SET007 Axioms: SET007+228.ax
%------------------------------------------------------------------------------
% File : SET007+228 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Ordered Affine Spaces Defined in Directed Parallelity - Part I
% 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 : diraf [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 67 ( 9 unt; 0 def)
% Number of atoms : 791 ( 44 equ)
% Maximal formula atoms : 57 ( 11 avg)
% Number of connectives : 916 ( 192 ~; 14 |; 329 &)
% ( 13 <=>; 368 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-5 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-4 aty)
% Number of variables : 355 ( 340 !; 15 ?)
% 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(fc1_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( ~ v3_struct_0(k2_diraf(A))
& v1_analoaf(k2_diraf(A)) ) ) ).
fof(rc1_diraf,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v1_diraf(A) ) ).
fof(rc2_diraf,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v1_diraf(A)
& v2_diraf(A) ) ).
fof(d1_diraf,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( C = k1_diraf(A,B)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),C)
<=> ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),B)
| r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,G,F)),B) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> k2_diraf(A) = g1_analoaf(u1_struct_0(A),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ).
fof(t1_diraf,axiom,
$true ).
fof(t2_diraf,axiom,
$true ).
fof(t3_diraf,axiom,
$true ).
fof(t4_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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(t5_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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,E,D)
& r2_analoaf(A,D,E,B,C)
& r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t6_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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(t7_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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)
& r2_analoaf(A,C,D,B,B) ) ) ) ) ) ).
fof(t8_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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)
& B != C
& D != E ) ) ) ) ) ) ).
fof(t9_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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,C,D)
| r2_analoaf(A,B,D,D,C) ) ) ) ) ) ) ).
fof(d3_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(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_diraf(A,B,C,D)
<=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) ).
fof(t10_diraf,axiom,
$true ).
fof(t11_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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)
<=> ( r1_diraf(A,B,C,D)
| r1_diraf(A,B,D,C) ) ) ) ) ) ) ).
fof(t12_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_diraf(A,B,C,B)
=> B = C ) ) ) ) ).
fof(t13_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
=> r1_diraf(A,D,C,B) ) ) ) ) ) ).
fof(t14_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_diraf(A,B,B,C)
& r1_diraf(A,B,C,C) ) ) ) ) ).
fof(t15_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r1_diraf(A,B,D,E) )
=> r1_diraf(A,C,D,E) ) ) ) ) ) ) ).
fof(t16_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,D,B,C)
& r1_diraf(A,B,C,E) )
=> ( B = C
| r1_diraf(A,D,C,E) ) ) ) ) ) ) ) ).
fof(t17_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& C != D ) ) ) ) ).
fof(t18_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r1_diraf(A,C,B,D) )
=> B = C ) ) ) ) ) ).
fof(t19_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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
& r1_diraf(A,B,C,D)
& r1_diraf(A,B,C,E)
& ~ r1_diraf(A,C,D,E)
& ~ r1_diraf(A,C,E,D) ) ) ) ) ) ) ).
fof(t20_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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
& r1_diraf(A,B,C,D)
& r1_diraf(A,B,C,E)
& ~ r1_diraf(A,B,D,E)
& ~ r1_diraf(A,B,E,D) ) ) ) ) ) ) ).
fof(t21_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r1_diraf(A,B,E,D)
& ~ r1_diraf(A,B,C,E)
& ~ r1_diraf(A,B,E,C) ) ) ) ) ) ) ).
fof(d4_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(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_diraf(A,B,C,D,E)
<=> ( r2_analoaf(A,B,C,D,E)
| r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ).
fof(t22_diraf,axiom,
$true ).
fof(t23_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(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)),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ) ) ) ) ) ).
fof(t24_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_diraf(A,B,C,C,B)
& r2_diraf(A,B,C,B,C) ) ) ) ) ).
fof(t25_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D,D)
& r2_diraf(A,D,D,B,C) ) ) ) ) ) ).
fof(t26_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,B,D)
=> r2_diraf(A,C,B,C,D) ) ) ) ) ) ).
fof(t27_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D,E)
=> ( r2_diraf(A,B,C,E,D)
& r2_diraf(A,C,B,D,E)
& r2_diraf(A,C,B,E,D)
& r2_diraf(A,D,E,B,C)
& r2_diraf(A,D,E,C,B)
& r2_diraf(A,E,D,B,C)
& r2_diraf(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t28_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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))
=> ~ ( B != C
& ~ ( ~ ( r2_diraf(A,B,C,D,E)
& r2_diraf(A,B,C,F,G) )
& ~ ( r2_diraf(A,B,C,D,E)
& r2_diraf(A,F,G,B,C) )
& ~ ( r2_diraf(A,D,E,B,C)
& r2_diraf(A,F,G,B,C) )
& ~ ( r2_diraf(A,D,E,B,C)
& r2_diraf(A,B,C,F,G) ) )
& ~ r2_diraf(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t29_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,B,D) ) ) ) ) ).
fof(t30_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D,E)
& D != E ) ) ) ) ) ).
fof(t31_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D,E)
& r2_diraf(A,B,D,C,E) ) ) ) ) ) ).
fof(t32_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,C,D)
& C != B
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_diraf(A,E,C,C,F)
& r2_diraf(A,E,B,D,F) ) ) ) ) ) ) ) ) ).
fof(d5_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(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_diraf(A,B,C,D)
<=> r2_diraf(A,B,C,B,D) ) ) ) ) ) ).
fof(t33_diraf,axiom,
$true ).
fof(t34_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
=> r3_diraf(A,B,C,D) ) ) ) ) ) ).
fof(t35_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& ~ r1_diraf(A,B,C,D)
& ~ r1_diraf(A,C,B,D)
& ~ r1_diraf(A,B,D,C) ) ) ) ) ) ).
fof(t36_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
=> ( r3_diraf(A,B,D,C)
& r3_diraf(A,C,B,D)
& r3_diraf(A,C,D,B)
& r3_diraf(A,D,B,C)
& r3_diraf(A,D,C,B) ) ) ) ) ) ) ).
fof(t37_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_diraf(A,B,B,C)
& r3_diraf(A,B,C,C)
& r3_diraf(A,B,C,B) ) ) ) ) ).
fof(t38_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r3_diraf(A,B,C,E)
& r3_diraf(A,B,C,F) )
=> ( B = C
| r3_diraf(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t39_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r2_diraf(A,B,C,D,E) )
=> ( B = C
| r3_diraf(A,B,C,E) ) ) ) ) ) ) ) ).
fof(t40_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D)
& r3_diraf(A,B,C,E) )
=> r2_diraf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t41_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,D,E,B)
& r3_diraf(A,D,E,C)
& r3_diraf(A,B,C,F) )
=> ( B = C
| r3_diraf(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t42_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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_diraf(A,B,C,D) ) ) ) ) ).
fof(t43_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(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))
=> r3_diraf(A,B,C,D) ) ) ) ) ) ).
fof(t44_diraf,axiom,
$true ).
fof(t45_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_analoaf(B) )
=> ( B = k2_diraf(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(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(B))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(B))
=> ( ( C = G
& D = H
& E = I
& F = J )
=> ( r2_analoaf(B,G,H,I,J)
<=> r2_diraf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_analoaf(B) )
=> ( B = k2_diraf(A)
=> ( ~ ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> C = D ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( r2_analoaf(B,C,D,D,C)
& r2_analoaf(B,C,D,E,E)
& ( ( r2_analoaf(B,C,D,E,F)
& r2_analoaf(B,C,D,G,H) )
=> ( C = D
| r2_analoaf(B,E,F,G,H) ) )
& ( r2_analoaf(B,C,D,C,E)
=> r2_analoaf(B,D,C,D,E) ) ) ) ) ) ) ) )
& ~ ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r2_analoaf(B,C,D,C,E) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& r2_analoaf(B,C,E,D,F)
& D != F ) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& r2_analoaf(B,C,D,E,F)
& r2_analoaf(B,C,E,D,F) ) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( r2_analoaf(B,E,C,C,F)
& C != E
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( r2_analoaf(B,D,C,C,G)
& r2_analoaf(B,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_diraf,axiom,
$true ).
fof(d7_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_diraf(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,C,B)
& r2_analoaf(A,B,C,D,D)
& ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) )
& ( 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,D,C,E)
& 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))
& 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))
=> ~ ( r2_analoaf(A,D,B,B,E)
& B != D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(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))
=> ( r2_analoaf(A,B,C,C,B)
& r2_analoaf(A,B,C,D,D)
& ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) )
& ( 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,D,C,E)
& 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))
& 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))
=> ~ ( r2_analoaf(A,D,B,B,E)
& B != D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t48_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ( ~ v3_struct_0(k2_diraf(A))
& ~ v3_realset2(k2_diraf(A))
& v1_diraf(k2_diraf(A))
& l1_analoaf(k2_diraf(A)) ) ) ).
fof(t49_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(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))
=> ( r2_analoaf(A,B,C,C,B)
& r2_analoaf(A,B,C,D,D)
& ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) )
& ( 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,D,C,E)
& 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))
& 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))
=> ~ ( r2_analoaf(A,D,B,B,E)
& B != D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) )
<=> ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) ) ) ) ).
fof(t50_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& v3_analoaf(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_diraf(A,B,C,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_diraf(A,B,C,B,F)
& r2_diraf(A,D,E,D,F) ) ) ) ) ) ) ) ) ).
fof(t51_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v3_realset2(B)
& v2_analoaf(B)
& v3_analoaf(B)
& l1_analoaf(B) )
=> ( A = k2_diraf(B)
=> ! [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,C,D,E,F)
& ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,D,C,G)
& r2_analoaf(A,E,F,E,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v2_diraf(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)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,B,C,B,F)
& r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) ).
fof(t52_diraf,axiom,
$true ).
fof(t53_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& v3_analoaf(A)
& l1_analoaf(A) )
=> ( ~ v3_struct_0(k2_diraf(A))
& ~ v3_realset2(k2_diraf(A))
& v1_diraf(k2_diraf(A))
& v2_diraf(k2_diraf(A))
& l1_analoaf(k2_diraf(A)) ) ) ).
fof(t54_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(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))
=> ( r2_analoaf(A,B,C,C,B)
& r2_analoaf(A,B,C,D,D)
& ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G) )
=> ( B = C
| r2_analoaf(A,D,E,F,G) ) )
& ( 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,D,C,E)
& 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))
& 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))
=> ~ ( r2_analoaf(A,D,B,B,E)
& B != D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) )
& ! [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)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,B,C,B,F)
& r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_diraf,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
=> m2_relset_1(k1_diraf(A,B),k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) ) ).
fof(dt_k2_diraf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_analoaf(k2_diraf(A))
& l1_analoaf(k2_diraf(A)) ) ) ).
%------------------------------------------------------------------------------