SET007 Axioms: SET007+235.ax
%------------------------------------------------------------------------------
% File : SET007+235 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Construction of an Abstract Space of Congruence of Vectors
% 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 : tdgroup [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 415 ( 27 equ)
% Maximal formula atoms : 59 ( 11 avg)
% Number of connectives : 417 ( 38 ~; 0 |; 183 &)
% ( 8 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-3 aty)
% Number of variables : 177 ( 164 !; 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(fc1_tdgroup,axiom,
( ~ v3_struct_0(k1_vectsp_1)
& v1_rlvect_1(k1_vectsp_1)
& v3_rlvect_1(k1_vectsp_1)
& v4_rlvect_1(k1_vectsp_1)
& v5_rlvect_1(k1_vectsp_1)
& v6_rlvect_1(k1_vectsp_1)
& v13_vectsp_1(k1_vectsp_1)
& v1_tdgroup(k1_vectsp_1) ) ).
fof(rc1_tdgroup,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& v1_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A) ) ).
fof(fc2_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( ~ v3_struct_0(k2_tdgroup(A))
& v1_analoaf(k2_tdgroup(A)) ) ) ).
fof(rc2_tdgroup,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v2_tdgroup(A) ) ).
fof(t1_tdgroup,axiom,
$true ).
fof(t2_tdgroup,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
=> ? [B] :
( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
& k4_rlvect_1(k1_vectsp_1,B,B) = A ) ) ).
fof(t3_tdgroup,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
=> ( k4_rlvect_1(k1_vectsp_1,A,A) = k1_rlvect_1(k1_vectsp_1)
=> A = k1_rlvect_1(k1_vectsp_1) ) ) ).
fof(d1_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v1_tdgroup(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k2_rlvect_1(A,C,C) = B ) ) ) ) ).
fof(t4_tdgroup,axiom,
$true ).
fof(t5_tdgroup,axiom,
$true ).
fof(t6_tdgroup,axiom,
$true ).
fof(t7_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k4_rlvect_1(A,C,C) = B ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k4_rlvect_1(A,B,B) = k1_rlvect_1(A)
=> B = k1_rlvect_1(A) ) ) ) ) ) ).
fof(d2_tdgroup,axiom,
$true ).
fof(d3_tdgroup,axiom,
$true ).
fof(d4_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( B = k1_tdgroup(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_hidden(k4_tarski(k4_tarski(C,D),k4_tarski(E,F)),B)
<=> k2_rlvect_1(A,C,F) = k2_rlvect_1(A,D,E) ) ) ) ) ) ) ) ) ).
fof(d5_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> k2_tdgroup(A) = g1_analoaf(u1_struct_0(A),k1_tdgroup(A)) ) ).
fof(t8_tdgroup,axiom,
$true ).
fof(t9_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ( u1_struct_0(k2_tdgroup(A)) = u1_struct_0(A)
& u1_analoaf(k2_tdgroup(A)) = k1_tdgroup(A) ) ) ).
fof(d6_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( r1_tdgroup(A,B,C,D,E)
<=> r2_hidden(k4_tarski(k4_tarski(B,C),k4_tarski(D,E)),u1_analoaf(k2_tdgroup(A))) ) ) ) ) ) ) ).
fof(t10_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( r1_tdgroup(A,B,C,D,E)
<=> k2_rlvect_1(A,B,E) = k2_rlvect_1(A,C,D) ) ) ) ) ) ) ).
fof(t11_tdgroup,axiom,
~ ! [A] :
( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
=> A = B ) ) ).
fof(t12_tdgroup,axiom,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = C ) ) ) ).
fof(t13_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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_tdgroup(A,B,C,D,D)
=> B = C ) ) ) ) ) ).
fof(t14_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( ( r1_tdgroup(A,B,C,D,E)
& r1_tdgroup(A,F,G,D,E) )
=> r1_tdgroup(A,B,C,F,G) ) ) ) ) ) ) ) ) ).
fof(t15_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
& r1_tdgroup(A,B,C,D,E) ) ) ) ) ) ).
fof(t16_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( ( r1_tdgroup(A,B,C,D,E)
& r1_tdgroup(A,B,F,D,G) )
=> r1_tdgroup(A,C,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t17_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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_tdgroup(A,B,D,D,C) ) ) ) ) ).
fof(t18_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( ( r1_tdgroup(A,B,C,C,D)
& r1_tdgroup(A,B,E,E,D) )
=> C = E ) ) ) ) ) ) ).
fof(t19_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_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))
=> ( r1_tdgroup(A,B,C,D,E)
=> r1_tdgroup(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t20_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_rlvect_1(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(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> B = C ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ( r2_analoaf(k2_tdgroup(A),B,C,D,D)
=> B = C ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_tdgroup(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_tdgroup(A)))
=> ( ( r2_analoaf(k2_tdgroup(A),B,C,F,G)
& r2_analoaf(k2_tdgroup(A),D,E,F,G) )
=> r2_analoaf(k2_tdgroup(A),B,C,D,E) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
& r2_analoaf(k2_tdgroup(A),B,C,D,E) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_tdgroup(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_tdgroup(A)))
=> ( ( r2_analoaf(k2_tdgroup(A),B,C,E,F)
& r2_analoaf(k2_tdgroup(A),B,D,E,G) )
=> r2_analoaf(k2_tdgroup(A),C,D,F,G) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
& r2_analoaf(k2_tdgroup(A),B,D,D,C) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
=> ( ( r2_analoaf(k2_tdgroup(A),B,C,C,D)
& r2_analoaf(k2_tdgroup(A),B,E,E,D) )
=> C = E ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_tdgroup(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_tdgroup(A)))
=> ( r2_analoaf(k2_tdgroup(A),B,C,D,E)
=> r2_analoaf(k2_tdgroup(A),B,D,C,E) ) ) ) ) ) ) ) ) ).
fof(d7_tdgroup,axiom,
$true ).
fof(d8_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v2_tdgroup(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,D,D)
=> 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,F,G)
& r2_analoaf(A,D,E,F,G) )
=> r2_analoaf(A,B,C,D,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) ) ) ) )
& ! [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_analoaf(A,B,D,E,G) )
=> r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_analoaf(A,B,D,D,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))
=> ( ( r2_analoaf(A,B,C,C,D)
& r2_analoaf(A,B,E,E,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,B,C,D,E)
=> r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ).
fof(t21_tdgroup,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))
=> ( r2_analoaf(A,B,C,D,D)
=> 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,F,G)
& r2_analoaf(A,D,E,F,G) )
=> r2_analoaf(A,B,C,D,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) ) ) ) )
& ! [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_analoaf(A,B,D,E,G) )
=> r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_analoaf(A,B,D,D,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))
=> ( ( r2_analoaf(A,B,C,C,D)
& r2_analoaf(A,B,E,E,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,B,C,D,E)
=> r2_analoaf(A,B,D,C,E) ) ) ) ) ) )
<=> ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A) ) ) ) ).
fof(t22_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = C ) )
=> ( ~ v3_struct_0(k2_tdgroup(A))
& ~ v3_realset2(k2_tdgroup(A))
& v2_tdgroup(k2_tdgroup(A))
& l1_analoaf(k2_tdgroup(A)) ) ) ) ).
fof(dt_k1_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> m2_relset_1(k1_tdgroup(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k2_tdgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v1_analoaf(k2_tdgroup(A))
& l1_analoaf(k2_tdgroup(A)) ) ) ).
%------------------------------------------------------------------------------