SET007 Axioms: SET007+342.ax
%------------------------------------------------------------------------------
% File : SET007+342 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Oriented Metric-Affine Plane - Part II
% 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 : dirort [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 31 ( 2 unt; 0 def)
% Number of atoms : 425 ( 27 equ)
% Maximal formula atoms : 45 ( 13 avg)
% Number of connectives : 477 ( 83 ~; 7 |; 197 &)
% ( 11 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 14 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-5 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-3 aty)
% Number of variables : 167 ( 154 !; 13 ?)
% 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_dirort,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_dirort(A) ) ).
fof(rc2_dirort,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_dirort(A)
& v2_dirort(A)
& v3_dirort(A)
& v4_dirort(A)
& v5_dirort(A) ) ).
fof(rc3_dirort,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_dirort(A)
& v2_dirort(A)
& v3_dirort(A)
& v4_dirort(A)
& v6_dirort(A) ) ).
fof(t1_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k6_analort(A,B,C)))
=> ( r2_analoaf(k6_analort(A,B,C),D,D,F,H)
& r2_analoaf(k6_analort(A,B,C),D,F,H,H)
& ~ ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
& r2_analoaf(k6_analort(A,B,C),D,F,G,E)
& D != F
& E != G )
& ~ ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
& r2_analoaf(k6_analort(A,B,C),D,F,E,H)
& ~ r2_analoaf(k6_analort(A,B,C),D,F,G,H)
& ~ r2_analoaf(k6_analort(A,B,C),D,F,H,G) )
& ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
=> r2_analoaf(k6_analort(A,B,C),F,D,G,E) )
& ( ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
& r2_analoaf(k6_analort(A,B,C),D,F,G,H) )
=> r2_analoaf(k6_analort(A,B,C),D,F,E,H) )
& ~ ( r2_analoaf(k6_analort(A,B,C),D,E,F,G)
& ~ r2_analoaf(k6_analort(A,B,C),F,G,D,E)
& ~ r2_analoaf(k6_analort(A,B,C),F,G,E,D) ) ) ) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
& F != G
& r2_analoaf(k6_analort(A,B,C),F,G,D,E) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
& F != G
& r2_analoaf(k6_analort(A,B,C),D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t2_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k7_analort(A,B,C)))
=> ( r2_analoaf(k7_analort(A,B,C),D,D,F,H)
& r2_analoaf(k7_analort(A,B,C),D,F,H,H)
& ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
& r2_analoaf(k7_analort(A,B,C),D,F,G,E)
& D != F
& E != G )
& ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
& r2_analoaf(k7_analort(A,B,C),D,F,E,H)
& ~ r2_analoaf(k7_analort(A,B,C),D,F,G,H)
& ~ r2_analoaf(k7_analort(A,B,C),D,F,H,G) )
& ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
=> r2_analoaf(k7_analort(A,B,C),F,D,G,E) )
& ( ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
& r2_analoaf(k7_analort(A,B,C),D,F,G,H) )
=> r2_analoaf(k7_analort(A,B,C),D,F,E,H) )
& ~ ( r2_analoaf(k7_analort(A,B,C),D,E,F,G)
& ~ r2_analoaf(k7_analort(A,B,C),F,G,D,E)
& ~ r2_analoaf(k7_analort(A,B,C),F,G,E,D) ) ) ) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
& F != G
& r2_analoaf(k7_analort(A,B,C),F,G,D,E) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
& F != G
& r2_analoaf(k7_analort(A,B,C),D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(d1_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_dirort(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,B,D,F)
& r2_analoaf(A,B,D,F,F)
& ~ ( r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,D,E,C)
& B != D
& C != E )
& ~ ( r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,D,C,F)
& ~ r2_analoaf(A,B,D,E,F)
& ~ r2_analoaf(A,B,D,F,E) )
& ( r2_analoaf(A,B,D,C,E)
=> r2_analoaf(A,D,B,E,C) )
& ( ( r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,D,E,F) )
=> r2_analoaf(A,B,D,C,F) )
& ~ ( r2_analoaf(A,B,C,D,E)
& ~ r2_analoaf(A,D,E,B,C)
& ~ r2_analoaf(A,D,E,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))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& D != E
& r2_analoaf(A,D,E,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))
& D != E
& r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t3_dirort,axiom,
$true ).
fof(t4_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k7_analort(A,B,C))
& v1_dirort(k7_analort(A,B,C))
& l1_analoaf(k7_analort(A,B,C)) ) ) ) ) ) ).
fof(t5_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k6_analort(A,B,C))
& v1_dirort(k6_analort(A,B,C))
& l1_analoaf(k6_analort(A,B,C)) ) ) ) ) ) ).
fof(t6_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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,E,D,B,C)
& E != D ) ) ) ) ) ).
fof(t7_dirort,axiom,
$true ).
fof(t8_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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 != E
& ( r2_analoaf(A,C,D,B,E)
| r2_analoaf(A,C,D,E,B) ) ) ) ) ) ) ).
fof(d2_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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_dirort(A,B,C,D,E)
<=> ( r2_analoaf(A,B,C,D,E)
| r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ).
fof(d3_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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_dirort(A,B,C,D,E)
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& F != G
& r2_analoaf(A,F,G,B,C)
& r2_analoaf(A,F,G,D,E) ) ) ) ) ) ) ) ) ).
fof(d4_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v2_dirort(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,E,F)
& r2_analoaf(A,H,I,E,F)
& r2_analoaf(A,H,I,D,G)
& H != I
& E != F
& ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v3_dirort(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,E,F)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,D,G,H,I)
& H != I
& E != F
& ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v4_dirort(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,E,F)
& r2_analoaf(A,E,F,H,I)
& r2_analoaf(A,B,C,D,G)
& B != C
& E != F
& ~ r2_analoaf(A,D,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v5_dirort(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,C,B) ) ) ) ) ) ) ) ).
fof(d8_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v6_dirort(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(t9_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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_dirort(A,B,C,D,D)
& r2_dirort(A,D,D,B,C) ) ) ) ) ) ).
fof(t10_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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_dirort(A,B,C,D,E)
=> r2_dirort(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t11_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(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_dirort(A,B,C,D,E)
=> r2_dirort(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t12_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v4_dirort(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_dirort(A,B,C,F,G)
& r2_analoaf(A,B,C,D,E) )
=> ( B = C
| r2_analoaf(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v2_dirort(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,E,F)
& r2_dirort(A,E,F,D,G) )
=> ( E = F
| r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v2_dirort(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_dirort(A,B,C,D,E)
& r2_dirort(A,D,E,F,G) )
=> ( D = E
| r2_dirort(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_dirort(D)
& l1_analoaf(D) )
=> ( ( r1_analmetr(A,B,C)
& D = k6_analort(A,B,C) )
=> ( v5_dirort(D)
& v4_dirort(D)
& v3_dirort(D)
& v2_dirort(D) ) ) ) ) ) ) ).
fof(t16_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_dirort(D)
& l1_analoaf(D) )
=> ( ( r1_analmetr(A,B,C)
& D = k7_analort(A,B,C) )
=> ( v6_dirort(D)
& v4_dirort(D)
& v3_dirort(D)
& v2_dirort(D) ) ) ) ) ) ) ).
fof(t17_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v4_dirort(A)
=> v3_dirort(A) ) ) ).
fof(t18_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v4_dirort(A)
=> v2_dirort(A) ) ) ).
fof(t19_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v2_dirort(A)
=> ( v3_dirort(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,F,G)
& r2_analoaf(A,D,E,F,G) )
=> ( F = G
| r2_dirort(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_dirort,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dirort(A)
& l1_analoaf(A) )
=> ( v3_dirort(A)
=> ( ( ~ v5_dirort(A)
& ~ v6_dirort(A) )
| v4_dirort(A) ) ) ) ).
%------------------------------------------------------------------------------