SET007 Axioms: SET007+744.ax
%------------------------------------------------------------------------------
% File : SET007+744 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Topology of Real Unitary Space
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : rusub_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 72 ( 0 unt; 0 def)
% Number of atoms : 852 ( 48 equ)
% Maximal formula atoms : 21 ( 11 avg)
% Number of connectives : 905 ( 125 ~; 4 |; 544 &)
% ( 12 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 0 prp; 1-3 aty)
% Number of functors : 40 ( 40 usr; 3 con; 0-3 aty)
% Number of variables : 220 ( 208 !; 12 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> v2_pre_topc(k5_rusub_5(A)) ) ).
fof(fc2_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ~ v3_struct_0(k5_rusub_5(A))
& v2_pre_topc(k5_rusub_5(A)) ) ) ).
fof(d1_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_rusub_5(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k6_rusub_4(A,C,k1_struct_0(A,D)) ) ) ) ) ) ).
fof(t1_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_rusub_5(A,B,B) ) ) ).
fof(t2_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_rusub_5(A,B,C)
=> r1_rusub_5(A,C,B) ) ) ) ) ).
fof(t3_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v2_rusub_4(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( r1_rusub_5(A,B,C)
& r1_rusub_5(A,C,D) )
=> r1_rusub_5(A,B,D) ) ) ) ) ) ).
fof(t4_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_rusub_4(k1_rusub_5(A,B,C),A) ) ) ) ).
fof(t5_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_xboole_0(B)
| v1_xboole_0(C) )
=> v1_xboole_0(k6_rusub_4(A,B,C)) ) ) ) ) ).
fof(t6_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k6_rusub_4(A,B,C)) ) ) ) ).
fof(t7_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_xboole_0(B)
| v1_xboole_0(C) )
=> v1_xboole_0(k1_rusub_5(A,B,C)) ) ) ) ) ).
fof(t8_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k1_rusub_5(A,B,C)) ) ) ) ).
fof(t9_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( B = k7_rusub_4(A,C,k1_struct_0(A,D))
<=> k1_rusub_5(A,B,k1_struct_0(A,D)) = C ) ) ) ) ) ).
fof(t10_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r1_tarski(k7_rusub_4(A,B,k1_struct_0(A,D)),k7_rusub_4(A,B,C)) ) ) ) ) ) ).
fof(t11_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r1_tarski(k1_rusub_5(A,B,k1_struct_0(A,D)),k1_rusub_5(A,B,C)) ) ) ) ) ) ).
fof(t12_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k1_rlvect_1(A),k1_rusub_5(A,B,B)) ) ) ).
fof(t13_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v3_rusub_4(B,A)
& r2_hidden(C,B) )
=> r1_tarski(k7_rusub_4(A,B,k1_struct_0(A,C)),B) ) ) ) ) ).
fof(t14_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v2_rusub_4(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( v3_rusub_4(C,A)
& v3_rusub_4(D,A)
& r1_rusub_5(A,B,C)
& r1_rusub_5(A,B,D) )
=> C = D ) ) ) ) ) ).
fof(t15_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r2_hidden(k1_rlvect_1(A),k1_rusub_5(A,B,k1_struct_0(A,C))) ) ) ) ) ).
fof(t16_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( ( ~ v1_xboole_0(D)
& v2_rusub_4(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( D = k1_rusub_5(A,B,k1_struct_0(A,C))
& r1_rusub_5(A,B,D)
& v3_rusub_4(D,A) ) ) ) ) ) ) ).
fof(t17_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> k1_rusub_5(A,B,k1_struct_0(A,D)) = k1_rusub_5(A,B,k1_struct_0(A,C)) ) ) ) ) ) ).
fof(t20_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( ~ v1_xboole_0(C)
& v2_rusub_4(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& C = k1_rusub_5(A,B,B)
& v3_rusub_4(C,A)
& r1_rusub_5(A,B,C) ) ) ) ).
fof(t21_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> r1_rlvect_1(k2_rusub_5(A,B),k1_rlvect_1(A)) ) ) ).
fof(t22_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k2_rusub_5(A,k1_rusub_1(A)) = k2_rusub_1(A) ) ).
fof(t23_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k2_rusub_5(A,k2_rusub_1(A)) = k1_rusub_1(A) ) ).
fof(t24_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( C != k1_rlvect_1(A)
& r1_rlvect_1(B,C)
& r1_rlvect_1(k2_rusub_5(A,B),C) ) ) ) ) ).
fof(t25_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_tarski(B,u1_struct_0(k2_rusub_5(A,k3_rusub_5(A,B)))) ) ) ).
fof(t26_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(B,C)
=> r1_tarski(u1_struct_0(k3_rusub_5(A,C)),u1_struct_0(k3_rusub_5(A,B))) ) ) ) ) ).
fof(t27_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = u1_struct_0(B)
=> k3_rusub_5(A,C) = k2_rusub_5(A,B) ) ) ) ) ).
fof(t28_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_rusub_5(A,B) = k2_rusub_5(A,k2_rusub_5(A,k3_rusub_5(A,B))) ) ) ).
fof(t29_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k7_square_1(k3_bhsp_1(A,k4_rlvect_1(A,B,C))) = k3_real_1(k3_real_1(k7_square_1(k3_bhsp_1(A,B)),k4_real_1(np__2,k2_bhsp_1(A,B,C))),k7_square_1(k3_bhsp_1(A,C)))
& k7_square_1(k3_bhsp_1(A,k6_rlvect_1(A,B,C))) = k3_real_1(k5_real_1(k7_square_1(k3_bhsp_1(A,B)),k4_real_1(np__2,k2_bhsp_1(A,B,C))),k7_square_1(k3_bhsp_1(A,C))) ) ) ) ) ).
fof(t30_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_bhsp_1(A,B,C)
=> k7_square_1(k3_bhsp_1(A,k4_rlvect_1(A,B,C))) = k3_real_1(k7_square_1(k3_bhsp_1(A,B)),k7_square_1(k3_bhsp_1(A,C))) ) ) ) ) ).
fof(t31_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_real_1(k7_square_1(k3_bhsp_1(A,k4_rlvect_1(A,B,C))),k7_square_1(k3_bhsp_1(A,k6_rlvect_1(A,B,C)))) = k3_real_1(k4_real_1(np__2,k7_square_1(k3_bhsp_1(A,B))),k4_real_1(np__2,k7_square_1(k3_bhsp_1(A,C)))) ) ) ) ).
fof(d5_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = k4_rusub_5(A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& r1_tarski(k4_bhsp_2(A,D,E),C) ) ) ) ) ) ) ) ) ) ).
fof(t33_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r1_xreal_0(C,D)
=> r1_tarski(k4_bhsp_2(A,B,C),k4_bhsp_2(A,B,D)) ) ) ) ) ) ).
fof(t34_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,k1_numbers)
& ~ r1_xreal_0(C,np__0)
& r1_tarski(k4_bhsp_2(A,B,C),u1_struct_0(A)) ) ) ) ).
fof(t35_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r2_hidden(C,k4_bhsp_2(A,B,D))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& r1_tarski(k4_bhsp_2(A,C,E),k4_bhsp_2(A,B,D)) ) ) ) ) ) ) ) ).
fof(t36_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( r2_hidden(C,k5_subset_1(u1_struct_0(A),k4_bhsp_2(A,B,E),k4_bhsp_2(A,D,F)))
& ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( r1_tarski(k4_bhsp_2(A,C,G),k4_bhsp_2(A,B,E))
& r1_tarski(k4_bhsp_2(A,C,G),k4_bhsp_2(A,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(t37_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r2_hidden(k4_bhsp_2(A,B,C),k4_rusub_5(A)) ) ) ) ).
fof(t38_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> r2_hidden(u1_struct_0(A),k4_rusub_5(A)) ) ).
fof(t39_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(B,k4_rusub_5(A))
& r2_hidden(C,k4_rusub_5(A)) )
=> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k4_rusub_5(A)) ) ) ) ) ).
fof(t40_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(B,k4_rusub_5(A))
=> r2_hidden(k5_setfam_1(u1_struct_0(A),B),k4_rusub_5(A)) ) ) ) ).
fof(t41_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_rusub_5(A)))
& l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_rusub_5(A))) ) ) ).
fof(d6_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k5_rusub_5(A) = g1_pre_topc(u1_struct_0(A),k4_rusub_5(A)) ) ).
fof(t42_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ( B = k2_pre_topc(A)
=> ( v3_pre_topc(B,k5_rusub_5(A))
& v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ).
fof(t43_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ( B = k1_pre_topc(A)
=> ( v3_pre_topc(B,k5_rusub_5(A))
& v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ).
fof(t44_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( u1_struct_0(A) = k1_struct_0(A,k1_rlvect_1(A))
=> ( C = np__0
| v1_xboole_0(k6_bhsp_2(A,B,C)) ) ) ) ) ) ).
fof(t45_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( u1_struct_0(A) != k1_struct_0(A,k1_rlvect_1(A))
& ~ r1_xreal_0(C,np__0)
& v1_xboole_0(k6_bhsp_2(A,B,C)) ) ) ) ) ).
fof(t46_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( C = np__0
=> v1_xboole_0(k4_bhsp_2(A,B,C)) ) ) ) ) ).
fof(t47_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( u1_struct_0(A) = k1_struct_0(A,k1_rlvect_1(A))
=> ( r1_xreal_0(C,np__0)
| k4_bhsp_2(A,B,C) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ) ) ) ).
fof(t48_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( u1_struct_0(A) != k1_struct_0(A,k1_rlvect_1(A))
& ~ r1_xreal_0(C,np__0)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( D != B
& r2_hidden(D,k4_bhsp_2(A,B,C)) ) ) ) ) ) ) ).
fof(t49_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( u1_struct_0(A) = u1_struct_0(k5_rusub_5(A))
& u1_pre_topc(k5_rusub_5(A)) = k4_rusub_5(A) ) ) ).
fof(t50_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( B = k4_bhsp_2(A,D,C)
=> v3_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) ).
fof(t51_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ( v3_pre_topc(B,k5_rusub_5(A))
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& r1_tarski(k4_bhsp_2(A,C,D),B) ) ) ) ) ) ) ) ).
fof(t52_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,k1_numbers)
& r1_tarski(k4_subset_1(u1_struct_0(A),k4_bhsp_2(A,B,D),k4_bhsp_2(A,C,E)),k4_bhsp_2(A,F,G)) ) ) ) ) ) ) ) ).
fof(t53_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( B = k5_bhsp_2(A,C,D)
=> v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) ).
fof(t54_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( B = k6_bhsp_2(A,C,D)
=> v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) ).
fof(dt_k1_rusub_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_rusub_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_rusub_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ( v1_bhsp_1(k2_rusub_5(A,B))
& m1_rusub_1(k2_rusub_5(A,B),A) ) ) ).
fof(dt_k3_rusub_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_bhsp_1(k3_rusub_5(A,B))
& m1_rusub_1(k3_rusub_5(A,B),A) ) ) ).
fof(dt_k4_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> m1_subset_1(k4_rusub_5(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k5_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> l1_pre_topc(k5_rusub_5(A)) ) ).
fof(d2_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k1_rusub_5(A,B,C) = a_3_0_rusub_5(A,B,C) ) ) ) ).
fof(t18_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_rusub_5(A,B,B) = k3_tarski(a_2_0_rusub_5(A,B)) ) ) ).
fof(t19_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_rusub_4(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k1_rusub_5(A,B,k1_struct_0(A,C)) = k3_tarski(a_2_0_rusub_5(A,B)) ) ) ) ) ).
fof(d3_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( C = k2_rusub_5(A,B)
<=> u1_struct_0(C) = a_2_1_rusub_5(A,B) ) ) ) ) ).
fof(d4_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( C = k3_rusub_5(A,B)
<=> u1_struct_0(C) = a_2_2_rusub_5(A,B) ) ) ) ) ).
fof(t32_rusub_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_rusub_1(C,A)
& u1_struct_0(C) = a_2_3_rusub_5(A,B) ) ) ) ).
fof(fraenkel_a_3_0_rusub_5,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_rusub_5(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k6_rlvect_1(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_2_0_rusub_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B)
& ~ v1_xboole_0(C)
& v2_rusub_4(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_rusub_5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k1_rusub_5(B,C,k1_struct_0(B,D))
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_1_rusub_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_rusub_1(C,B) )
=> ( r2_hidden(A,a_2_1_rusub_5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_rlvect_1(C,E)
=> r1_bhsp_1(B,E,D) ) ) ) ) ) ).
fof(fraenkel_a_2_2_rusub_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_2_rusub_5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,C)
=> r1_bhsp_1(B,E,D) ) ) ) ) ) ).
fof(fraenkel_a_2_3_rusub_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_3_rusub_5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& k2_bhsp_1(B,D,C) = np__0 ) ) ) ).
%------------------------------------------------------------------------------