SET007 Axioms: SET007+420.ax
%------------------------------------------------------------------------------
% File : SET007+420 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Decomposition of the Continuity
% 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 : decomp_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 105 ( 0 unt; 0 def)
% Number of atoms : 625 ( 63 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 572 ( 52 ~; 0 |; 264 &)
% ( 52 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 32 ( 31 usr; 0 prp; 1-3 aty)
% Number of functors : 43 ( 43 usr; 0 con; 1-4 aty)
% Number of variables : 225 ( 209 !; 16 ?)
% 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(d1_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_decomp_1(B,A)
<=> r1_tarski(B,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) ) ).
fof(d2_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_decomp_1(B,A)
<=> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ).
fof(d3_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_decomp_1(B,A)
<=> r1_tarski(B,k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ).
fof(d4_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_decomp_1(B,A)
<=> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))) ) ) ) ).
fof(d5_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_decomp_1(B,A)
<=> r1_tarski(B,k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B)))) ) ) ) ).
fof(d6_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_decomp_1(A,B) = k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ).
fof(d7_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_decomp_1(A,B) = k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,k6_pre_topc(A,B))) ) ) ).
fof(d8_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k3_decomp_1(A,B) = k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) ).
fof(d9_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k4_decomp_1(A,B) = k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))) ) ) ).
fof(d10_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k5_decomp_1(A,B) = k4_subset_1(u1_struct_0(A),k1_decomp_1(A,B),k2_decomp_1(A,B)) ) ) ).
fof(t1_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( k3_decomp_1(A,B) = k2_decomp_1(A,B)
<=> k1_decomp_1(A,B) = k4_decomp_1(A,B) ) ) ) ).
fof(t2_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_decomp_1(B,A)
<=> B = k3_decomp_1(A,B) ) ) ) ).
fof(t3_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_decomp_1(B,A)
<=> B = k1_decomp_1(A,B) ) ) ) ).
fof(t4_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_decomp_1(B,A)
<=> B = k2_decomp_1(A,B) ) ) ) ).
fof(t5_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_decomp_1(B,A)
<=> B = k4_decomp_1(A,B) ) ) ) ).
fof(t6_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_decomp_1(B,A)
<=> B = k5_decomp_1(A,B) ) ) ) ).
fof(t7_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k6_decomp_1(A),k11_decomp_1(A)) = u1_pre_topc(A) ) ).
fof(t8_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k7_decomp_1(A),k13_decomp_1(A)) = u1_pre_topc(A) ) ).
fof(t9_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k8_decomp_1(A),k12_decomp_1(A)) = u1_pre_topc(A) ) ).
fof(t10_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_decomp_1(A),k14_decomp_1(A)) = u1_pre_topc(A) ) ).
fof(t11_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k8_decomp_1(A),k15_decomp_1(A)) = k6_decomp_1(A) ) ).
fof(t12_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k7_decomp_1(A),k16_decomp_1(A)) = k6_decomp_1(A) ) ).
fof(t13_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_decomp_1(A),k17_decomp_1(A)) = k6_decomp_1(A) ) ).
fof(t14_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k9_decomp_1(A),k18_decomp_1(A)) = k8_decomp_1(A) ) ).
fof(t15_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_decomp_1(A),k19_decomp_1(A)) = k8_decomp_1(A) ) ).
fof(t16_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_decomp_1(A),k15_decomp_1(A)) = k7_decomp_1(A) ) ).
fof(t17_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_decomp_1(A),k20_decomp_1(A)) = k9_decomp_1(A) ) ).
fof(d26_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k7_decomp_1(A)) ) ) ) ) ) ) ).
fof(d27_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v6_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k8_decomp_1(A)) ) ) ) ) ) ) ).
fof(d28_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v7_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k6_decomp_1(A)) ) ) ) ) ) ) ).
fof(d29_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v8_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k10_decomp_1(A)) ) ) ) ) ) ) ).
fof(d30_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v9_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k9_decomp_1(A)) ) ) ) ) ) ) ).
fof(d31_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v10_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k11_decomp_1(A)) ) ) ) ) ) ) ).
fof(d32_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v11_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k13_decomp_1(A)) ) ) ) ) ) ) ).
fof(d33_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v12_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k12_decomp_1(A)) ) ) ) ) ) ) ).
fof(d34_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v13_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k14_decomp_1(A)) ) ) ) ) ) ) ).
fof(d35_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v14_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k15_decomp_1(A)) ) ) ) ) ) ) ).
fof(d36_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v15_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k16_decomp_1(A)) ) ) ) ) ) ) ).
fof(d37_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v16_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k17_decomp_1(A)) ) ) ) ) ) ) ).
fof(d38_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v17_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k19_decomp_1(A)) ) ) ) ) ) ) ).
fof(d39_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v18_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k18_decomp_1(A)) ) ) ) ) ) ) ).
fof(d40_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v19_decomp_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(D,B)
=> r2_hidden(k5_pre_topc(A,B,C,D),k20_decomp_1(A)) ) ) ) ) ) ) ).
fof(t18_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v7_decomp_1(C,A,B)
<=> ( v6_decomp_1(C,A,B)
& v14_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t19_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v7_decomp_1(C,A,B)
<=> ( v5_decomp_1(C,A,B)
& v15_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t20_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v7_decomp_1(C,A,B)
<=> ( v8_decomp_1(C,A,B)
& v16_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t21_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v6_decomp_1(C,A,B)
<=> ( v9_decomp_1(C,A,B)
& v18_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t22_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v6_decomp_1(C,A,B)
<=> ( v8_decomp_1(C,A,B)
& v17_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t23_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_decomp_1(C,A,B)
<=> ( v8_decomp_1(C,A,B)
& v14_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t24_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v9_decomp_1(C,A,B)
<=> ( v8_decomp_1(C,A,B)
& v19_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t25_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> ( v7_decomp_1(C,A,B)
& v10_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t26_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> ( v5_decomp_1(C,A,B)
& v11_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t27_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> ( v6_decomp_1(C,A,B)
& v12_decomp_1(C,A,B) ) ) ) ) ) ).
fof(t28_decomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> ( v8_decomp_1(C,A,B)
& v13_decomp_1(C,A,B) ) ) ) ) ) ).
fof(dt_m1_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_decomp_1(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_decomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m1_decomp_1(B,A) ) ).
fof(dt_k1_decomp_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_decomp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_decomp_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_decomp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k3_decomp_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k3_decomp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_decomp_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k4_decomp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_decomp_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_decomp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k6_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k7_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k7_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k8_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k8_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k9_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k9_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k10_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k10_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k11_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k11_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k12_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k12_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k13_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k13_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k14_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k14_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k15_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k15_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k16_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k16_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k17_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k17_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k18_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k18_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k19_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k19_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k20_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> m1_subset_1(k20_decomp_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(d11_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k6_decomp_1(A) = a_1_0_decomp_1(A) ) ).
fof(d12_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k7_decomp_1(A) = a_1_1_decomp_1(A) ) ).
fof(d13_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k8_decomp_1(A) = a_1_2_decomp_1(A) ) ).
fof(d14_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k9_decomp_1(A) = a_1_3_decomp_1(A) ) ).
fof(d15_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k10_decomp_1(A) = a_1_4_decomp_1(A) ) ).
fof(d16_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k11_decomp_1(A) = a_1_5_decomp_1(A) ) ).
fof(d17_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k12_decomp_1(A) = a_1_6_decomp_1(A) ) ).
fof(d18_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k13_decomp_1(A) = a_1_7_decomp_1(A) ) ).
fof(d19_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k14_decomp_1(A) = a_1_8_decomp_1(A) ) ).
fof(d20_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k15_decomp_1(A) = a_1_9_decomp_1(A) ) ).
fof(d21_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k16_decomp_1(A) = a_1_10_decomp_1(A) ) ).
fof(d22_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k17_decomp_1(A) = a_1_11_decomp_1(A) ) ).
fof(d23_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k18_decomp_1(A) = a_1_12_decomp_1(A) ) ).
fof(d24_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k19_decomp_1(A) = a_1_13_decomp_1(A) ) ).
fof(d25_decomp_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k20_decomp_1(A) = a_1_14_decomp_1(A) ) ).
fof(fraenkel_a_1_0_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_0_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& m1_decomp_1(C,B) ) ) ) ).
fof(fraenkel_a_1_1_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_1_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& v1_decomp_1(C,B) ) ) ) ).
fof(fraenkel_a_1_2_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_2_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& v2_decomp_1(C,B) ) ) ) ).
fof(fraenkel_a_1_3_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_3_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& v4_decomp_1(C,B) ) ) ) ).
fof(fraenkel_a_1_4_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_4_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& v3_decomp_1(C,B) ) ) ) ).
fof(fraenkel_a_1_5_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_5_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k1_tops_1(B,C) = k3_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_6_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_6_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k1_tops_1(B,C) = k2_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_7_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_7_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k1_tops_1(B,C) = k1_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_8_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_8_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k1_tops_1(B,C) = k4_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_9_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_9_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k3_decomp_1(B,C) = k2_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_10_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_10_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k3_decomp_1(B,C) = k1_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_11_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_11_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k3_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_12_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_12_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k2_decomp_1(B,C) = k5_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_13_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_13_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k2_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_14_decomp_1,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_14_decomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& k5_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) ).
%------------------------------------------------------------------------------