%------------------------------------------------------------------------------
% File : SET007+230 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Classical Configurations in Affine 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 : aff_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 548 ( 47 equ)
% Maximal formula atoms : 38 ( 12 avg)
% Number of connectives : 563 ( 58 ~; 53 |; 258 &)
% ( 19 <=>; 175 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 13 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-5 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 151 ( 151 !; 0 ?)
% 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_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v1_aff_2(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( v1_aff_1(B,A)
& v1_aff_1(C,A)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r2_hidden(G,C)
& r2_hidden(H,C)
& r2_hidden(I,C)
& r2_analoaf(A,D,H,E,G)
& r2_analoaf(A,E,I,F,H) )
=> r2_analoaf(A,D,I,F,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ( v2_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& v1_aff_1(C,A)
& r2_hidden(D,B)
& r2_hidden(D,C)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r2_hidden(G,B)
& r2_hidden(H,C)
& r2_hidden(I,C)
& r2_hidden(J,C)
& r2_analoaf(A,E,I,F,H)
& r2_analoaf(A,F,J,G,I) )
=> ( B = C
| D = E
| D = H
| D = F
| D = I
| D = G
| D = J
| r2_analoaf(A,E,J,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v3_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& v1_aff_1(C,A)
& r2_hidden(D,B)
& r2_hidden(D,C)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r2_hidden(G,B)
& r2_hidden(I,C)
& r2_hidden(J,C)
& r2_analoaf(A,E,I,F,H)
& r2_analoaf(A,F,J,G,I)
& r2_analoaf(A,E,J,G,H) )
=> ( B = C
| D = E
| D = H
| D = F
| D = I
| D = G
| D = J
| F = G
| r2_hidden(H,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ( v4_aff_2(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,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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_hidden(E,C)
& r2_hidden(E,D)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r2_hidden(G,C)
& r2_hidden(J,C)
& r2_hidden(H,D)
& r2_hidden(K,D)
& v1_aff_1(B,A)
& v1_aff_1(C,A)
& v1_aff_1(D,A)
& r2_analoaf(A,F,G,I,J)
& r2_analoaf(A,F,H,I,K) )
=> ( E = F
| E = G
| E = H
| B = C
| B = D
| r2_analoaf(A,G,H,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v5_aff_2(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,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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_hidden(E,C)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r2_hidden(G,C)
& r2_hidden(J,C)
& r2_hidden(H,D)
& r2_hidden(K,D)
& v1_aff_1(B,A)
& v1_aff_1(C,A)
& v1_aff_1(D,A)
& r2_analoaf(A,F,G,I,J)
& r2_analoaf(A,F,H,I,K)
& r2_analoaf(A,G,H,J,K) )
=> ( E = F
| E = G
| E = H
| B = C
| B = D
| r1_aff_1(A,F,G,H)
| H = K
| r2_hidden(E,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v6_aff_2(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,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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_hidden(E,C)
& r2_hidden(E,D)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r2_hidden(G,C)
& r2_hidden(J,C)
& r2_hidden(H,D)
& v1_aff_1(B,A)
& v1_aff_1(C,A)
& v1_aff_1(D,A)
& r2_analoaf(A,F,G,I,J)
& r2_analoaf(A,F,H,I,K)
& r2_analoaf(A,G,H,J,K) )
=> ( E = F
| E = G
| E = H
| B = C
| B = D
| r2_hidden(K,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ( v7_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& r2_hidden(C,B)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r1_aff_1(A,C,D,G)
& r1_aff_1(A,C,E,H)
& r2_analoaf(A,D,E,G,H)
& r2_analoaf(A,D,F,G,I)
& r2_aff_1(A,D,E,B) )
=> ( r2_hidden(D,B)
| C = F
| D = E
| r2_analoaf(A,E,F,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v8_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& r2_hidden(C,B)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r1_aff_1(A,C,D,G)
& r2_analoaf(A,D,E,G,H)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,D,F,G,I)
& r2_aff_1(A,D,E,B) )
=> ( r2_hidden(D,B)
| C = F
| D = E
| r1_aff_1(A,C,E,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v9_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& r2_hidden(C,B)
& r2_hidden(F,B)
& r2_hidden(I,B)
& r1_aff_1(A,C,D,G)
& r1_aff_1(A,C,E,H)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,D,F,G,I)
& r2_aff_1(A,D,E,B) )
=> ( r2_hidden(D,B)
| C = F
| D = E
| r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d10_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v10_aff_2(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))
=> ! [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))
=> ( ( v1_aff_1(B,A)
& r2_hidden(C,B)
& r2_hidden(F,B)
& r1_aff_1(A,C,D,G)
& r1_aff_1(A,C,E,H)
& r2_analoaf(A,D,E,G,H)
& r2_analoaf(A,D,F,G,I)
& r2_analoaf(A,E,F,H,I)
& r2_aff_1(A,D,E,B) )
=> ( r2_hidden(D,B)
| C = F
| D = E
| r2_hidden(I,B) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ( v11_aff_2(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,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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r4_aff_1(A,B,C)
& r4_aff_1(A,B,D)
& r2_hidden(E,B)
& r2_hidden(H,B)
& r2_hidden(F,C)
& r2_hidden(I,C)
& r2_hidden(G,D)
& r2_hidden(J,D)
& v1_aff_1(B,A)
& v1_aff_1(C,A)
& v1_aff_1(D,A)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,E,G,H,J) )
=> ( B = C
| B = D
| r2_analoaf(A,F,G,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v12_aff_2(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,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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r4_aff_1(A,B,C)
& r2_hidden(E,B)
& r2_hidden(H,B)
& r2_hidden(F,C)
& r2_hidden(I,C)
& r2_hidden(G,D)
& r2_hidden(J,D)
& v1_aff_1(B,A)
& v1_aff_1(C,A)
& v1_aff_1(D,A)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,E,G,H,J)
& r2_analoaf(A,F,G,I,J) )
=> ( B = C
| B = D
| r1_aff_1(A,E,F,G)
| G = J
| r4_aff_1(A,B,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ( v13_aff_2(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( v1_aff_1(B,A)
& v1_aff_1(C,A)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r4_aff_1(A,B,C)
& r2_hidden(G,C)
& r2_hidden(H,C)
& r2_hidden(I,C)
& r2_analoaf(A,D,H,E,G)
& r2_analoaf(A,E,I,F,H) )
=> ( B = C
| r2_analoaf(A,D,I,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v14_aff_2(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( v1_aff_1(B,A)
& v1_aff_1(C,A)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r4_aff_1(A,B,C)
& r2_hidden(G,C)
& r2_hidden(H,C)
& r2_analoaf(A,D,H,E,G)
& r2_analoaf(A,E,I,F,H)
& r2_analoaf(A,D,I,F,G) )
=> ( B = C
| G = H
| r2_hidden(I,C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_aff_2,axiom,
$true ).
fof(t2_aff_2,axiom,
$true ).
fof(t3_aff_2,axiom,
$true ).
fof(t4_aff_2,axiom,
$true ).
fof(t5_aff_2,axiom,
$true ).
fof(t6_aff_2,axiom,
$true ).
fof(t7_aff_2,axiom,
$true ).
fof(t8_aff_2,axiom,
$true ).
fof(t9_aff_2,axiom,
$true ).
fof(t10_aff_2,axiom,
$true ).
fof(t11_aff_2,axiom,
$true ).
fof(t12_aff_2,axiom,
$true ).
fof(t13_aff_2,axiom,
$true ).
fof(t14_aff_2,axiom,
$true ).
fof(t15_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v2_aff_2(A)
<=> v3_aff_2(A) ) ) ).
fof(t16_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v4_aff_2(A)
<=> v5_aff_2(A) ) ) ).
fof(t17_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v7_aff_2(A)
=> v8_aff_2(A) ) ) ).
fof(t18_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v8_aff_2(A)
=> v9_aff_2(A) ) ) ).
fof(t19_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v9_aff_2(A)
=> v10_aff_2(A) ) ) ).
fof(t20_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v10_aff_2(A)
=> v7_aff_2(A) ) ) ).
fof(t21_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v11_aff_2(A)
<=> v12_aff_2(A) ) ) ).
fof(t22_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v13_aff_2(A)
<=> v14_aff_2(A) ) ) ).
fof(t23_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v2_aff_2(A)
=> v13_aff_2(A) ) ) ).
fof(t24_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v1_aff_2(A)
<=> ( v2_aff_2(A)
& v13_aff_2(A) ) ) ) ).
fof(t25_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v2_aff_2(A)
=> v4_aff_2(A) ) ) ).
fof(t26_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v4_aff_2(A)
=> v7_aff_2(A) ) ) ).
fof(t27_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v8_aff_2(A)
=> v12_aff_2(A) ) ) ).
fof(t28_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v7_aff_2(A)
=> v11_aff_2(A) ) ) ).
fof(t29_aff_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ( v11_aff_2(A)
=> v13_aff_2(A) ) ) ).
%------------------------------------------------------------------------------