SET007 Axioms: SET007+681.ax
%------------------------------------------------------------------------------
% File : SET007+681 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lower Tolerance. Preliminaries to Wroclaw Taxonomy
% 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 : taxonom1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 61 ( 0 unt; 0 def)
% Number of atoms : 440 ( 37 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 443 ( 64 ~; 1 |; 193 &)
% ( 12 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-4 aty)
% Number of functors : 32 ( 32 usr; 4 con; 0-5 aty)
% Number of variables : 162 ( 155 !; 7 ?)
% 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(rc1_taxonom1,axiom,
? [A] :
( v1_xreal_0(A)
& ~ v3_xreal_0(A)
& v1_xcmplx_0(A) ) ).
fof(fc1_taxonom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v1_xboole_0(B)
& v6_tbsp_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_xreal_0(k2_tbsp_1(A,B))
& ~ v3_xreal_0(k2_tbsp_1(A,B))
& v1_xcmplx_0(k2_tbsp_1(A,B)) ) ) ).
fof(t1_taxonom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A))
=> ( r2_hidden(B,k4_finseq_1(A))
| B = np__0 ) ) ) ) ).
fof(t2_taxonom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k4_finseq_1(A))
& r2_hidden(k1_nat_1(D,np__1),k4_finseq_1(A)) )
=> k1_funct_1(A,D) = k1_funct_1(A,k1_nat_1(D,np__1)) ) ) )
=> k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ).
fof(t3_taxonom1,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( r1_relat_2(B,A)
=> k4_relset_1(A,A,B) = A ) ) ).
fof(t4_taxonom1,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( r1_relat_2(B,A)
=> k5_relset_1(A,A,B) = A ) ) ).
fof(t5_taxonom1,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( r1_relat_2(B,A)
=> r1_relat_2(k17_finseq_1(B),A) ) ) ).
fof(t6_taxonom1,axiom,
! [A,B,C,D] :
( m2_relset_1(D,A,A)
=> ( ( r1_relat_2(D,A)
& r1_rewrite1(D,B,C)
& r2_hidden(B,A) )
=> r2_hidden(k4_tarski(B,C),k17_finseq_1(D)) ) ) ).
fof(t7_taxonom1,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( ( r1_relat_2(B,A)
& r3_relat_2(B,A) )
=> r3_relat_2(k17_finseq_1(B),A) ) ) ).
fof(t8_taxonom1,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( r1_relat_2(B,A)
=> r8_relat_2(k17_finseq_1(B),A) ) ) ).
fof(t9_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ( ( r1_relat_2(B,A)
& r3_relat_2(B,A) )
=> ( v3_relat_2(k17_lang1(A,B))
& v8_relat_2(k17_lang1(A,B))
& v1_partfun1(k17_lang1(A,B),A,A)
& m2_relset_1(k17_lang1(A,B),A,A) ) ) ) ) ).
fof(t10_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m2_relset_1(C,A,A)
=> ( r1_tarski(B,C)
=> r1_tarski(k17_lang1(A,B),k17_lang1(A,C)) ) ) ) ) ).
fof(t11_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> r1_setfam_1(k3_pua2mss1(A),k1_tarski(A)) ) ).
fof(d1_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
=> ( m1_taxonom1(B,A)
<=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& ~ r1_setfam_1(C,D)
& ~ r1_setfam_1(D,C) ) ) ) ) ) ) ).
fof(t12_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m1_taxonom1(k1_tarski(k1_tarski(A)),A) ) ).
fof(t13_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m1_taxonom1(k1_tarski(k3_pua2mss1(A)),A) ) ).
fof(t14_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
=> ( B = k2_tarski(k1_tarski(A),k3_pua2mss1(A))
=> m1_taxonom1(B,A) ) ) ) ).
fof(d2_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
=> ( m2_taxonom1(B,A)
<=> ( m1_taxonom1(B,A)
& r2_hidden(k1_tarski(A),B)
& r2_hidden(k3_pua2mss1(A),B) ) ) ) ) ).
fof(t15_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
=> ( B = k2_tarski(k1_tarski(A),k3_pua2mss1(A))
=> m2_taxonom1(B,A) ) ) ) ).
fof(d3_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m2_relset_1(D,A,A)
=> ( D = k1_taxonom1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(k4_tarski(E,F),D)
<=> r1_xreal_0(k1_metric_1(A,A,B,E,F),C) ) ) ) ) ) ) ) ) ).
fof(t16_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( ( v2_metric_1(B,A)
& r1_xreal_0(np__0,C) )
=> r1_relat_2(k1_taxonom1(A,B,C),A) ) ) ) ) ).
fof(t17_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( v4_metric_1(B,A)
=> r3_relat_2(k1_taxonom1(A,B,C),A) ) ) ) ) ).
fof(t18_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(np__0,C)
& v2_metric_1(B,A)
& v4_metric_1(B,A) )
=> ( v1_relat_2(k1_taxonom1(A,B,C))
& v3_relat_2(k1_taxonom1(A,B,C))
& v1_partfun1(k1_taxonom1(A,B,C),A,A)
& m2_relset_1(k1_taxonom1(A,B,C),A,A) ) ) ) ) ) ).
fof(t19_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> r1_tarski(k1_taxonom1(A,B,C),k1_taxonom1(A,B,D)) ) ) ) ) ) ).
fof(d4_taxonom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ( v1_taxonom1(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> r1_xreal_0(np__0,k1_metric_1(A,A,B,C,D)) ) ) ) ) ).
fof(t20_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C,D] :
( ( v1_taxonom1(B,A)
& v2_metric_1(B,A)
& v3_metric_1(B,A)
& r2_hidden(k4_tarski(C,D),k1_taxonom1(A,B,np__0)) )
=> C = D ) ) ) ).
fof(t21_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,A)
=> ( ( v2_metric_1(B,A)
& v3_metric_1(B,A) )
=> r2_hidden(k4_tarski(C,C),k1_taxonom1(A,B,np__0)) ) ) ) ) ).
fof(t22_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_relat_2(k1_taxonom1(A,B,C),A)
& v4_metric_1(B,A) )
=> ( v3_relat_2(k17_lang1(A,k1_taxonom1(A,B,C)))
& v8_relat_2(k17_lang1(A,k1_taxonom1(A,B,C)))
& v1_partfun1(k17_lang1(A,k1_taxonom1(A,B,C)),A,A)
& m2_relset_1(k17_lang1(A,k1_taxonom1(A,B,C)),A,A) ) ) ) ) ) ).
fof(t23_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ( ( v1_taxonom1(B,A)
& v2_metric_1(B,A)
& v3_metric_1(B,A) )
=> k17_lang1(A,k1_taxonom1(A,B,np__0)) = k1_taxonom1(A,B,np__0) ) ) ) ).
fof(t24_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( v3_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ( ( C = k17_lang1(A,k1_taxonom1(A,B,np__0))
& v1_taxonom1(B,A)
& v2_metric_1(B,A)
& v3_metric_1(B,A) )
=> C = k6_relat_1(A) ) ) ) ) ).
fof(t25_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( v3_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ( ( C = k17_lang1(A,k1_taxonom1(A,B,np__0))
& v1_taxonom1(B,A)
& v2_metric_1(B,A)
& v3_metric_1(B,A) )
=> k8_eqrel_1(A,C) = k3_pua2mss1(A) ) ) ) ) ).
fof(t26_taxonom1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
=> ! [D] :
( v1_xreal_0(D)
=> ( ( C = k5_relset_1(k2_zfmisc_1(A,A),k1_numbers,B)
& r1_xreal_0(k1_pre_circ(C),D) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,A)
=> ! [F] :
( m2_subset_1(F,k1_numbers,A)
=> r1_xreal_0(k1_metric_1(A,A,B,E,F),D) ) ) ) ) ) ) ) ).
fof(t27_taxonom1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
=> ! [D] :
( v1_xreal_0(D)
=> ( ( C = k5_relset_1(k2_zfmisc_1(A,A),k1_numbers,B)
& r1_xreal_0(k1_pre_circ(C),D) )
=> ! [E] :
( ( v3_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,A,A)
& m2_relset_1(E,A,A) )
=> ( E = k17_lang1(A,k1_taxonom1(A,B,D))
=> k8_eqrel_1(A,E) = k1_tarski(A) ) ) ) ) ) ) ) ).
fof(t28_taxonom1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
=> ! [D] :
( v1_xreal_0(D)
=> ( ( C = k5_relset_1(k2_zfmisc_1(A,A),k1_numbers,B)
& r1_xreal_0(k1_pre_circ(C),D) )
=> k17_lang1(A,k1_taxonom1(A,B,D)) = k1_taxonom1(A,B,D) ) ) ) ) ) ).
fof(d5_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_partit1(A)))
=> ( C = k2_taxonom1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_xreal_0(E)
& ~ v3_xreal_0(E)
& ? [F] :
( v3_relat_2(F)
& v8_relat_2(F)
& v1_partfun1(F,A,A)
& m2_relset_1(F,A,A)
& F = k17_lang1(A,k1_taxonom1(A,B,E))
& k8_eqrel_1(A,F) = D ) ) ) ) ) ) ) ).
fof(t29_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ! [C] :
( ( v1_xreal_0(C)
& ~ v3_xreal_0(C) )
=> ( ( r1_relat_2(k1_taxonom1(A,B,C),A)
& v4_metric_1(B,A) )
=> ~ v1_xboole_0(k2_taxonom1(A,B)) ) ) ) ) ).
fof(t30_taxonom1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ( ( v4_metric_1(B,A)
& v1_taxonom1(B,A) )
=> r2_hidden(k1_tarski(A),k2_taxonom1(A,B)) ) ) ) ).
fof(t31_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> m1_taxonom1(k2_taxonom1(A,B),A) ) ) ).
fof(t32_taxonom1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
& m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> ( ( r2_hidden(k3_pua2mss1(A),k2_taxonom1(A,B))
& v4_metric_1(B,A)
& v1_taxonom1(B,A) )
=> m2_taxonom1(k2_taxonom1(A,B),A) ) ) ) ).
fof(d6_taxonom1,axiom,
! [A] :
( l1_metric_1(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_taxonom1(A,B,C,D)
<=> r1_xreal_0(k2_metric_1(A,C,D),B) ) ) ) ) ) ).
fof(d7_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_metric_1(A) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ( C = k3_taxonom1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(D,E),C)
<=> r1_taxonom1(A,B,D,E) ) ) ) ) ) ) ) ).
fof(t33_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_metric_1(A) )
=> ! [B] :
( v1_xreal_0(B)
=> k3_taxonom1(A,B) = k1_taxonom1(u1_struct_0(A),u1_metric_1(A),B) ) ) ).
fof(t34_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ( ( C = k3_taxonom1(A,B)
& r1_xreal_0(np__0,B) )
=> ( v1_relat_2(C)
& v3_relat_2(C)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ) ).
fof(d8_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_partit1(u1_struct_0(A))))
=> ( B = k4_taxonom1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( v1_xreal_0(D)
& ~ v3_xreal_0(D)
& ? [E] :
( v3_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A))
& E = k17_lang1(u1_struct_0(A),k3_taxonom1(A,D))
& k8_eqrel_1(u1_struct_0(A),E) = C ) ) ) ) ) ) ).
fof(t35_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& l1_metric_1(A) )
=> k4_taxonom1(A) = k2_taxonom1(u1_struct_0(A),u1_metric_1(A)) ) ).
fof(t36_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( B = k17_lang1(u1_struct_0(A),k3_taxonom1(A,np__0))
=> k8_eqrel_1(u1_struct_0(A),B) = k3_pua2mss1(u1_struct_0(A)) ) ) ) ).
fof(t37_taxonom1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v8_metric_1(B)
& v5_tbsp_1(B)
& l1_metric_1(B) )
=> ( r1_xreal_0(k2_tbsp_1(B,k2_pre_topc(B)),A)
=> k3_taxonom1(B,A) = k1_eqrel_1(u1_struct_0(B)) ) ) ) ).
fof(t38_taxonom1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v8_metric_1(B)
& v5_tbsp_1(B)
& l1_metric_1(B) )
=> ( r1_xreal_0(k2_tbsp_1(B,k2_pre_topc(B)),A)
=> k3_taxonom1(B,A) = k17_lang1(u1_struct_0(B),k3_taxonom1(B,A)) ) ) ) ).
fof(t39_taxonom1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v8_metric_1(B)
& v5_tbsp_1(B)
& l1_metric_1(B) )
=> ( r1_xreal_0(k2_tbsp_1(B,k2_pre_topc(B)),A)
=> k17_lang1(u1_struct_0(B),k3_taxonom1(B,A)) = k1_eqrel_1(u1_struct_0(B)) ) ) ) ).
fof(t40_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& v5_tbsp_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_xreal_0(C)
& ~ v3_xreal_0(C) )
=> ( ( r1_xreal_0(k2_tbsp_1(A,k2_pre_topc(A)),C)
& B = k17_lang1(u1_struct_0(A),k3_taxonom1(A,C)) )
=> k8_eqrel_1(u1_struct_0(A),B) = k1_tarski(u1_struct_0(A)) ) ) ) ) ).
fof(t41_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& v5_tbsp_1(A)
& l1_metric_1(A) )
=> r2_hidden(k1_tarski(u1_struct_0(A)),k4_taxonom1(A)) ) ).
fof(t42_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& l1_metric_1(A) )
=> m1_taxonom1(k4_taxonom1(A),u1_struct_0(A)) ) ).
fof(t43_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& v5_tbsp_1(A)
& l1_metric_1(A) )
=> m2_taxonom1(k4_taxonom1(A),u1_struct_0(A)) ) ).
fof(dt_m1_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_taxonom1(B,A)
=> m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) ) ) ).
fof(existence_m1_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] : m1_taxonom1(B,A) ) ).
fof(dt_m2_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_taxonom1(B,A)
=> m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) ) ) ).
fof(existence_m2_taxonom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] : m2_taxonom1(B,A) ) ).
fof(dt_k1_taxonom1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers)
& v1_xreal_0(C) )
=> m2_relset_1(k1_taxonom1(A,B,C),A,A) ) ).
fof(dt_k2_taxonom1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
=> m1_subset_1(k2_taxonom1(A,B),k1_zfmisc_1(k1_partit1(A))) ) ).
fof(dt_k3_taxonom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_metric_1(A)
& v1_xreal_0(B) )
=> m2_relset_1(k3_taxonom1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k4_taxonom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v8_metric_1(A)
& l1_metric_1(A) )
=> m1_subset_1(k4_taxonom1(A),k1_zfmisc_1(k1_partit1(u1_struct_0(A)))) ) ).
%------------------------------------------------------------------------------