SET007 Axioms: SET007+240.ax
%------------------------------------------------------------------------------
% File : SET007+240 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Projective Spaces
% 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 : anproj_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 1 unt; 0 def)
% Number of atoms : 1422 ( 280 equ)
% Maximal formula atoms : 48 ( 22 avg)
% Number of connectives : 1573 ( 213 ~; 51 |; 799 &)
% ( 17 <=>; 493 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 22 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-8 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-6 aty)
% Number of variables : 540 ( 413 !; 127 ?)
% 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_anproj_2,axiom,
? [A] :
( l2_rlvect_1(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)
& v1_anproj_2(A) ) ).
fof(cc1_anproj_2,axiom,
! [A] :
( l2_rlvect_1(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)
& v1_anproj_2(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)
& ~ v3_realset2(A) ) ) ) ).
fof(fc1_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k6_anproj_1(A))
& v1_collsp(k6_anproj_1(A))
& v2_collsp(k6_anproj_1(A))
& v3_collsp(k6_anproj_1(A)) ) ) ).
fof(fc2_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k6_anproj_1(A))
& v1_collsp(k6_anproj_1(A))
& v2_collsp(k6_anproj_1(A))
& v3_collsp(k6_anproj_1(A))
& v2_anproj_2(k6_anproj_1(A)) ) ) ).
fof(fc3_anproj_2,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)
& v1_anproj_2(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k6_anproj_1(A))
& v1_collsp(k6_anproj_1(A))
& v2_collsp(k6_anproj_1(A))
& v3_collsp(k6_anproj_1(A))
& v4_collsp(k6_anproj_1(A))
& v2_anproj_2(k6_anproj_1(A)) ) ) ).
fof(fc4_anproj_2,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)
& v1_anproj_2(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k6_anproj_1(A))
& v1_collsp(k6_anproj_1(A))
& v2_collsp(k6_anproj_1(A))
& v3_collsp(k6_anproj_1(A))
& v4_collsp(k6_anproj_1(A))
& v2_anproj_2(k6_anproj_1(A))
& v3_anproj_2(k6_anproj_1(A)) ) ) ).
fof(rc2_anproj_2,axiom,
? [A] :
( l1_collsp(A)
& ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A) ) ).
fof(fc5_anproj_2,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)
& v1_anproj_2(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k6_anproj_1(A))
& v1_collsp(k6_anproj_1(A))
& v2_collsp(k6_anproj_1(A))
& v3_collsp(k6_anproj_1(A))
& v4_collsp(k6_anproj_1(A))
& v2_anproj_2(k6_anproj_1(A))
& v3_anproj_2(k6_anproj_1(A))
& v4_anproj_2(k6_anproj_1(A))
& v5_anproj_2(k6_anproj_1(A))
& v6_anproj_2(k6_anproj_1(A)) ) ) ).
fof(rc3_anproj_2,axiom,
? [A] :
( l1_collsp(A)
& ~ v3_struct_0(A)
& v1_collsp(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& v4_anproj_2(A)
& v5_anproj_2(A)
& v6_anproj_2(A)
& v7_anproj_2(A) ) ).
fof(rc4_anproj_2,axiom,
? [A] :
( l1_collsp(A)
& ~ v3_struct_0(A)
& v1_collsp(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& v4_anproj_2(A)
& v5_anproj_2(A)
& v6_anproj_2(A)
& ~ v7_anproj_2(A)
& v8_anproj_2(A) ) ).
fof(t1_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) )
=> ( v8_rlvect_1(B,A)
& v8_rlvect_1(C,A)
& v8_rlvect_1(D,A)
& ~ r2_anproj_1(A,B,C,D)
& ~ r1_anproj_1(A,B,C) ) ) ) ) ) ) ).
fof(t2_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) )
=> ( v8_rlvect_1(B,A)
& v8_rlvect_1(C,A)
& ~ r1_anproj_1(A,B,C)
& v8_rlvect_1(D,A)
& v8_rlvect_1(E,A)
& ~ r1_anproj_1(A,D,E)
& ~ r2_anproj_1(A,B,C,D)
& ~ r2_anproj_1(A,D,E,B) ) ) ) ) ) ) ) ).
fof(t3_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) )
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) ) )
=> ! [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_anproj_1(A,B,C,G)
& r2_anproj_1(A,E,F,G)
& v8_rlvect_1(G,A) ) ) ) ) ) ) ) ) ).
fof(t4_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) ) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( v8_rlvect_1(F,A)
& v8_rlvect_1(G,A)
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ~ ( r2_anproj_1(A,F,G,I)
& r2_anproj_1(A,C,D,H)
& r2_anproj_1(A,B,I,H)
& v8_rlvect_1(H,A)
& v8_rlvect_1(I,A) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( v8_rlvect_1(F,A)
& r2_anproj_1(A,B,C,F)
& r2_anproj_1(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(d1_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_anproj_2(A,B,C,D)
<=> ( v8_rlvect_1(B,A)
& v8_rlvect_1(C,A)
& v8_rlvect_1(D,A) ) ) ) ) ) ) ).
fof(d2_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r2_anproj_2(A,B,C,D,E,F,G)
<=> ( r2_anproj_1(A,B,C,G)
& r2_anproj_1(A,B,D,F)
& r2_anproj_1(A,C,D,E) ) ) ) ) ) ) ) ) ) ).
fof(d3_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r3_anproj_2(A,B,C,D,E,F,G,H)
<=> ( r2_anproj_1(A,B,C,F)
& r2_anproj_1(A,B,D,G)
& r2_anproj_1(A,B,E,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_anproj_1(A,B,C,D)
& r1_anproj_2(A,B,C,D) )
=> ( r1_anproj_1(A,B,C)
| r1_anproj_1(A,B,D)
| r1_anproj_1(A,C,D)
| ( ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& k3_rlvect_1(A,D,F) = k4_rlvect_1(A,B,k3_rlvect_1(A,C,E))
& E != np__0
& F != np__0 ) )
& ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,E))
& F != np__0
& E != np__0 ) ) ) ) ) ) ) ) ) ).
fof(t7_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_anproj_1(A,B,C,D)
& ~ r1_anproj_1(A,B,C)
& r1_anproj_2(A,B,C,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> D != k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ).
fof(t8_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( v8_rlvect_1(B,A)
& r1_anproj_2(A,C,D,E)
& r1_anproj_2(A,F,G,H)
& r1_anproj_2(A,I,J,K)
& r3_anproj_2(A,B,C,D,E,F,G,H)
& r2_anproj_2(A,C,D,E,I,J,K)
& r2_anproj_2(A,F,G,H,I,J,K) )
=> ( r1_anproj_1(A,B,F)
| r1_anproj_1(A,B,G)
| r1_anproj_1(A,B,H)
| r1_anproj_1(A,C,F)
| r1_anproj_1(A,D,G)
| r1_anproj_1(A,E,H)
| r2_anproj_1(A,B,C,D)
| r2_anproj_1(A,B,C,E)
| r2_anproj_1(A,B,D,E)
| r2_anproj_1(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r4_anproj_2(A,B,C,D,E,F,G,H)
<=> ( ~ r2_anproj_1(A,B,C,F)
& r2_anproj_1(A,B,C,D)
& r2_anproj_1(A,B,C,E)
& r2_anproj_1(A,B,F,G)
& r2_anproj_1(A,B,F,H) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r5_anproj_2(A,B,C,D,E,F,G,H)
<=> ( ~ r1_anproj_1(A,B,D)
& ~ r1_anproj_1(A,B,E)
& ~ r1_anproj_1(A,B,G)
& ~ r1_anproj_1(A,B,H)
& ~ r1_anproj_1(A,C,D)
& ~ r1_anproj_1(A,C,E)
& ~ r1_anproj_1(A,F,G)
& ~ r1_anproj_1(A,F,H)
& ~ r1_anproj_1(A,D,E)
& ~ r1_anproj_1(A,G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( v8_rlvect_1(B,A)
& r1_anproj_2(A,C,D,E)
& r1_anproj_2(A,F,G,H)
& r1_anproj_2(A,I,J,K)
& r4_anproj_2(A,B,C,D,E,F,G,H)
& r5_anproj_2(A,B,C,D,E,F,G,H)
& r2_anproj_1(A,C,G,K)
& r2_anproj_1(A,F,D,K)
& r2_anproj_1(A,C,H,J)
& r2_anproj_1(A,E,F,J)
& r2_anproj_1(A,D,H,I)
& r2_anproj_1(A,E,G,I) )
=> r2_anproj_1(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ? [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ? [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ? [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = B
=> k1_funct_1(E,H) = np__1 )
& ( H != B
=> k1_funct_1(E,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = C
=> k1_funct_1(F,H) = np__1 )
& ( H != C
=> k1_funct_1(F,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = D
=> k1_funct_1(G,H) = np__1 )
& ( H != D
=> k1_funct_1(G,H) = np__0 ) ) ) ) ) ) ) ) ) ) ).
fof(t11_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ( ( r2_hidden(E,A)
& r2_hidden(F,A)
& r2_hidden(G,A)
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = E
=> k1_funct_1(B,H) = np__1 )
& ( H != E
=> k1_funct_1(B,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = F
=> k1_funct_1(C,H) = np__1 )
& ( H != F
=> k1_funct_1(C,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = G
=> k1_funct_1(D,H) = np__1 )
& ( H != G
=> k1_funct_1(D,H) = np__0 ) ) ) )
=> ( E = F
| E = G
| F = G
| ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,D))) = k9_funcsdom(A)
=> ( H = np__0
& I = np__0
& J = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& r2_hidden(D,A)
& B != C
& B != D
& C != D
& ! [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,G))) = k9_funcsdom(A)
& ~ ( H = np__0
& I = np__0
& J = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ( ( A = k8_domain_1(A,E,F,G)
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = E
=> k1_funct_1(B,H) = np__1 )
& ( H != E
=> k1_funct_1(B,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = F
=> k1_funct_1(C,H) = np__1 )
& ( H != F
=> k1_funct_1(C,H) = np__0 ) ) )
& ! [H] :
( r2_hidden(H,A)
=> ( ( H = G
=> k1_funct_1(D,H) = np__1 )
& ( H != G
=> k1_funct_1(D,H) = np__0 ) ) ) )
=> ( E = F
| E = G
| F = G
| ! [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& ? [K] :
( m1_subset_1(K,k1_numbers)
& H = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ~ ( A = k8_domain_1(A,B,C,D)
& B != C
& B != D
& C != D
& ! [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ! [I] :
( m1_subset_1(I,k1_numbers)
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ! [K] :
( m1_subset_1(K,k1_numbers)
=> H != k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ~ ( A = k8_domain_1(A,B,C,D)
& B != C
& B != D
& C != D
& ! [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ~ ( ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,G))) = k9_funcsdom(A)
=> ( H = np__0
& I = np__0
& J = np__0 ) ) ) ) )
& ! [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& ? [K] :
( m1_subset_1(K,k1_numbers)
& H = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A)
& ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) ) ) ).
fof(t17_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ? [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ? [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ? [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ? [I] :
( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = B
=> k1_funct_1(F,J) = np__1 )
& ( J != B
=> k1_funct_1(F,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = C
=> k1_funct_1(G,J) = np__1 )
& ( J != C
=> k1_funct_1(G,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = D
=> k1_funct_1(H,J) = np__1 )
& ( J != D
=> k1_funct_1(H,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = E
=> k1_funct_1(I,J) = np__1 )
& ( J != E
=> k1_funct_1(I,J) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ( ( r2_hidden(F,A)
& r2_hidden(G,A)
& r2_hidden(H,A)
& r2_hidden(I,A)
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = F
=> k1_funct_1(B,J) = np__1 )
& ( J != F
=> k1_funct_1(B,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = G
=> k1_funct_1(C,J) = np__1 )
& ( J != G
=> k1_funct_1(C,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = H
=> k1_funct_1(D,J) = np__1 )
& ( J != H
=> k1_funct_1(D,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = I
=> k1_funct_1(E,J) = np__1 )
& ( J != I
=> k1_funct_1(E,J) = np__0 ) ) ) )
=> ( F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| ! [J] :
( m1_subset_1(J,k1_numbers)
=> ! [K] :
( m1_subset_1(K,k1_numbers)
=> ! [L] :
( m1_subset_1(L,k1_numbers)
=> ! [M] :
( m1_subset_1(M,k1_numbers)
=> ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,D))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,E))) = k9_funcsdom(A)
=> ( J = np__0
& K = np__0
& L = np__0
& M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& r2_hidden(D,A)
& r2_hidden(E,A)
& B != C
& B != D
& B != E
& C != D
& C != E
& D != E
& ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [I] :
( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [J] :
( m1_subset_1(J,k1_numbers)
& ? [K] :
( m1_subset_1(K,k1_numbers)
& ? [L] :
( m1_subset_1(L,k1_numbers)
& ? [M] :
( m1_subset_1(M,k1_numbers)
& k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,I))) = k9_funcsdom(A)
& ~ ( J = np__0
& K = np__0
& L = np__0
& M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [E] :
( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ( ( A = k9_domain_1(A,F,G,H,I)
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = F
=> k1_funct_1(B,J) = np__1 )
& ( J != F
=> k1_funct_1(B,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = G
=> k1_funct_1(C,J) = np__1 )
& ( J != G
=> k1_funct_1(C,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = H
=> k1_funct_1(D,J) = np__1 )
& ( J != H
=> k1_funct_1(D,J) = np__0 ) ) )
& ! [J] :
( r2_hidden(J,A)
=> ( ( J = I
=> k1_funct_1(E,J) = np__1 )
& ( J != I
=> k1_funct_1(E,J) = np__0 ) ) ) )
=> ( F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| ! [J] :
( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [K] :
( m1_subset_1(K,k1_numbers)
& ? [L] :
( m1_subset_1(L,k1_numbers)
& ? [M] :
( m1_subset_1(M,k1_numbers)
& ? [N] :
( m1_subset_1(N,k1_numbers)
& J = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,D))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ~ ( A = k9_domain_1(A,B,C,D,E)
& B != C
& B != D
& B != E
& C != D
& C != E
& D != E
& ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [I] :
( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [J] :
( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
& ! [K] :
( m1_subset_1(K,k1_numbers)
=> ! [L] :
( m1_subset_1(L,k1_numbers)
=> ! [M] :
( m1_subset_1(M,k1_numbers)
=> ! [N] :
( m1_subset_1(N,k1_numbers)
=> J != k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_anproj_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ~ ( A = k9_domain_1(A,B,C,D,E)
& B != C
& B != D
& B != E
& C != D
& C != E
& D != E
& ! [F] :
( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [G] :
( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [H] :
( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [I] :
( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ~ ( ! [J] :
( m1_subset_1(J,k1_numbers)
=> ! [K] :
( m1_subset_1(K,k1_numbers)
=> ! [L] :
( m1_subset_1(L,k1_numbers)
=> ! [M] :
( m1_subset_1(M,k1_numbers)
=> ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,I))) = k9_funcsdom(A)
=> ( J = np__0
& K = np__0
& L = np__0
& M = np__0 ) ) ) ) ) )
& ! [J] :
( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ? [K] :
( m1_subset_1(K,k1_numbers)
& ? [L] :
( m1_subset_1(L,k1_numbers)
& ? [M] :
( m1_subset_1(M,k1_numbers)
& ? [N] :
( m1_subset_1(N,k1_numbers)
& J = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A)
& ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_anproj_2,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) )
=> ( v1_anproj_2(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,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) ) ) ) ) ) ) ).
fof(d7_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_collsp(A) )
=> ( v2_collsp(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_collsp(A,B,C,B)
& r1_collsp(A,B,B,C)
& r1_collsp(A,B,C,C) ) ) ) ) ) ) ).
fof(d8_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_collsp(A) )
=> ( v3_collsp(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_collsp(A,B,C,D)
& r1_collsp(A,B,C,E)
& r1_collsp(A,B,C,F) )
=> ( B = C
| r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ) ).
fof(d9_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_collsp(A) )
=> ( v2_anproj_2(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_collsp(A,B,C,E)
& r1_collsp(A,C,D,F)
& ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r1_collsp(A,B,D,G)
& r1_collsp(A,E,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d10_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_collsp(A) )
=> ( v3_anproj_2(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 != D
& C != D
& r1_collsp(A,B,C,D) ) ) ) ) ) ).
fof(t24_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ( r1_collsp(k6_anproj_1(A),B,C,D)
<=> ? [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 = k3_anproj_1(A,E)
& C = k3_anproj_1(A,F)
& D = k3_anproj_1(A,G)
& v8_rlvect_1(E,A)
& v8_rlvect_1(F,A)
& v8_rlvect_1(G,A)
& r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t25_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ( r1_collsp(k6_anproj_1(A),B,C,D)
=> ( r1_collsp(k6_anproj_1(A),B,D,C)
& r1_collsp(k6_anproj_1(A),C,B,D)
& r1_collsp(k6_anproj_1(A),D,C,B)
& r1_collsp(k6_anproj_1(A),D,B,C)
& r1_collsp(k6_anproj_1(A),C,D,B) ) ) ) ) ) ) ).
fof(t26_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) )
=> v3_anproj_2(k6_anproj_1(A)) ) ) ).
fof(d11_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v4_anproj_2(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))
=> ~ ( r1_collsp(A,B,C,D)
& r1_collsp(A,E,F,D)
& r1_collsp(A,B,E,G)
& r1_collsp(A,C,F,G)
& r1_collsp(A,B,F,H)
& r1_collsp(A,C,E,H)
& r1_collsp(A,G,D,H)
& ~ r1_collsp(A,B,C,F)
& ~ r1_collsp(A,B,C,E)
& ~ r1_collsp(A,B,E,F)
& ~ r1_collsp(A,C,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v5_anproj_2(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))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,C,D,K)
& r1_collsp(A,F,G,K)
& r1_collsp(A,D,E,I)
& r1_collsp(A,G,H,I)
& r1_collsp(A,C,E,J)
& r1_collsp(A,F,H,J)
& r1_collsp(A,B,C,F)
& r1_collsp(A,B,D,G)
& r1_collsp(A,B,E,H) )
=> ( B = F
| C = F
| B = G
| D = G
| B = H
| E = H
| r1_collsp(A,B,C,D)
| r1_collsp(A,B,C,E)
| r1_collsp(A,B,D,E)
| r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v6_anproj_2(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))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,B,C,D)
& r1_collsp(A,B,C,E)
& r1_collsp(A,B,F,G)
& r1_collsp(A,B,F,H)
& r1_collsp(A,C,G,K)
& r1_collsp(A,F,D,K)
& r1_collsp(A,C,H,J)
& r1_collsp(A,E,F,J)
& r1_collsp(A,D,H,I)
& r1_collsp(A,E,G,I) )
=> ( B = D
| B = E
| D = E
| C = D
| C = E
| B = G
| B = H
| G = H
| F = G
| F = H
| r1_collsp(A,B,C,F)
| r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v7_anproj_2(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_collsp(A,B,C,F)
& r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ).
fof(d15_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v8_anproj_2(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))
& r1_collsp(A,B,D,G)
& r1_collsp(A,C,E,H)
& r1_collsp(A,F,G,H) ) ) ) ) ) ) ) ) ) ).
fof(t27_anproj_2,axiom,
$true ).
fof(t28_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
=> ~ ( r1_collsp(k6_anproj_1(A),B,C,D)
& r1_collsp(k6_anproj_1(A),E,F,D)
& r1_collsp(k6_anproj_1(A),B,E,G)
& r1_collsp(k6_anproj_1(A),C,F,G)
& r1_collsp(k6_anproj_1(A),B,F,H)
& r1_collsp(k6_anproj_1(A),C,E,H)
& r1_collsp(k6_anproj_1(A),G,D,H)
& ~ r1_collsp(k6_anproj_1(A),B,C,F)
& ~ r1_collsp(k6_anproj_1(A),B,C,E)
& ~ r1_collsp(k6_anproj_1(A),B,E,F)
& ~ r1_collsp(k6_anproj_1(A),C,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t29_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
& r1_collsp(k6_anproj_1(A),B,C,F)
& r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) ) ) ) ) ).
fof(t30_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
& B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
& r1_collsp(k6_anproj_1(A),B,C,F)
& r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
& r1_collsp(k6_anproj_1(A),B,C,F)
& r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) ) ) ) ).
fof(t31_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) )
& ! [B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& v2_anproj_2(B)
& v3_anproj_2(B)
& l1_collsp(B) )
=> ~ ( B = k6_anproj_1(A)
& v7_anproj_2(B) ) ) ) ) ).
fof(t32_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
=> ~ ( ~ r1_collsp(k6_anproj_1(A),B,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
& ? [H] :
( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
& r1_collsp(k6_anproj_1(A),E,F,H)
& r1_collsp(k6_anproj_1(A),C,D,G)
& r1_collsp(k6_anproj_1(A),B,H,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( v4_collsp(k6_anproj_1(A))
& v3_anproj_2(k6_anproj_1(A))
& ? [B] :
( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
& ? [D] :
( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
& ~ r1_collsp(k6_anproj_1(A),B,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
& ? [H] :
( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
& r1_collsp(k6_anproj_1(A),E,F,H)
& r1_collsp(k6_anproj_1(A),C,D,G)
& r1_collsp(k6_anproj_1(A),B,H,G) ) ) ) ) ) ) )
& ! [B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& v2_anproj_2(B)
& v3_anproj_2(B)
& l1_collsp(B) )
=> ~ ( B = k6_anproj_1(A)
& v8_anproj_2(B) ) ) ) ) ).
fof(t34_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) ) ) ) ) )
& ! [B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& v2_anproj_2(B)
& v3_anproj_2(B)
& l1_collsp(B) )
=> ~ ( B = k6_anproj_1(A)
& v8_anproj_2(B) ) ) ) ) ).
fof(t35_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) ) ) ) ) )
& ! [B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& v2_anproj_2(B)
& v3_anproj_2(B)
& l1_collsp(B) )
=> ~ ( B = k6_anproj_1(A)
& ~ v7_anproj_2(B) ) ) ) ) ).
fof(t36_anproj_2,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)
& ~ v3_realset2(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& ? [J] :
( m1_subset_1(J,k1_numbers)
& F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
=> ( F = np__0
& G = np__0
& H = np__0
& I = np__0 ) ) ) ) ) ) ) ) ) )
& ! [B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& v2_anproj_2(B)
& v3_anproj_2(B)
& l1_collsp(B) )
=> ~ ( B = k6_anproj_1(A)
& ~ v7_anproj_2(B)
& v8_anproj_2(B) ) ) ) ) ).
fof(t37_anproj_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_collsp(A) )
=> ( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& v7_anproj_2(A)
& l1_collsp(A) )
<=> ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v3_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,F)
& r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------