SET007 Axioms: SET007+288.ax
%------------------------------------------------------------------------------
% File : SET007+288 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Semi-Affine Space
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : semi_af1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 146 ( 28 unt; 0 def)
% Number of atoms : 1389 ( 90 equ)
% Maximal formula atoms : 92 ( 9 avg)
% Number of connectives : 1508 ( 265 ~; 23 |; 495 &)
% ( 10 <=>; 715 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-6 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-4 aty)
% Number of variables : 658 ( 649 !; 9 ?)
% 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_semi_af1,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_semi_af1(A) ) ).
fof(d1_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_semi_af1(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analoaf(A,B,C,C,B) ) )
& ! [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))
=> r2_analoaf(A,B,C,D,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))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) )
& ! [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))
=> ( r2_analoaf(A,B,C,B,D)
=> r2_analoaf(A,C,B,C,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))
=> r2_analoaf(A,B,C,B,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))
& r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,D,C,E) ) ) ) )
& ! [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))
=> ( r2_analoaf(A,B,C,B,D)
& ~ ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r2_analoaf(A,B,D,B,E)
& ~ ( r2_analoaf(A,B,F,B,G)
& r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) ) )
& ! [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))
=> ( ( r2_analoaf(A,B,C,B,D)
& r2_analoaf(A,B,E,B,F)
& r2_analoaf(A,B,G,B,H)
& r2_analoaf(A,C,E,D,F)
& r2_analoaf(A,C,G,D,H) )
=> ( r2_analoaf(A,B,C,B,E)
| r2_analoaf(A,B,C,B,G)
| r2_analoaf(A,E,G,F,H) ) ) ) ) ) ) ) ) )
& ! [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))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,F,C,G) )
=> ( r2_analoaf(A,B,C,B,D)
| r2_analoaf(A,B,C,B,F)
| r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) )
& ! [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))
=> ( ( r2_analoaf(A,B,C,B,D)
& r2_analoaf(A,E,F,E,G)
& r2_analoaf(A,B,F,C,E)
& r2_analoaf(A,C,G,D,F) )
=> r2_analoaf(A,D,E,B,G) ) ) ) ) ) ) )
& ! [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_analoaf(A,B,C,B,D)
& r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,E,C,D) ) ) ) ) ) ) ) ) ).
fof(t1_semi_af1,axiom,
$true ).
fof(t2_semi_af1,axiom,
$true ).
fof(t3_semi_af1,axiom,
$true ).
fof(t4_semi_af1,axiom,
$true ).
fof(t5_semi_af1,axiom,
$true ).
fof(t6_semi_af1,axiom,
$true ).
fof(t7_semi_af1,axiom,
$true ).
fof(t8_semi_af1,axiom,
$true ).
fof(t9_semi_af1,axiom,
$true ).
fof(t10_semi_af1,axiom,
$true ).
fof(t11_semi_af1,axiom,
$true ).
fof(t12_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analoaf(A,B,C,B,C) ) ) ) ).
fof(t13_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t14_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> r2_analoaf(A,B,B,C,D) ) ) ) ) ).
fof(t15_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,C,B,D,E) ) ) ) ) ) ) ).
fof(t16_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t17_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,D,E)
=> ( r2_analoaf(A,C,B,D,E)
& r2_analoaf(A,B,C,E,D)
& r2_analoaf(A,C,B,E,D)
& r2_analoaf(A,D,E,B,C)
& r2_analoaf(A,E,D,B,C)
& r2_analoaf(A,D,E,C,B)
& r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t18_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,B,D)
=> ( r2_analoaf(A,B,D,B,C)
& r2_analoaf(A,C,B,B,D)
& r2_analoaf(A,B,C,D,B)
& r2_analoaf(A,B,D,C,B)
& r2_analoaf(A,C,B,D,B)
& r2_analoaf(A,D,B,B,C)
& r2_analoaf(A,D,B,C,B)
& r2_analoaf(A,C,B,C,D)
& r2_analoaf(A,B,C,C,D)
& r2_analoaf(A,C,B,D,C)
& r2_analoaf(A,C,D,C,B)
& r2_analoaf(A,B,C,D,C)
& r2_analoaf(A,D,C,C,B)
& r2_analoaf(A,C,D,B,C)
& r2_analoaf(A,D,C,B,C)
& r2_analoaf(A,D,B,D,C)
& r2_analoaf(A,B,D,D,C)
& r2_analoaf(A,D,B,C,D)
& r2_analoaf(A,B,D,C,D)
& r2_analoaf(A,D,C,D,B)
& r2_analoaf(A,C,D,D,B)
& r2_analoaf(A,D,C,B,D)
& r2_analoaf(A,C,D,B,D) ) ) ) ) ) ) ).
fof(t19_semi_af1,axiom,
$true ).
fof(t20_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_analoaf(A,D,E,B,C)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t21_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ r2_analoaf(A,B,C,B,D)
=> ( B != C
& C != D
& D != B ) ) ) ) ) ) ).
fof(t22_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ r2_analoaf(A,B,C,D,E)
=> ( B != C
& D != E ) ) ) ) ) ) ) ).
fof(t23_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_analoaf(A,B,C,B,D)
& r2_analoaf(A,C,E,C,D)
& r2_analoaf(A,E,B,E,D) )
=> r2_analoaf(A,B,C,B,E) ) ) ) ) ) ) ).
fof(t24_semi_af1,axiom,
$true ).
fof(t25_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r2_analoaf(A,B,C,B,D)
& E != F
& r2_analoaf(A,E,F,E,B)
& r2_analoaf(A,E,F,E,C)
& r2_analoaf(A,E,F,E,D) ) ) ) ) ) ) ) ).
fof(t26_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ).
fof(t27_semi_af1,axiom,
$true ).
fof(t28_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ r2_analoaf(A,B,C,B,D)
=> ( ~ r2_analoaf(A,B,C,D,B)
& ~ r2_analoaf(A,C,B,B,D)
& ~ r2_analoaf(A,C,B,D,B)
& ~ r2_analoaf(A,B,D,B,C)
& ~ r2_analoaf(A,B,D,C,B)
& ~ r2_analoaf(A,D,B,B,C)
& ~ r2_analoaf(A,D,B,C,B)
& ~ r2_analoaf(A,C,B,C,D)
& ~ r2_analoaf(A,C,B,D,C)
& ~ r2_analoaf(A,B,C,C,D)
& ~ r2_analoaf(A,B,C,D,C)
& ~ r2_analoaf(A,C,D,C,B)
& ~ r2_analoaf(A,C,D,B,C)
& ~ r2_analoaf(A,D,C,B,C)
& ~ r2_analoaf(A,D,C,C,B)
& ~ r2_analoaf(A,D,C,D,B)
& ~ r2_analoaf(A,D,C,B,D)
& ~ r2_analoaf(A,C,D,D,B)
& ~ r2_analoaf(A,C,D,B,D)
& ~ r2_analoaf(A,D,B,D,C)
& ~ r2_analoaf(A,D,B,C,D)
& ~ r2_analoaf(A,B,D,C,D)
& ~ r2_analoaf(A,B,D,D,C) ) ) ) ) ) ) ).
fof(t29_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,D,E,H,I)
& F != G
& H != I
& r2_analoaf(A,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r2_analoaf(A,B,C,B,D)
& r2_analoaf(A,B,C,E,F)
& r2_analoaf(A,B,D,E,G)
& r2_analoaf(A,C,D,F,G)
& E != F
& r2_analoaf(A,E,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t31_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_analoaf(A,B,D,E,F)
& r2_analoaf(A,C,D,E,F) )
=> ( r2_analoaf(A,B,C,B,D)
| E = F ) ) ) ) ) ) ) ) ).
fof(t32_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_analoaf(A,B,D,B,E)
& r2_analoaf(A,C,D,C,E) )
=> ( r2_analoaf(A,B,C,B,D)
| D = E ) ) ) ) ) ) ) ).
fof(t33_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_analoaf(A,B,C,E,F)
& r2_analoaf(A,B,D,E,G)
& r2_analoaf(A,B,D,E,H)
& r2_analoaf(A,C,D,F,G)
& r2_analoaf(A,C,D,F,H) )
=> ( r2_analoaf(A,B,C,B,D)
| G = H ) ) ) ) ) ) ) ) ) ) ).
fof(t34_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ ( B != C
& D != E
& ~ ( B = D
& C = E )
& ~ ( B = E
& C = D ) )
=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t35_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ ( B != C
& B != D
& C != D )
=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ).
fof(d2_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r1_semi_af1(A,B,C,D)
<=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ).
fof(t36_semi_af1,axiom,
$true ).
fof(t37_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r1_semi_af1(A,B,C,D)
=> ( r1_semi_af1(A,B,D,C)
& r1_semi_af1(A,C,B,D)
& r1_semi_af1(A,C,D,B)
& r1_semi_af1(A,D,B,C)
& r1_semi_af1(A,D,C,B) ) ) ) ) ) ) ).
fof(t38_semi_af1,axiom,
$true ).
fof(t39_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,E,F)
& r2_analoaf(A,B,D,E,G)
& E != F
& E != G
& r1_semi_af1(A,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t40_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ ( B != C
& C != D
& D != B )
=> r1_semi_af1(A,B,C,D) ) ) ) ) ) ).
fof(t41_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_semi_af1(A,B,C,D) ) ) ) ) ) ).
fof(t42_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r1_semi_af1(A,B,C,E) )
=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t43_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,D,E)
& r1_semi_af1(A,B,C,E) ) ) ) ) ) ) ).
fof(t44_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,D,E)
& D != E
& r1_semi_af1(A,D,E,F)
& r1_semi_af1(A,B,C,F) ) ) ) ) ) ) ) ).
fof(t45_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,E)
& r1_semi_af1(A,B,D,E) )
=> ( r1_semi_af1(A,B,C,D)
| B = E ) ) ) ) ) ) ) ).
fof(t46_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r1_semi_af1(A,B,C,E)
& r1_semi_af1(A,B,D,F) )
=> ( B = C
| B = D
| r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t47_semi_af1,axiom,
$true ).
fof(t48_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,F)
& r1_semi_af1(A,B,C,G)
& r1_semi_af1(A,D,E,F)
& r1_semi_af1(A,D,E,G) )
=> ( r2_analoaf(A,B,C,D,E)
| F = G ) ) ) ) ) ) ) ) ) ).
fof(t49_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,D,E) )
=> ( B = C
| r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t50_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,D,E) )
=> ( B = C
| r2_analoaf(A,D,C,D,E) ) ) ) ) ) ) ) ).
fof(t51_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,E)
& r1_semi_af1(A,B,D,F)
& r1_semi_af1(A,B,D,G)
& r2_analoaf(A,C,D,E,F)
& r2_analoaf(A,C,D,E,F)
& r2_analoaf(A,C,D,E,G) )
=> ( r1_semi_af1(A,B,C,D)
| F = G ) ) ) ) ) ) ) ) ) ).
fof(t52_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r1_semi_af1(A,B,C,E) )
=> ( B = C
| r1_semi_af1(A,B,D,E) ) ) ) ) ) ) ) ).
fof(d3_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
<=> ( ~ r1_semi_af1(A,B,C,D)
& r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t53_semi_af1,axiom,
$true ).
fof(t54_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> ( B != C
& B != D
& D != C
& B != E
& C != E
& D != E ) ) ) ) ) ) ) ).
fof(t55_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> ( ~ r1_semi_af1(A,B,C,D)
& ~ r1_semi_af1(A,C,B,E)
& ~ r1_semi_af1(A,D,E,B)
& ~ r1_semi_af1(A,E,D,C) ) ) ) ) ) ) ) ).
fof(t56_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> ( ~ r1_semi_af1(A,B,C,D)
& ~ r1_semi_af1(A,B,D,C)
& ~ r1_semi_af1(A,B,C,E)
& ~ r1_semi_af1(A,B,E,C)
& ~ r1_semi_af1(A,B,D,E)
& ~ r1_semi_af1(A,B,E,D)
& ~ r1_semi_af1(A,C,B,D)
& ~ r1_semi_af1(A,C,D,B)
& ~ r1_semi_af1(A,C,B,E)
& ~ r1_semi_af1(A,C,E,B)
& ~ r1_semi_af1(A,C,D,E)
& ~ r1_semi_af1(A,C,E,D)
& ~ r1_semi_af1(A,D,B,C)
& ~ r1_semi_af1(A,D,C,B)
& ~ r1_semi_af1(A,D,B,E)
& ~ r1_semi_af1(A,D,E,B)
& ~ r1_semi_af1(A,D,C,E)
& ~ r1_semi_af1(A,D,E,C)
& ~ r1_semi_af1(A,E,B,C)
& ~ r1_semi_af1(A,E,C,B)
& ~ r1_semi_af1(A,E,B,D)
& ~ r1_semi_af1(A,E,D,B)
& ~ r1_semi_af1(A,E,C,D)
& ~ r1_semi_af1(A,E,D,C) ) ) ) ) ) ) ) ).
fof(t57_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( r2_semi_af1(A,B,C,D,E)
& r1_semi_af1(A,B,C,F)
& r1_semi_af1(A,D,E,F) ) ) ) ) ) ) ) ).
fof(t58_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> r2_semi_af1(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t59_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> r2_semi_af1(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t60_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> r2_semi_af1(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t61_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> ( r2_semi_af1(A,B,D,C,E)
& r2_semi_af1(A,D,E,B,C)
& r2_semi_af1(A,C,B,E,D)
& r2_semi_af1(A,D,B,E,C)
& r2_semi_af1(A,E,C,D,B)
& r2_semi_af1(A,C,E,B,D) ) ) ) ) ) ) ) ).
fof(t62_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ r2_semi_af1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t63_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_semi_af1(A,B,C,D,E)
& r2_semi_af1(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t64_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( r2_semi_af1(A,B,C,D,E)
& r2_analoaf(A,B,E,C,D) ) ) ) ) ) ) ).
fof(t65_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( r2_semi_af1(A,B,C,D,E)
& r2_semi_af1(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t66_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_semi_af1(A,B,C,D)
& D != B
& D != C ) ) ) ) ) ) ).
fof(t67_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_semi_af1(A,B,C,D,E)
& r2_semi_af1(A,B,C,F,G) )
=> r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t68_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_semi_af1(A,E,F,B,C)
& r2_semi_af1(A,E,F,D,G) )
=> ( r1_semi_af1(A,B,C,D)
| r2_semi_af1(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ).
fof(t69_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r1_semi_af1(A,B,C,D)
& r2_semi_af1(A,B,E,C,F)
& r2_semi_af1(A,B,E,D,G) )
=> ( C = D
| r2_semi_af1(A,C,F,D,G) ) ) ) ) ) ) ) ) ) ).
fof(t70_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r2_semi_af1(A,B,C,D,E)
& r2_semi_af1(A,B,C,F,G)
& r2_semi_af1(A,D,E,H,I) )
=> r2_analoaf(A,F,H,G,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t71_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ r2_semi_af1(A,B,D,E,C) ) ) ) ) ) ) ).
fof(d4_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
<=> ~ ( ~ ( B = C
& D = E )
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r2_semi_af1(A,F,G,B,C)
& r2_semi_af1(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t72_semi_af1,axiom,
$true ).
fof(t73_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,B,C,D)
=> C = D ) ) ) ) ) ).
fof(t74_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,D)
=> B = C ) ) ) ) ) ).
fof(t75_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_semi_af1(A,B,C,C,B)
=> B = C ) ) ) ) ).
fof(t76_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t77_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t78_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> ( r1_semi_af1(A,B,C,D)
| r2_semi_af1(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t79_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_semi_af1(A,B,C,D,E)
=> r3_semi_af1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t80_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r1_semi_af1(A,B,C,D)
& r2_semi_af1(A,F,G,B,C) )
=> r2_semi_af1(A,F,G,D,E) ) ) ) ) ) ) ) ) ).
fof(t81_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r3_semi_af1(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t82_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
& r3_semi_af1(A,B,C,D,E) ) ) ) ) ) ).
fof(t83_semi_af1,axiom,
$true ).
fof(t84_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_semi_af1(A,B,C,B,C) ) ) ) ).
fof(t85_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r3_semi_af1(A,B,C,F,G) )
=> r3_semi_af1(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t86_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> r3_semi_af1(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t87_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> r3_semi_af1(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t88_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> r3_semi_af1(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t89_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r3_semi_af1(A,B,C,D,E)
=> ( r3_semi_af1(A,D,E,B,C)
& r3_semi_af1(A,C,B,E,D)
& r3_semi_af1(A,B,D,C,E)
& r3_semi_af1(A,E,D,C,B)
& r3_semi_af1(A,C,E,B,D)
& r3_semi_af1(A,D,B,E,C)
& r3_semi_af1(A,E,C,D,B) ) ) ) ) ) ) ) ).
fof(t90_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r3_semi_af1(A,C,F,E,G) )
=> r3_semi_af1(A,B,F,D,G) ) ) ) ) ) ) ) ) ).
fof(t91_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r3_semi_af1(A,F,C,D,G) )
=> r3_semi_af1(A,B,F,G,E) ) ) ) ) ) ) ) ) ).
fof(t92_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,C,D)
& r3_semi_af1(A,E,C,C,F) )
=> r3_semi_af1(A,B,E,F,D) ) ) ) ) ) ) ) ).
fof(t93_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,D,E)
& r3_semi_af1(A,F,C,D,G) )
=> r2_analoaf(A,B,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t94_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r3_semi_af1(A,B,C,C,D)
& r3_semi_af1(A,E,C,C,F) )
=> r2_analoaf(A,B,E,D,F) ) ) ) ) ) ) ) ).
fof(d5_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( E = k1_semi_af1(A,B,C,D)
<=> r3_semi_af1(A,D,B,C,E) ) ) ) ) ) ) ).
fof(d6_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( D = k2_semi_af1(A,B,C)
<=> k1_semi_af1(A,B,D,C) = C ) ) ) ) ) ).
fof(d7_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> k3_semi_af1(A,B,C,D) = k1_semi_af1(A,B,k2_semi_af1(A,C,D),D) ) ) ) ) ).
fof(t95_semi_af1,axiom,
$true ).
fof(t96_semi_af1,axiom,
$true ).
fof(t97_semi_af1,axiom,
$true ).
fof(t98_semi_af1,axiom,
$true ).
fof(t99_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_semi_af1(A,B,C,C) = B ) ) ) ).
fof(t100_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
& k1_semi_af1(A,B,D,C) = C ) ) ) ) ).
fof(t101_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> k1_semi_af1(A,k1_semi_af1(A,B,C,D),E,D) = k1_semi_af1(A,B,k1_semi_af1(A,C,E,D),D) ) ) ) ) ) ).
fof(t102_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> k1_semi_af1(A,B,C,D) = k1_semi_af1(A,C,B,D) ) ) ) ) ).
fof(t103_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_semi_af1(A,B,B,C) = C
=> B = C ) ) ) ) ).
fof(t104_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( k1_semi_af1(A,B,C,D) = k1_semi_af1(A,B,E,D)
=> C = E ) ) ) ) ) ) ).
fof(t105_semi_af1,axiom,
$true ).
fof(t106_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_semi_af1(A,B,C,C,k2_semi_af1(A,B,C)) ) ) ) ).
fof(t107_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( k2_semi_af1(A,B,C) = k2_semi_af1(A,D,C)
=> B = D ) ) ) ) ) ).
fof(t108_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> r2_analoaf(A,B,C,k2_semi_af1(A,B,D),k2_semi_af1(A,C,D)) ) ) ) ) ).
fof(t109_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_semi_af1(A,B,B) = B ) ) ).
fof(t110_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> r2_analoaf(A,B,C,k1_semi_af1(A,B,D,E),k1_semi_af1(A,C,D,E)) ) ) ) ) ) ).
fof(t111_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,B,C,k1_semi_af1(A,B,D,F),k1_semi_af1(A,C,E,F)) ) ) ) ) ) ) ) ).
fof(t112_semi_af1,axiom,
$true ).
fof(t113_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( k3_semi_af1(A,B,C,D) = D
<=> B = C ) ) ) ) ) ).
fof(t114_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> r2_analoaf(A,B,k3_semi_af1(A,C,D,B),D,C) ) ) ) ) ).
fof(t115_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r1_semi_af1(A,B,k3_semi_af1(A,C,D,B),k3_semi_af1(A,E,F,B))
<=> r2_analoaf(A,D,C,F,E) ) ) ) ) ) ) ) ).
fof(d8_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r4_semi_af1(A,B,C,D,E,F)
<=> ( ~ r1_semi_af1(A,F,B,D)
& r1_semi_af1(A,F,B,C)
& r1_semi_af1(A,F,D,E)
& r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ).
fof(d9_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r5_semi_af1(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))
=> ( r1_semi_af1(A,B,C,D)
& ~ ( r1_semi_af1(A,B,E,F)
& r2_analoaf(A,C,E,D,F) ) ) ) ) ) ) ) ) ) ).
fof(t116_semi_af1,axiom,
$true ).
fof(t117_semi_af1,axiom,
$true ).
fof(t118_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r4_semi_af1(A,B,C,D,E,F)
=> ( F != B
& B != D
& D != F ) ) ) ) ) ) ) ) ).
fof(t119_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r4_semi_af1(A,B,C,D,E,F)
& r4_semi_af1(A,B,C,D,G,F) )
=> E = G ) ) ) ) ) ) ) ) ).
fof(t120_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ~ r1_semi_af1(A,B,C,D)
=> r4_semi_af1(A,C,B,D,B,B) ) ) ) ) ) ).
fof(t121_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r4_semi_af1(A,B,C,D,E,F)
=> r4_semi_af1(A,D,E,B,C,F) ) ) ) ) ) ) ) ).
fof(t122_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( B != C
& r4_semi_af1(A,D,C,E,F,B)
& B = F ) ) ) ) ) ) ) ).
fof(t123_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( B != C
& r4_semi_af1(A,D,C,E,F,B)
& r1_semi_af1(A,B,C,F) ) ) ) ) ) ) ) ).
fof(t124_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r4_semi_af1(A,D,C,E,F,B)
=> ( B = C
| r4_semi_af1(A,C,D,F,E,B) ) ) ) ) ) ) ) ) ).
fof(t125_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( r4_semi_af1(A,E,C,F,D,B)
=> ( ( B != C
& B != D )
| ( B = C
& B = D ) ) ) ) ) ) ) ) ) ).
fof(t126_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r4_semi_af1(A,B,C,D,E,F)
& r4_semi_af1(A,B,C,G,H,F) )
=> r2_analoaf(A,D,G,E,H) ) ) ) ) ) ) ) ) ) ).
fof(t127_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ( ( r4_semi_af1(A,B,C,D,E,F)
& r4_semi_af1(A,B,C,G,H,F) )
=> ( r1_semi_af1(A,F,D,G)
| r4_semi_af1(A,D,E,G,H,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t128_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r4_semi_af1(A,B,C,D,E,F)
& r4_semi_af1(A,B,C,G,H,F)
& r4_semi_af1(A,D,E,I,J,F) )
=> r2_analoaf(A,G,I,H,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t129_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
& r1_semi_af1(A,B,C,D)
& r5_semi_af1(A,B,D) ) ) ) ) ).
fof(t130_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
& B != C
& C != D
& D != B ) ) ) ) ).
fof(t131_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r5_semi_af1(A,B,C)
& B = C ) ) ) ) ).
fof(t132_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r5_semi_af1(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& r5_semi_af1(A,B,D) ) ) ) ) ) ) ).
fof(t133_semi_af1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_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))
=> ~ ( ~ r1_semi_af1(A,B,C,D)
& r1_semi_af1(A,B,C,E)
& r5_semi_af1(A,B,C)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ r4_semi_af1(A,C,E,D,F,B) ) ) ) ) ) ) ) ).
fof(dt_k1_semi_af1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k1_semi_af1(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k2_semi_af1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_semi_af1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_semi_af1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v1_semi_af1(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k3_semi_af1(A,B,C,D),u1_struct_0(A)) ) ).
%------------------------------------------------------------------------------