SET007 Axioms: SET007+251.ax
%------------------------------------------------------------------------------
% File : SET007+251 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Analytical Metric Affine Spaces and Planes
% 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 : analmetr [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 131 ( 19 unt; 0 def)
% Number of atoms : 1431 ( 120 equ)
% Maximal formula atoms : 58 ( 10 avg)
% Number of connectives : 1536 ( 236 ~; 15 |; 700 &)
% ( 31 <=>; 554 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-7 aty)
% Number of functors : 26 ( 26 usr; 2 con; 0-4 aty)
% Number of variables : 570 ( 521 !; 49 ?)
% 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_analmetr,axiom,
? [A] :
( l1_analmetr(A)
& v1_analmetr(A) ) ).
fof(rc2_analmetr,axiom,
? [A] :
( l1_analmetr(A)
& ~ v3_struct_0(A) ) ).
fof(fc1_analmetr,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_analmetr(A,B,C))
& v1_analmetr(k2_analmetr(A,B,C)) ) ) ).
fof(fc2_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ( ~ v3_struct_0(k3_analmetr(A))
& v1_analoaf(k3_analmetr(A)) ) ) ).
fof(rc3_analmetr,axiom,
? [A] :
( l1_analmetr(A)
& ~ v3_struct_0(A)
& v1_analmetr(A)
& v2_analmetr(A) ) ).
fof(rc4_analmetr,axiom,
? [A] :
( l1_analmetr(A)
& ~ v3_struct_0(A)
& v1_analmetr(A)
& v3_analmetr(A) ) ).
fof(fc3_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ( ~ v3_struct_0(k3_analmetr(A))
& ~ v3_realset2(k3_analmetr(A))
& v1_analoaf(k3_analmetr(A))
& v1_diraf(k3_analmetr(A)) ) ) ).
fof(fc4_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(A) )
=> ( ~ v3_struct_0(k3_analmetr(A))
& ~ v3_realset2(k3_analmetr(A))
& v1_analoaf(k3_analmetr(A))
& v1_diraf(k3_analmetr(A))
& v2_diraf(k3_analmetr(A)) ) ) ).
fof(cc1_analmetr,axiom,
! [A] :
( l1_analmetr(A)
=> ( ( ~ v3_struct_0(A)
& v3_analmetr(A) )
=> ( ~ v3_struct_0(A)
& v2_analmetr(A) ) ) ) ).
fof(d1_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
<=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) )
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) ) ) ) ) ).
fof(d2_analmetr,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] :
( 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,u1_struct_0(A))
=> ( r2_analmetr(A,B,C,D,E)
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
& C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I))
& k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = np__0 ) ) ) ) ) ) ) ) ) ) ).
fof(t1_analmetr,axiom,
$true ).
fof(t2_analmetr,axiom,
$true ).
fof(t3_analmetr,axiom,
$true ).
fof(t4_analmetr,axiom,
$true ).
fof(t5_analmetr,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] :
( 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,u1_struct_0(A))
=> ( r1_analmetr(A,D,E)
=> ( r2_analmetr(A,B,C,D,E)
<=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( ( B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
& C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I)) )
=> k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analmetr(A,B,C,B,C) ) ) ) ).
fof(t7_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_analmetr(A,B,C) ) ) ) ).
fof(t8_analmetr,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] :
( 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,u1_struct_0(A))
=> ( r2_analmetr(A,B,C,D,E)
=> r2_analmetr(A,C,B,D,E) ) ) ) ) ) ) ).
fof(t9_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_analmetr(A,D,k1_rlvect_1(A),B,C)
& r2_analmetr(A,k1_rlvect_1(A),E,B,C) ) ) ) ) ) ) ) ).
fof(t10_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( r2_analmetr(A,B,C,D,E)
=> r2_analmetr(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ).
fof(t11_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( r2_analmetr(A,B,C,D,E)
=> ( r2_analmetr(A,k3_rlvect_1(A,B,F),C,D,E)
& r2_analmetr(A,B,k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ) ).
fof(t12_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r2_analmetr(A,D,E,B,C)
& E != k1_rlvect_1(A) ) ) ) ) ) ) ).
fof(t13_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_analmetr(A,B,C)
& r2_analmetr(A,D,E,B,C)
& r2_analmetr(A,D,F,B,C)
& D != k1_rlvect_1(A)
& ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( k3_rlvect_1(A,E,G) = k3_rlvect_1(A,F,H)
& ~ ( G = np__0
& H = np__0 ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& r2_analmetr(A,D,E,B,C)
& r2_analmetr(A,D,F,B,C) )
=> ( r2_analmetr(A,D,k4_rlvect_1(A,E,F),B,C)
& r2_analmetr(A,D,k6_rlvect_1(A,E,F),B,C) ) ) ) ) ) ) ) ) ).
fof(t15_analmetr,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] :
( 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))
=> ( ( r1_analmetr(A,B,C)
& r2_analmetr(A,D,D,B,C) )
=> D = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t16_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& r2_analmetr(A,D,k6_rlvect_1(A,E,F),B,C)
& r2_analmetr(A,E,k6_rlvect_1(A,F,D),B,C) )
=> r2_analmetr(A,F,k6_rlvect_1(A,D,E),B,C) ) ) ) ) ) ) ) ).
fof(t17_analmetr,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] :
( 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,u1_struct_0(A))
=> ~ ( r1_analmetr(A,B,C)
& D != k1_rlvect_1(A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ r2_analmetr(A,k6_rlvect_1(A,E,k3_rlvect_1(A,D,F)),D,B,C) ) ) ) ) ) ) ) ).
fof(t18_analmetr,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] :
( 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,u1_struct_0(A))
=> ( ~ ( ( r1_analoaf(A,B,C,D,E)
| r1_analoaf(A,B,C,E,D) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
& ~ ( F = np__0
& G = np__0 ) ) ) ) )
& ~ ( ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
& ~ ( F = np__0
& G = np__0 ) ) )
& ~ r1_analoaf(A,B,C,D,E)
& ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ).
fof(t19_analmetr,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] :
( 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,u1_struct_0(A))
=> ( r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k1_diraf(u1_struct_0(A),k1_analoaf(A)))
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
& ~ ( F = np__0
& G = np__0 ) ) ) ) ) ) ) ) ) ).
fof(d3_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r3_analmetr(A,B,C,D,E,F,G)
<=> r2_analmetr(A,k6_rlvect_1(A,C,B),k6_rlvect_1(A,E,D),F,G) ) ) ) ) ) ) ) ) ).
fof(d4_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( D = k1_analmetr(A,B,C)
<=> ! [E,F] :
( r2_hidden(k4_tarski(E,F),D)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
& F = k1_domain_1(u1_struct_0(A),u1_struct_0(A),I,J)
& r3_analmetr(A,G,H,I,J,B,C) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_analmetr,axiom,
$true ).
fof(t21_analmetr,axiom,
$true ).
fof(t22_analmetr,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) )
=> u1_struct_0(k2_diraf(k2_analoaf(A))) = u1_struct_0(A) ) ).
fof(t23_analmetr,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) )
=> u1_analoaf(k2_diraf(k2_analoaf(A))) = k1_diraf(u1_struct_0(A),k1_analoaf(A)) ) ).
fof(t24_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ( ( F = B
& G = C
& H = D
& I = E )
=> ( r2_analoaf(k2_diraf(k2_analoaf(A)),F,G,H,I)
<=> ? [J] :
( m1_subset_1(J,k1_numbers)
& ? [K] :
( m1_subset_1(K,k1_numbers)
& k3_rlvect_1(A,k6_rlvect_1(A,C,B),J) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),K)
& ~ ( J = np__0
& K = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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,u1_struct_0(A))
=> ( r4_analmetr(A,B,C,D,E)
<=> r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analoaf(A)) ) ) ) ) ) ) ).
fof(d6_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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,u1_struct_0(A))
=> ( r5_analmetr(A,B,C,D,E)
<=> r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analmetr(A)) ) ) ) ) ) ) ).
fof(d7_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_analmetr(A,B,C) = g1_analmetr(u1_struct_0(A),k1_diraf(u1_struct_0(A),k1_analoaf(A)),k1_analmetr(A,B,C)) ) ) ) ).
fof(t25_analmetr,axiom,
$true ).
fof(t26_analmetr,axiom,
$true ).
fof(t27_analmetr,axiom,
$true ).
fof(t28_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( u1_struct_0(k2_analmetr(A,B,C)) = u1_struct_0(A)
& u1_analoaf(k2_analmetr(A,B,C)) = k1_diraf(u1_struct_0(A),k1_analoaf(A))
& u1_analmetr(k2_analmetr(A,B,C)) = k1_analmetr(A,B,C) ) ) ) ) ).
fof(d8_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> k3_analmetr(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ).
fof(t29_analmetr,axiom,
$true ).
fof(t30_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_analmetr(k2_analmetr(A,B,C)) = k2_diraf(k2_analoaf(A)) ) ) ) ).
fof(t31_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k2_analmetr(A,F,G)))
=> ( ( H = B
& I = C
& J = D
& K = E )
=> ( r5_analmetr(k2_analmetr(A,F,G),H,J,I,K)
<=> r3_analmetr(A,B,D,C,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_analmetr,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] :
( 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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
=> ( ( H = D
& I = E
& J = F
& K = G )
=> ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
<=> ? [L] :
( m1_subset_1(L,k1_numbers)
& ? [M] :
( m1_subset_1(M,k1_numbers)
& k3_rlvect_1(A,k6_rlvect_1(A,E,D),L) = k3_rlvect_1(A,k6_rlvect_1(A,G,F),M)
& ~ ( L = np__0
& M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
=> r5_analmetr(k2_analmetr(A,B,C),F,G,D,E) ) ) ) ) ) ) ) ) ).
fof(t34_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
=> r5_analmetr(k2_analmetr(A,B,C),D,E,G,F) ) ) ) ) ) ) ) ) ).
fof(t35_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> r5_analmetr(k2_analmetr(A,B,C),D,E,F,F) ) ) ) ) ) ) ) ).
fof(t36_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
=> ~ ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
& r4_analmetr(k2_analmetr(A,B,C),D,E,H,I)
& D != E
& ~ r5_analmetr(k2_analmetr(A,B,C),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
& r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
& F != G ) ) ) ) ) ) ) ) ).
fof(t38_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
=> ~ ( r1_analmetr(A,B,C)
& r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
& r5_analmetr(k2_analmetr(A,B,C),D,E,H,I)
& D != E
& ~ r4_analmetr(k2_analmetr(A,B,C),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
=> ( ( r1_analmetr(A,B,C)
& r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
& r5_analmetr(k2_analmetr(A,B,C),D,E,F,H) )
=> r5_analmetr(k2_analmetr(A,B,C),D,E,G,H) ) ) ) ) ) ) ) ) ) ).
fof(t40_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ( ( r1_analmetr(A,B,C)
& r5_analmetr(k2_analmetr(A,B,C),D,E,D,E) )
=> D = E ) ) ) ) ) ) ).
fof(t41_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
=> ( ( r1_analmetr(A,B,C)
& r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
& r5_analmetr(k2_analmetr(A,B,C),F,E,G,D) )
=> r5_analmetr(k2_analmetr(A,B,C),G,E,D,F) ) ) ) ) ) ) ) ) ).
fof(t42_analmetr,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] :
( 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(k2_analmetr(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
=> ( r1_analmetr(A,B,C)
=> ( D = E
| ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
& r4_analmetr(k2_analmetr(A,B,C),D,E,D,G)
& r5_analmetr(k2_analmetr(A,B,C),D,E,G,F) ) ) ) ) ) ) ) ) ) ).
fof(d9_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ( v2_analmetr(A)
<=> ( ~ v3_struct_0(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& ~ v3_realset2(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& v1_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& l1_analoaf(g1_analoaf(u1_struct_0(A),u1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( r5_analmetr(A,B,C,B,C)
=> B = C )
& r5_analmetr(A,B,C,D,D)
& ( r5_analmetr(A,B,C,D,E)
=> ( r5_analmetr(A,B,C,E,D)
& r5_analmetr(A,D,E,B,C) ) )
& ~ ( r5_analmetr(A,B,C,F,G)
& r4_analmetr(A,B,C,H,I)
& ~ r5_analmetr(A,F,G,H,I)
& B != C )
& ( ( r5_analmetr(A,B,C,F,G)
& r5_analmetr(A,B,C,F,I) )
=> r5_analmetr(A,B,C,G,I) ) ) ) ) ) ) ) ) ) )
& ! [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))
=> ~ ( B != C
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r4_analmetr(A,B,C,B,E)
& r5_analmetr(A,B,C,E,D) ) ) ) ) ) )
& ! [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,u1_struct_0(A))
& r5_analmetr(A,B,C,D,E)
& D != E ) ) ) ) ) ) ) ).
fof(t43_analmetr,axiom,
$true ).
fof(t44_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k2_analmetr(A,B,C))
& v2_analmetr(k2_analmetr(A,B,C))
& l1_analmetr(k2_analmetr(A,B,C)) ) ) ) ) ) ).
fof(d10_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ( v3_analmetr(A)
<=> ( ~ v3_struct_0(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& ~ v3_realset2(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& v1_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& v2_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
& l1_analoaf(g1_analoaf(u1_struct_0(A),u1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( r5_analmetr(A,B,C,B,C)
=> B = C )
& r5_analmetr(A,B,C,D,D)
& ( r5_analmetr(A,B,C,D,E)
=> ( r5_analmetr(A,B,C,E,D)
& r5_analmetr(A,D,E,B,C) ) )
& ~ ( r5_analmetr(A,B,C,F,G)
& r4_analmetr(A,B,C,H,I)
& ~ r5_analmetr(A,F,G,H,I)
& B != C )
& ~ ( r5_analmetr(A,B,C,F,G)
& r5_analmetr(A,B,C,H,I)
& ~ r4_analmetr(A,F,G,H,I)
& B != C ) ) ) ) ) ) ) ) ) )
& ! [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,u1_struct_0(A))
& r5_analmetr(A,B,C,D,E)
& D != E ) ) ) ) ) ) ) ).
fof(t45_analmetr,axiom,
$true ).
fof(t46_analmetr,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k2_analmetr(A,B,C))
& v3_analmetr(k2_analmetr(A,B,C))
& l1_analmetr(k2_analmetr(A,B,C)) ) ) ) ) ) ).
fof(t47_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
<=> m1_subset_1(B,u1_struct_0(k3_analmetr(A))) ) ) ).
fof(t48_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_analmetr(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k3_analmetr(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k3_analmetr(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k3_analmetr(A)))
=> ( ( B = F
& C = G
& D = H
& E = I )
=> ( r4_analmetr(A,B,C,D,E)
<=> r2_analoaf(k3_analmetr(A),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(A) )
=> ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) ) ) ).
fof(t50_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ( ( ~ v3_struct_0(k3_analmetr(A))
& ~ v3_realset2(k3_analmetr(A))
& v1_diraf(k3_analmetr(A))
& v2_diraf(k3_analmetr(A))
& l1_analoaf(k3_analmetr(A)) )
=> ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(A) ) ) ) ).
fof(t51_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ( v3_analmetr(A)
<=> ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = C ) )
& ! [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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( r4_analmetr(A,B,C,C,B)
& r4_analmetr(A,B,C,D,D)
& ~ ( r4_analmetr(A,B,C,F,G)
& r4_analmetr(A,B,C,H,I)
& ~ r4_analmetr(A,F,G,H,I)
& B != C )
& ( r4_analmetr(A,B,C,B,D)
=> r4_analmetr(A,C,B,C,D) )
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& r4_analmetr(A,B,C,D,J)
& r4_analmetr(A,B,D,C,J) )
& ~ ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> r4_analmetr(A,J,K,J,L) ) ) )
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& r4_analmetr(A,B,C,D,J)
& D != J )
& ~ ( r4_analmetr(A,B,C,C,E)
& C != B
& ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ~ ( r4_analmetr(A,D,C,C,J)
& r4_analmetr(A,D,B,E,J) ) ) )
& ( r5_analmetr(A,B,C,B,C)
=> B = C )
& r5_analmetr(A,B,C,D,D)
& ( r5_analmetr(A,B,C,D,E)
=> ( r5_analmetr(A,B,C,E,D)
& r5_analmetr(A,D,E,B,C) ) )
& ~ ( r5_analmetr(A,B,C,F,G)
& r4_analmetr(A,B,C,H,I)
& ~ r5_analmetr(A,F,G,H,I)
& B != C )
& ~ ( r5_analmetr(A,B,C,F,G)
& r5_analmetr(A,B,C,H,I)
& ~ r4_analmetr(A,F,G,H,I)
& B != C )
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& r5_analmetr(A,B,C,D,J)
& D != J )
& ~ ( ~ r4_analmetr(A,B,C,D,E)
& ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ~ ( r4_analmetr(A,B,C,B,J)
& r4_analmetr(A,D,E,D,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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))
=> ( r6_analmetr(A,B,C,D)
<=> r4_analmetr(A,B,C,B,D) ) ) ) ) ) ).
fof(d12_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
=> ( D = k4_analmetr(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,D)
<=> r6_analmetr(A,B,C,E) ) ) ) ) ) ) ) ).
fof(d13_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_analmetr(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C != D
& B = k4_analmetr(A,C,D) ) ) ) ) ) ).
fof(t52_analmetr,axiom,
$true ).
fof(t53_analmetr,axiom,
$true ).
fof(t54_analmetr,axiom,
$true ).
fof(t55_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,u1_struct_0(k3_analmetr(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_analmetr(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k3_analmetr(A)))
=> ( ( B = E
& C = F
& D = G )
=> ( r6_analmetr(A,B,C,D)
<=> r1_aff_1(k3_analmetr(A),E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t56_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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(k3_analmetr(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_analmetr(A)))
=> ( ( B = D
& C = E )
=> k4_analmetr(A,B,C) = k2_aff_1(k3_analmetr(A),D,E) ) ) ) ) ) ) ).
fof(t57_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
<=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) ) ) ).
fof(t58_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
=> ( B = C
=> ( v4_analmetr(B,A)
<=> v1_aff_1(C,k3_analmetr(A)) ) ) ) ) ) ).
fof(d14_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
=> ( r7_analmetr(A,B,C,D)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& E != F
& D = k4_analmetr(A,E,F)
& r5_analmetr(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(d15_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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)))
=> ( r8_analmetr(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& D != E
& B = k4_analmetr(A,D,E)
& r7_analmetr(A,D,E,C) ) ) ) ) ) ) ).
fof(d16_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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)))
=> ( r9_analmetr(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& D != E
& F != G
& B = k4_analmetr(A,D,E)
& C = k4_analmetr(A,F,G)
& r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t59_analmetr,axiom,
$true ).
fof(t60_analmetr,axiom,
$true ).
fof(t61_analmetr,axiom,
$true ).
fof(t62_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r7_analmetr(A,B,C,D)
=> v4_analmetr(D,A) )
& ( r8_analmetr(A,D,E)
=> ( v4_analmetr(D,A)
& v4_analmetr(E,A) ) ) ) ) ) ) ) ) ).
fof(t63_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(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)))
=> ( r8_analmetr(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& D != E
& F != G
& B = k4_analmetr(A,D,E)
& C = k4_analmetr(A,F,G)
& r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t64_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
=> ( ( B = D
& C = E )
=> ( r9_analmetr(A,B,C)
<=> r4_aff_1(k3_analmetr(A),D,E) ) ) ) ) ) ) ) ).
fof(t65_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v4_analmetr(B,A)
=> r7_analmetr(A,C,C,B) ) ) ) ) ).
fof(t66_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r7_analmetr(A,C,D,B)
=> ( ( ~ r4_analmetr(A,C,D,E,F)
& ~ r4_analmetr(A,E,F,C,D) )
| C = D
| r7_analmetr(A,E,F,B) ) ) ) ) ) ) ) ) ).
fof(t67_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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))
=> ( r7_analmetr(A,C,D,B)
=> r7_analmetr(A,D,C,B) ) ) ) ) ) ).
fof(t68_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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)))
=> ( r9_analmetr(A,B,C)
=> r9_analmetr(A,C,B) ) ) ) ) ).
fof(t69_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r7_analmetr(A,D,E,B)
=> ( ( ~ r9_analmetr(A,B,C)
& ~ r9_analmetr(A,C,B) )
| r7_analmetr(A,D,E,C) ) ) ) ) ) ) ) ).
fof(t70_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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)))
=> ( r8_analmetr(A,B,C)
=> r8_analmetr(A,C,B) ) ) ) ) ).
fof(t71_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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)
& r7_analmetr(A,C,D,B) )
=> C = D ) ) ) ) ) ).
fof(t72_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ r11_analmetr(A,B,B) ) ) ).
fof(t73_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( ( r11_analmetr(A,B,C)
| r11_analmetr(A,C,B) )
& ( r10_analmetr(A,B,D)
| r10_analmetr(A,D,B) )
& ~ ( r11_analmetr(A,C,D)
& r11_analmetr(A,D,C) ) ) ) ) ) ) ).
fof(t74_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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)))
=> ~ ( r10_analmetr(A,B,C)
& r11_analmetr(A,B,C) ) ) ) ) ).
fof(t75_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B)
& r7_analmetr(A,E,F,B) )
=> ( r5_analmetr(A,E,F,C,D)
& r5_analmetr(A,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t76_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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)
& v4_analmetr(B,A) )
=> ( C = D
| B = k4_analmetr(A,C,D) ) ) ) ) ) ) ).
fof(t77_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B)
& v4_analmetr(B,A) )
=> ( C = D
| ( ~ r5_analmetr(A,C,D,E,F)
& ~ r5_analmetr(A,E,F,C,D) )
| r7_analmetr(A,E,F,B) ) ) ) ) ) ) ) ) ).
fof(t78_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,C)
& r2_hidden(G,C)
& r11_analmetr(A,B,C) )
=> r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t79_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r2_hidden(F,B)
& r2_hidden(F,C)
& r2_hidden(G,B)
& r2_hidden(H,C)
& r2_hidden(G,D)
& r2_hidden(H,D)
& r11_analmetr(A,E,B)
& r11_analmetr(A,E,C)
& v4_analmetr(D,A) )
=> ( G = H
| r11_analmetr(A,E,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t80_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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))
=> ( r5_analmetr(A,B,C,D,D)
& r5_analmetr(A,D,D,B,C)
& r4_analmetr(A,B,C,D,D)
& r4_analmetr(A,D,D,B,C) ) ) ) ) ) ).
fof(t81_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ( r4_analmetr(A,B,C,D,E)
=> ( r4_analmetr(A,B,C,E,D)
& r4_analmetr(A,C,B,D,E)
& r4_analmetr(A,C,B,E,D)
& r4_analmetr(A,D,E,B,C)
& r4_analmetr(A,D,E,C,B)
& r4_analmetr(A,E,D,B,C)
& r4_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t82_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( B != C
& ~ ( ~ ( r4_analmetr(A,B,C,D,E)
& r4_analmetr(A,B,C,F,G) )
& ~ ( r4_analmetr(A,B,C,D,E)
& r4_analmetr(A,F,G,B,C) )
& ~ ( r4_analmetr(A,D,E,B,C)
& r4_analmetr(A,F,G,B,C) )
& ~ ( r4_analmetr(A,D,E,B,C)
& r4_analmetr(A,B,C,F,G) ) )
& ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t83_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ( r5_analmetr(A,B,C,D,E)
=> ( r5_analmetr(A,B,C,E,D)
& r5_analmetr(A,C,B,D,E)
& r5_analmetr(A,C,B,E,D)
& r5_analmetr(A,D,E,B,C)
& r5_analmetr(A,D,E,C,B)
& r5_analmetr(A,E,D,B,C)
& r5_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t84_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( B != C
& ~ ( ~ ( r4_analmetr(A,B,C,D,E)
& r5_analmetr(A,B,C,F,G) )
& ~ ( r4_analmetr(A,B,C,F,G)
& r5_analmetr(A,B,C,D,E) )
& ~ ( r4_analmetr(A,B,C,D,E)
& r5_analmetr(A,F,G,B,C) )
& ~ ( r4_analmetr(A,B,C,F,G)
& r5_analmetr(A,D,E,B,C) )
& ~ ( r4_analmetr(A,D,E,B,C)
& r5_analmetr(A,F,G,B,C) )
& ~ ( r4_analmetr(A,F,G,B,C)
& r5_analmetr(A,D,E,B,C) )
& ~ ( r4_analmetr(A,D,E,B,C)
& r5_analmetr(A,B,C,F,G) )
& ~ ( r4_analmetr(A,F,G,B,C)
& r5_analmetr(A,B,C,D,E) ) )
& ~ r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t85_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( B != C
& ~ ( ~ ( r5_analmetr(A,B,C,D,E)
& r5_analmetr(A,B,C,F,G) )
& ~ ( r5_analmetr(A,B,C,D,E)
& r5_analmetr(A,F,G,B,C) )
& ~ ( r5_analmetr(A,D,E,B,C)
& r5_analmetr(A,F,G,B,C) )
& ~ ( r5_analmetr(A,D,E,B,C)
& r5_analmetr(A,B,C,F,G) ) )
& ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t86_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,B)
& v4_analmetr(B,A)
& r2_hidden(F,C)
& r2_hidden(G,C)
& v4_analmetr(C,A)
& r4_analmetr(A,D,E,F,G) )
=> ( D = E
| F = G
| r10_analmetr(A,B,C) ) ) ) ) ) ) ) ) ) ).
fof(t87_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( ( r11_analmetr(A,B,C)
| r11_analmetr(A,C,B) )
& ( r11_analmetr(A,B,D)
| r11_analmetr(A,D,B) )
& ~ ( r10_analmetr(A,C,D)
& r10_analmetr(A,D,C) ) ) ) ) ) ) ).
fof(t88_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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)))
=> ~ ( r11_analmetr(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(D,C) ) ) ) ) ) ) ).
fof(t89_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
=> ~ ( r5_analmetr(A,B,C,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r6_analmetr(A,B,C,F)
& r6_analmetr(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t90_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( 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))
=> ~ ( r7_analmetr(A,C,D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r6_analmetr(A,C,D,E)
& r2_hidden(E,B) ) ) ) ) ) ) ) ).
fof(t91_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(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,u1_struct_0(A))
& r5_analmetr(A,B,E,C,D)
& r6_analmetr(A,C,D,E) ) ) ) ) ) ).
fof(t92_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_analmetr(A)
& l1_analmetr(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( v4_analmetr(B,A)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r7_analmetr(A,C,D,B)
& r2_hidden(D,B) ) ) ) ) ) ) ).
fof(dt_l1_analmetr,axiom,
! [A] :
( l1_analmetr(A)
=> l1_analoaf(A) ) ).
fof(existence_l1_analmetr,axiom,
? [A] : l1_analmetr(A) ).
fof(abstractness_v1_analmetr,axiom,
! [A] :
( l1_analmetr(A)
=> ( v1_analmetr(A)
=> A = g1_analmetr(u1_struct_0(A),u1_analoaf(A),u1_analmetr(A)) ) ) ).
fof(symmetry_r10_analmetr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r10_analmetr(A,B,C)
=> r10_analmetr(A,C,B) ) ) ).
fof(redefinition_r10_analmetr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r10_analmetr(A,B,C)
<=> r9_analmetr(A,B,C) ) ) ).
fof(symmetry_r11_analmetr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r11_analmetr(A,B,C)
=> r11_analmetr(A,C,B) ) ) ).
fof(redefinition_r11_analmetr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_analmetr(A)
& l1_analmetr(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r11_analmetr(A,B,C)
<=> r8_analmetr(A,B,C) ) ) ).
fof(dt_k1_analmetr,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_relset_1(k1_analmetr(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k2_analmetr,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_analmetr(k2_analmetr(A,B,C))
& l1_analmetr(k2_analmetr(A,B,C)) ) ) ).
fof(dt_k3_analmetr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A) )
=> ( v1_analoaf(k3_analmetr(A))
& l1_analoaf(k3_analmetr(A)) ) ) ).
fof(dt_k4_analmetr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_analmetr(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_analmetr(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_u1_analmetr,axiom,
! [A] :
( l1_analmetr(A)
=> m2_relset_1(u1_analmetr(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_g1_analmetr,axiom,
! [A,B,C] :
( ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
& m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
=> ( v1_analmetr(g1_analmetr(A,B,C))
& l1_analmetr(g1_analmetr(A,B,C)) ) ) ).
fof(free_g1_analmetr,axiom,
! [A,B,C] :
( ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
& m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
=> ! [D,E,F] :
( g1_analmetr(A,B,C) = g1_analmetr(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
%------------------------------------------------------------------------------