_relstr_subset(X1,boole_POSet(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47]),skolemize(X2,sK46(X0,X1)),skolemize(X3,sK47(X0,X1))],[f418]) ).
fof(f422,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f423,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ( ~ in(X2,neighborhood_system(X0,X1))
| point_neighbourhood(X2,X0,X1) )
& ( ~ point_neighbourhood(X2,X0,X1)
| in(X2,neighborhood_system(X0,X1)) ) ) ) ),
inference(nnf_transformation,[],[f347]) ).
fof(f424,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& ( is_a_convergence_point_of_set(X0,X2,X1)
| subset(neighborhood_system(X0,X1),X2) )
& ( ~ is_a_convergence_point_of_set(X0,X2,X1)
| ~ subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(nnf_transformation,[],[f352]) ).
fof(f425,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& ( is_a_convergence_point_of_set(X0,X2,X1)
| subset(neighborhood_system(X0,X1),X2) )
& ( ~ is_a_convergence_point_of_set(X0,X2,X1)
| ~ subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(flattening,[],[f424]) ).
fof(f426,plain,
( top_str(sK49)
& topological_space(sK49)
& ~ empty_carrier(sK49)
& element(sK50,the_carrier(sK49))
& element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49)))))
& upper_relstr_subset(sK51,boole_POSet(cast_as_carrier_subset(sK49)))
& ( is_a_convergence_point_of_set(sK49,sK51,sK50)
| subset(neighborhood_system(sK49,sK50),sK51) )
& ( ~ is_a_convergence_point_of_set(sK49,sK51,sK50)
| ~ subset(neighborhood_system(sK49,sK50),sK51) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50,sK51]),skolemize(X0,sK49),skolemize(X1,sK50),skolemize(X2,sK51)],[f425]) ).
fof(f491,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,[],[f364]) ).
fof(f493,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ),
inference(cnf_transformation,[],[f254]) ).
fof(f494,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f367]) ).
fof(f495,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f367]) ).
fof(f496,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f367]) ).
fof(f497,plain,
! [X2,X0,X1,X4] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X2,X4)
| ~ open_subset(X4,X0)
| in(X4,X1) ),
inference(cnf_transformation,[],[f370]) ).
fof(f498,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK3(X0,X1,X2),powerset(the_carrier(X0)))
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f370]) ).
fof(f499,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| in(X2,sK3(X0,X1,X2))
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f370]) ).
fof(f500,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(sK3(X0,X1,X2),X0)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f370]) ).
fof(f501,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(sK3(X0,X1,X2),X1)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f370]) ).
fof(f504,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f260]) ).
fof(f510,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f511,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,[],[f267]) ).
fof(f568,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(interior(X0,X1),X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f600,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ in(X0,a_2_0_yellow19(X1,X2))
| sK11(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f381]) ).
fof(f601,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ in(X0,a_2_0_yellow19(X1,X2))
| point_neighbourhood(sK11(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f381]) ).
fof(f602,plain,
! [X2,X3,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| X0 != X3
| ~ point_neighbourhood(X3,X1,X2)
| in(X0,a_2_0_yellow19(X1,X2)) ),
inference(cnf_transformation,[],[f381]) ).
fof(f747,plain,
! [X0,X1,X4,X5] :
( ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ in(X4,X1)
| ~ subset(X5,X0)
| ~ subset(X4,X5)
| in(X5,X1) ),
inference(cnf_transformation,[],[f419]) ).
fof(f752,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f757,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f422]) ).
fof(f758,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f422]) ).
fof(f759,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ in(X2,neighborhood_system(X0,X1))
| point_neighbourhood(X2,X0,X1) ),
inference(cnf_transformation,[],[f423]) ).
fof(f761,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ),
inference(cnf_transformation,[],[f348]) ).
fof(f763,plain,
top_str(sK49),
inference(cnf_transformation,[],[f426]) ).
fof(f764,plain,
topological_space(sK49),
inference(cnf_transformation,[],[f426]) ).
fof(f765,plain,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f426]) ).
fof(f766,plain,
element(sK50,the_carrier(sK49)),
inference(cnf_transformation,[],[f426]) ).
fof(f767,plain,
element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49))))),
inference(cnf_transformation,[],[f426]) ).
fof(f768,plain,
upper_relstr_subset(sK51,boole_POSet(cast_as_carrier_subset(sK49))),
inference(cnf_transformation,[],[f426]) ).
fof(f769,plain,
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| subset(neighborhood_system(sK49,sK50),sK51) ),
inference(cnf_transformation,[],[f426]) ).
fof(f770,plain,
( ~ is_a_convergence_point_of_set(sK49,sK51,sK50)
| ~ subset(neighborhood_system(sK49,sK50),sK51) ),
inference(cnf_transformation,[],[f426]) ).
fof(f771,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,[],[f354]) ).
fof(f776,plain,
! [X2,X3,X1] :
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ point_neighbourhood(X3,X1,X2)
| in(X3,a_2_0_yellow19(X1,X2)) ),
inference(equality_resolution,[],[f602]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,interior(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f491]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( neighborhood_system(X1,X0) = a_2_0_yellow19(X1,X0) )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f493]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f496]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f495]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| open_subset(sK3(X0,X1,X2),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X2,X1)
| in(X1,sK3(X0,X2,X1))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f499]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| element(sK3(X0,X1,X2),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f498]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ open_subset(X0,X1)
| ~ in(X3,X0)
| ~ is_a_convergence_point_of_set(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f497]) ).
tcf(c_104,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,[],[f504]) ).
tcf(c_110,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( open_subset(interior(X1,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f568]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X0,a_2_0_yellow19(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2) ),
inference(cnf_transformation,[],[f776]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(sK11(X0,X1,X2),X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X0,a_2_0_yellow19(X1,X2)) ),
inference(cnf_transformation,[],[f601]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( sK11(X0,X1,X2) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X0,a_2_0_yellow19(X1,X2)) ),
inference(cnf_transformation,[],[f600]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| ~ subset(X3,X1)
| ~ subset(X2,X3)
| ~ in(X2,X0)
| ~ upper_relstr_subset(X0,boole_POSet(X1))
| ~ element(X0,powerset(the_carrier(boole_POSet(X1)))) ),
inference(cnf_transformation,[],[f747]) ).
tcf(c_352,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f752]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f758]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f757]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X0,X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X0,neighborhood_system(X1,X2)) ),
inference(cnf_transformation,[],[f759]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( subset(interior(X1,X0),X0)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f761]) ).
tcf(c_363,negated_conjecture,
( ~ is_a_convergence_point_of_set(sK49,sK51,sK50)
| ~ subset(neighborhood_system(sK49,sK50),sK51) ),
inference(cnf_transformation,[],[f770]) ).
tcf(c_364,negated_conjecture,
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| subset(neighborhood_system(sK49,sK50),sK51) ),
inference(cnf_transformation,[],[f769]) ).
tcf(c_365,negated_conjecture,
upper_relstr_subset(sK51,boole_POSet(cast_as_carrier_subset(sK49))),
inference(cnf_transformation,[],[f768]) ).
tcf(c_366,negated_conjecture,
element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49))))),
inference(cnf_transformation,[],[f767]) ).
tcf(c_367,negated_conjecture,
element(sK50,the_carrier(sK49)),
inference(cnf_transformation,[],[f766]) ).
tcf(c_368,negated_conjecture,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f765]) ).
tcf(c_369,negated_conjecture,
topological_space(sK49),
inference(cnf_transformation,[],[f764]) ).
tcf(c_370,negated_conjecture,
top_str(sK49),
inference(cnf_transformation,[],[f763]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X0,X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ open_subset(X0,X1)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f771]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,interior(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_92,c_111,c_92]) ).
tcf(c_657,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
tcf(c_689,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_352]) ).
tcf(c_5856,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| element(sK3(X0,X1,X2),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_369]) ).
tcf(c_5857,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| element(sK3(sK49,X0,X1),powerset(the_carrier(sK49)))
| ~ top_str(sK49) ),
inference(unflattening,[status(thm)],[c_5856]) ).
tcf(c_5859,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| element(sK3(sK49,X0,X1),powerset(the_carrier(sK49))) ),
inference(global_subsumption_just,[status(thm)],[c_5857,c_370,c_5857]) ).
tcf(c_5868,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X2,X1)
| in(X1,sK3(X0,X2,X1))
| ~ top_str(X0)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_99,c_369]) ).
tcf(c_5869,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X1,X0)
| in(X0,sK3(sK49,X1,X0))
| ~ top_str(sK49) ),
inference(unflattening,[status(thm)],[c_5868]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X1,X0)
| in(X0,sK3(sK49,X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_5869,c_370,c_5869]) ).
tcf(c_5880,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| open_subset(sK3(X0,X1,X2),X0)
| ~ top_str(X0)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_369]) ).
tcf(c_5881,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| open_subset(sK3(sK49,X0,X1),sK49)
| ~ top_str(sK49) ),
inference(unflattening,[status(thm)],[c_5880]) ).
tcf(c_5892,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_convergence_point_of_set(X0,X1,X2)
| ~ top_str(X0)
| ~ in(sK3(X0,X1,X2),X1)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_369]) ).
tcf(c_5893,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| ~ top_str(sK49)
| ~ in(sK3(sK49,X0,X1),X0) ),
inference(unflattening,[status(thm)],[c_5892]) ).
tcf(c_5895,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| ~ in(sK3(sK49,X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_5893,c_370,c_5893]) ).
tcf(c_5904,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 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_564,c_369]) ).
tcf(c_5905,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| in(X1,interior(sK49,X0))
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(unflattening,[status(thm)],[c_5904]) ).
tcf(c_5907,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1)
| in(X1,interior(sK49,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_5905,c_370,c_368,c_5905]) ).
tcf(c_5908,plain,
! [X0: $i,X1: $i] :
( in(X1,interior(sK49,X0))
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(renaming,[status(thm)],[c_5907]) ).
tcf(c_5919,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 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_371,c_369]) ).
tcf(c_5920,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| point_neighbourhood(X0,sK49,X1)
| ~ top_str(sK49)
| ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_5919]) ).
tcf(c_5921,plain,
! [X0: $i,X1: $i] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49)))
| point_neighbourhood(X0,sK49,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5920,c_370,c_368,c_5920]) ).
tcf(c_5922,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X0,sK49,X1)
| ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(renaming,[status(thm)],[c_5921]) ).
tcf(c_5938,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| point_neighbourhood(X1,X0,X2)
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ in(X1,neighborhood_system(X0,X2))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_360,c_369]) ).
tcf(c_5939,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| point_neighbourhood(X0,sK49,X1)
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,X1)) ),
inference(unflattening,[status(thm)],[c_5938]) ).
tcf(c_5941,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,X1))
| point_neighbourhood(X0,sK49,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5939,c_370,c_368,c_5939]) ).
tcf(c_5942,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,X1)) ),
inference(renaming,[status(thm)],[c_5941]) ).
tcf(c_5968,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( sK11(X1,X0,X2) = X1 )
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ in(X1,a_2_0_yellow19(X0,X2))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_202,c_369]) ).
tcf(c_5969,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| ( sK11(X0,sK49,X1) = X0 )
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(unflattening,[status(thm)],[c_5968]) ).
tcf(c_5971,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1))
| ( sK11(X0,sK49,X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_5969,c_370,c_368,c_5969]) ).
tcf(c_5972,plain,
! [X0: $i,X1: $i] :
( ( sK11(X0,sK49,X1) = X0 )
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(renaming,[status(thm)],[c_5971]) ).
tcf(c_5983,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| point_neighbourhood(sK11(X1,X0,X2),X0,X2)
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ in(X1,a_2_0_yellow19(X0,X2))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_201,c_369]) ).
tcf(c_5984,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| point_neighbourhood(sK11(X0,sK49,X1),sK49,X1)
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(unflattening,[status(thm)],[c_5983]) ).
tcf(c_5986,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1))
| point_neighbourhood(sK11(X0,sK49,X1),sK49,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5984,c_370,c_368,c_5984]) ).
tcf(c_5987,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(sK11(X0,sK49,X1),sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(renaming,[status(thm)],[c_5986]) ).
tcf(c_5998,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| in(X1,a_2_0_yellow19(X0,X2))
| ~ top_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ point_neighbourhood(X1,X0,X2)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_200,c_369]) ).
tcf(c_5999,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| in(X0,a_2_0_yellow19(sK49,X1))
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(unflattening,[status(thm)],[c_5998]) ).
tcf(c_6001,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1)
| in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_5999,c_370,c_368,c_5999]) ).
tcf(c_6002,plain,
! [X0: $i,X1: $i] :
( in(X0,a_2_0_yellow19(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(renaming,[status(thm)],[c_6001]) ).
tcf(c_6013,plain,
! [X0: $i,X1: $i] :
( open_subset(interior(X0,X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_168,c_369]) ).
tcf(c_6014,plain,
! [X0: $i] :
( open_subset(interior(sK49,X0),sK49)
| ~ top_str(sK49)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_6013]) ).
tcf(c_6049,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 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_111,c_369]) ).
tcf(c_6050,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK49)
| element(X0,powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(unflattening,[status(thm)],[c_6049]) ).
tcf(c_6052,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1)
| element(X0,powerset(the_carrier(sK49))) ),
inference(global_subsumption_just,[status(thm)],[c_6050,c_370,c_368,c_6050]) ).
tcf(c_6053,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(the_carrier(sK49)))
| ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1) ),
inference(renaming,[status(thm)],[c_6052]) ).
tcf(c_6076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ top_str(X0)
| ~ open_subset(X1,X0)
| ~ in(X3,X1)
| ~ is_a_convergence_point_of_set(X0,X2,X3)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_369]) ).
tcf(c_6077,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ top_str(sK49)
| ~ open_subset(X0,sK49)
| ~ in(X2,X0)
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_6076]) ).
tcf(c_6078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ in(X2,X0)
| ~ open_subset(X0,sK49) ),
inference(global_subsumption_just,[status(thm)],[c_6077,c_370,c_6077]) ).
tcf(c_6079,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ open_subset(X0,sK49)
| ~ in(X2,X0)
| ~ is_a_convergence_point_of_set(sK49,X1,X2)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(renaming,[status(thm)],[c_6078]) ).
tcf(c_6095,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| ( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) )
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_369]) ).
tcf(c_6096,plain,
! [X0: $i] :
( empty_carrier(sK49)
| ( neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0) )
| ~ top_str(sK49)
| ~ element(X0,the_carrier(sK49)) ),
inference(unflattening,[status(thm)],[c_6095]) ).
tcf(c_6098,plain,
! [X0: $i] :
( ~ element(X0,the_carrier(sK49))
| ( neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_6096,c_370,c_368,c_6096]) ).
tcf(c_6099,plain,
! [X0: $i] :
( ( neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0) )
| ~ element(X0,the_carrier(sK49)) ),
inference(renaming,[status(thm)],[c_6098]) ).
tcf(c_6258,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_657,c_370]) ).
tcf(c_6259,plain,
one_sorted_str(sK49),
inference(unflattening,[status(thm)],[c_6258]) ).
tcf(c_6317,plain,
! [X0: $i,X1: $i] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_361,c_370]) ).
tcf(c_6318,plain,
! [X0: $i] :
( subset(interior(sK49,X0),X0)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_6317]) ).
tcf(c_6350,plain,
! [X0: $i,X1: $i] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_370]) ).
tcf(c_6351,plain,
! [X0: $i] :
( element(interior(sK49,X0),powerset(the_carrier(sK49)))
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(unflattening,[status(thm)],[c_6350]) ).
tcf(c_6775,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK49 ) ),
inference(resolution_lifted,[status(thm)],[c_689,c_6259]) ).
tcf(c_6776,plain,
the_carrier(sK49) = cast_as_carrier_subset(sK49),
inference(unflattening,[status(thm)],[c_6775]) ).
tcf(c_27363,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| in(sK2(neighborhood_system(sK49,sK50),sK51),neighborhood_system(sK49,sK50)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_30764,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X1,sK49,X0)
| ~ open_subset(X1,sK49)
| ~ in(X0,X1)
| ~ subset(X1,the_carrier(sK49))
| ~ element(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_357,c_5922]) ).
tcf(c_30786,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| subset(sK3(sK49,X0,X1),the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_5859,c_358]) ).
tcf(c_35413,plain,
! [X0: $i] :
( point_neighbourhood(X0,sK49,sK50)
| ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ subset(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_367,c_30764]) ).
tcf(c_35445,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| point_neighbourhood(sK3(sK49,X0,X1),sK49,sK50)
| ~ open_subset(sK3(sK49,X0,X1),sK49)
| ~ in(sK50,sK3(sK49,X0,X1)) ),
inference(superposition,[status(thm)],[c_30786,c_35413]) ).
tcf(c_39674,plain,
upper_relstr_subset(sK51,boole_POSet(the_carrier(sK49))),
inference(light_normalisation,[status(thm)],[c_365,c_6776]) ).
tcf(c_39675,plain,
element(sK51,powerset(the_carrier(boole_POSet(the_carrier(sK49))))),
inference(light_normalisation,[status(thm)],[c_366,c_6776]) ).
tcf(c_39768,plain,
neighborhood_system(sK49,sK50) = a_2_0_yellow19(sK49,sK50),
inference(superposition,[status(thm)],[c_367,c_6099]) ).
tcf(c_39814,plain,
! [X0: $i] :
( in(X0,neighborhood_system(sK49,sK50))
| ~ element(sK50,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,sK50) ),
inference(superposition,[status(thm)],[c_39768,c_6002]) ).
tcf(c_39816,plain,
! [X0: $i] :
( in(X0,neighborhood_system(sK49,sK50))
| ~ point_neighbourhood(X0,sK49,sK50) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39814,c_367]) ).
tcf(c_39872,plain,
! [X0: $i] :
( ( sK11(X0,sK49,sK50) = X0 )
| ~ element(sK50,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_39768,c_5972]) ).
tcf(c_39873,plain,
! [X0: $i] :
( ( sK11(X0,sK49,sK50) = X0 )
| ~ in(X0,neighborhood_system(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39872,c_367]) ).
tcf(c_40038,plain,
! [X0: $i] :
( subset(neighborhood_system(sK49,sK50),X0)
| ( sK11(sK2(neighborhood_system(sK49,sK50),X0),sK49,sK50) = sK2(neighborhood_system(sK49,sK50),X0) ) ),
inference(superposition,[status(thm)],[c_95,c_39873]) ).
tcf(c_40041,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X1,sK49,X0)
| ~ open_subset(X1,sK49)
| ~ in(X0,X1)
| ~ subset(X1,the_carrier(sK49))
| ~ element(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_357,c_5922]) ).
tcf(c_40072,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| subset(sK3(sK49,X0,X1),the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_5859,c_358]) ).
tcf(c_40181,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ~ point_neighbourhood(X1,sK49,sK50)
| ~ subset(neighborhood_system(sK49,sK50),X0) ),
inference(superposition,[status(thm)],[c_39816,c_96]) ).
tcf(c_40336,plain,
! [X0: $i,X1: $i] :
( in(X0,sK51)
| ~ in(X1,sK51)
| ~ subset(X1,X0)
| ~ subset(X0,the_carrier(sK49))
| ~ upper_relstr_subset(sK51,boole_POSet(the_carrier(sK49))) ),
inference(superposition,[status(thm)],[c_39675,c_351]) ).
tcf(c_40338,plain,
! [X0: $i,X1: $i] :
( in(X0,sK51)
| ~ in(X1,sK51)
| ~ subset(X1,X0)
| ~ subset(X0,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40336,c_39674]) ).
tcf(c_40564,plain,
! [X0: $i] :
( in(X0,sK51)
| is_a_convergence_point_of_set(sK49,sK51,sK50)
| ~ point_neighbourhood(X0,sK49,sK50) ),
inference(superposition,[status(thm)],[c_364,c_40181]) ).
tcf(c_41641,plain,
( ( sK11(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50) = sK2(neighborhood_system(sK49,sK50),sK51) )
| ~ is_a_convergence_point_of_set(sK49,sK51,sK50) ),
inference(superposition,[status(thm)],[c_40038,c_363]) ).
tcf(c_41991,plain,
! [X0: $i] :
( point_neighbourhood(X0,sK49,sK50)
| ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ subset(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_367,c_40041]) ).
tcf(c_42009,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| point_neighbourhood(sK3(sK49,X0,X1),sK49,sK50)
| ~ open_subset(sK3(sK49,X0,X1),sK49)
| ~ in(sK50,sK3(sK49,X0,X1)) ),
inference(superposition,[status(thm)],[c_40072,c_41991]) ).
tcf(c_45179,plain,
( point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ element(sK50,the_carrier(sK49))
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),neighborhood_system(sK49,sK50)) ),
inference(instantiation,[status(thm)],[c_5942]) ).
tcf(c_47957,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| point_neighbourhood(sK3(sK49,X0,X1),sK49,sK50)
| ~ in(sK50,sK3(sK49,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_42009,c_370,c_5881,c_35445]) ).
tcf(c_47970,plain,
! [X0: $i,X1: $i] :
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| is_a_convergence_point_of_set(sK49,X0,X1)
| in(sK3(sK49,X0,X1),sK51)
| ~ in(sK50,sK3(sK49,X0,X1)) ),
inference(superposition,[status(thm)],[c_47957,c_40564]) ).
tcf(c_48064,plain,
! [X0: $i] :
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| is_a_convergence_point_of_set(sK49,X0,sK50)
| in(sK3(sK49,X0,sK50),sK51) ),
inference(superposition,[status(thm)],[c_5871,c_47970]) ).
tcf(c_48081,plain,
is_a_convergence_point_of_set(sK49,sK51,sK50),
inference(superposition,[status(thm)],[c_48064,c_5895]) ).
tcf(c_48084,plain,
sK11(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50) = sK2(neighborhood_system(sK49,sK50),sK51),
inference(backward_subsumption_resolution,[status(thm)],[c_41641,c_48081]) ).
tcf(c_48123,plain,
( point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ element(sK50,the_carrier(sK49))
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),a_2_0_yellow19(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_48084,c_5987]) ).
tcf(c_48127,plain,
( point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),a_2_0_yellow19(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48123,c_367]) ).
tcf(c_48132,plain,
point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50),
inference(global_subsumption_just,[status(thm)],[c_48127,c_367,c_363,c_27363,c_45179,c_48081]) ).
tcf(c_48136,plain,
( element(sK2(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ element(sK50,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_48132,c_6053]) ).
tcf(c_48141,plain,
element(sK2(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49))),
inference(forward_subsumption_resolution,[status(thm)],[c_48136,c_367]) ).
tcf(c_48142,plain,
subset(sK2(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49)),
inference(superposition,[status(thm)],[c_48141,c_358]) ).
tcf(c_48183,plain,
! [X0: $i] :
( in(sK2(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ in(X0,sK51)
| ~ subset(X0,sK2(neighborhood_system(sK49,sK50),sK51)) ),
inference(superposition,[status(thm)],[c_48142,c_40338]) ).
tcf(c_52513,plain,
( in(sK50,interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51)))
| ~ element(sK50,the_carrier(sK49))
| ~ point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50) ),
inference(instantiation,[status(thm)],[c_5908]) ).
tcf(c_59856,plain,
upper_relstr_subset(sK51,boole_POSet(the_carrier(sK49))),
inference(light_normalisation,[status(thm)],[c_365,c_6776]) ).
tcf(c_59857,plain,
element(sK51,powerset(the_carrier(boole_POSet(the_carrier(sK49))))),
inference(light_normalisation,[status(thm)],[c_366,c_6776]) ).
tcf(c_59858,negated_conjecture,
is_a_convergence_point_of_set(sK49,sK51,sK50),
inference(global_subsumption_just,[status(thm)],[c_364,c_48081]) ).
tcf(c_59860,plain,
~ subset(neighborhood_system(sK49,sK50),sK51),
inference(backward_subsumption_resolution,[status(thm)],[c_363,c_59858]) ).
tcf(c_59948,plain,
neighborhood_system(sK49,sK50) = a_2_0_yellow19(sK49,sK50),
inference(superposition,[status(thm)],[c_367,c_6099]) ).
tcf(c_60026,plain,
! [X0: $i] :
( ( sK11(X0,sK49,sK50) = X0 )
| ~ element(sK50,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_59948,c_5972]) ).
tcf(c_60027,plain,
! [X0: $i] :
( ( sK11(X0,sK49,sK50) = X0 )
| ~ in(X0,neighborhood_system(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60026,c_367]) ).
tcf(c_60239,plain,
! [X0: $i] :
( subset(neighborhood_system(sK49,sK50),X0)
| ( sK11(sK2(neighborhood_system(sK49,sK50),X0),sK49,sK50) = sK2(neighborhood_system(sK49,sK50),X0) ) ),
inference(superposition,[status(thm)],[c_95,c_60027]) ).
tcf(c_60243,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ~ open_subset(X2,sK49)
| ~ in(X1,X2)
| ~ subset(X2,the_carrier(sK49))
| ~ is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(superposition,[status(thm)],[c_357,c_6079]) ).
tcf(c_60267,plain,
! [X0: $i] :
( subset(interior(sK49,X0),the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(superposition,[status(thm)],[c_6351,c_358]) ).
tcf(c_60660,plain,
! [X0: $i,X1: $i] :
( in(X0,sK51)
| ~ in(X1,sK51)
| ~ subset(X1,X0)
| ~ subset(X0,the_carrier(sK49))
| ~ upper_relstr_subset(sK51,boole_POSet(the_carrier(sK49))) ),
inference(superposition,[status(thm)],[c_59857,c_351]) ).
tcf(c_60664,plain,
! [X0: $i,X1: $i] :
( in(X0,sK51)
| ~ in(X1,sK51)
| ~ subset(X1,X0)
| ~ subset(X0,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60660,c_59856]) ).
tcf(c_61707,plain,
sK11(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50) = sK2(neighborhood_system(sK49,sK50),sK51),
inference(superposition,[status(thm)],[c_60239,c_59860]) ).
tcf(c_61717,plain,
( point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ element(sK50,the_carrier(sK49))
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),a_2_0_yellow19(sK49,sK50)) ),
inference(superposition,[status(thm)],[c_61707,c_5987]) ).
tcf(c_61718,plain,
( point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),a_2_0_yellow19(sK49,sK50)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_61717,c_367]) ).
tcf(c_61738,plain,
point_neighbourhood(sK2(neighborhood_system(sK49,sK50),sK51),sK49,sK50),
inference(global_subsumption_just,[status(thm)],[c_61718,c_367,c_363,c_27363,c_45179,c_48081]) ).
tcf(c_61741,plain,
( element(sK2(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ element(sK50,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_61738,c_6053]) ).
tcf(c_61744,plain,
element(sK2(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49))),
inference(forward_subsumption_resolution,[status(thm)],[c_61741,c_367]) ).
tcf(c_61745,plain,
subset(sK2(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49)),
inference(superposition,[status(thm)],[c_61744,c_358]) ).
tcf(c_61751,plain,
subset(interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51)),sK2(neighborhood_system(sK49,sK50),sK51)),
inference(superposition,[status(thm)],[c_61744,c_6318]) ).
tcf(c_61757,plain,
! [X0: $i] :
( in(sK2(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ in(X0,sK51)
| ~ subset(X0,sK2(neighborhood_system(sK49,sK50),sK51)) ),
inference(superposition,[status(thm)],[c_61745,c_60664]) ).
tcf(c_61887,plain,
! [X0: $i] :
( in(X0,sK51)
| ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ subset(X0,the_carrier(sK49)) ),
inference(superposition,[status(thm)],[c_59858,c_60243]) ).
tcf(c_61901,plain,
! [X0: $i] :
( in(interior(sK49,X0),sK51)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ open_subset(interior(sK49,X0),sK49)
| ~ in(sK50,interior(sK49,X0)) ),
inference(superposition,[status(thm)],[c_60267,c_61887]) ).
tcf(c_63024,plain,
! [X0: $i] :
( in(interior(sK49,X0),sK51)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ in(sK50,interior(sK49,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_61901,c_370,c_6014,c_61901]) ).
tcf(c_63061,plain,
( in(interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51)),sK51)
| ~ in(sK50,interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51))) ),
inference(superposition,[status(thm)],[c_61744,c_63024]) ).
tcf(c_64425,plain,
in(interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51)),sK51),
inference(global_subsumption_just,[status(thm)],[c_63061,c_367,c_363,c_27363,c_45179,c_48081,c_52513,c_63061]) ).
tcf(c_83878,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| ~ in(sK2(neighborhood_system(sK49,sK50),sK51),sK51) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_93894,plain,
! [X0: $i] :
( ~ subset(X0,sK2(neighborhood_system(sK49,sK50),sK51))
| ~ in(X0,sK51) ),
inference(global_subsumption_just,[status(thm)],[c_61757,c_363,c_48081,c_48183,c_83878]) ).
tcf(c_93895,plain,
! [X0: $i] :
( ~ in(X0,sK51)
| ~ subset(X0,sK2(neighborhood_system(sK49,sK50),sK51)) ),
inference(renaming,[status(thm)],[c_93894]) ).
tcf(c_93917,plain,
~ in(interior(sK49,sK2(neighborhood_system(sK49,sK50),sK51)),sK51),
inference(superposition,[status(thm)],[c_61751,c_93895]) ).
tcf(c_93918,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_93917,c_64425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU389+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n010.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 13:56:59 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.44 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 53.20/12.97 % SZS status Started for theBenchmark.p
% 53.20/12.97 % SZS status Theorem for theBenchmark.p
% 53.20/12.97
% 53.20/12.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 53.20/12.97
% 53.20/12.97 % ------ iProver source info
% 53.20/12.97
% 53.20/12.97 % git: date: 2026-07-19 20:42:38 +0200
% 53.20/12.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 53.20/12.97 % git: non_committed_changes: false
% 53.20/12.97
% 53.20/12.97 % ------ Parsing...
% 53.20/12.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 53.20/12.97
% 53.20/12.97 % ------ Preprocessing... sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e %
% 53.20/12.97
% 53.20/12.97 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 53.20/12.97
% 53.20/12.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.20/12.97 % ------ Proving...
% 53.20/12.97 % ------ Problem Properties
% 53.20/12.97
% 53.20/12.97 %
% 53.20/12.97 % clauses 474
% 53.20/12.97 % conjectures 5
% 53.20/12.97 % EPR 30
% 53.20/12.97 % Horn 456
% 53.20/12.97 % unary 234
% 53.20/12.97 % binary 206
% 53.20/12.97 % lits 756
% 53.20/12.97 % lits eq 165
% 53.20/12.97 % fd_pure 0
% 53.20/12.97 % fd_pseudo 0
% 53.20/12.97 % fd_cond 1
% 53.20/12.97 % fd_pseudo_cond 5
% 53.20/12.97 % AC symbols 0
% 53.20/12.97
% 53.20/12.97 % ------ Input Options Time Limit: Unbounded
% 53.20/12.97
% 53.20/12.97
% 53.20/12.97 % ------
% 53.20/12.97 % Current options:
% 53.20/12.97 % ------
% 53.20/12.97
% 53.20/12.97
% 53.20/12.97 %
% 53.20/12.97
% 53.20/12.97 % ------ Proving...
% 53.20/12.97 %
% 53.20/12.97
% 53.20/12.97 % SZS status Theorem for theBenchmark.p
% 53.20/12.97
% 53.20/12.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 53.20/12.98
% 53.20/12.98
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