SET007 Axioms: SET007+211.ax
%------------------------------------------------------------------------------
% File : SET007+211 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subspaces and Cosets of Subspaces in Real Linear Space
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : rlsub_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 114 ( 16 unt; 0 def)
% Number of atoms : 1196 ( 76 equ)
% Maximal formula atoms : 24 ( 10 avg)
% Number of connectives : 1200 ( 118 ~; 3 |; 708 &)
% ( 27 <=>; 344 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-4 aty)
% Number of variables : 326 ( 315 !; 11 ?)
% 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_rlsub_1,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_rlsub_1(B,A)
& ~ v3_struct_0(B)
& v2_rlvect_1(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B) ) ) ).
fof(d1_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_rlvect_1(A,C,D),B) ) ) )
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r2_hidden(k3_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) ).
fof(t1_rlsub_1,axiom,
$true ).
fof(t2_rlsub_1,axiom,
$true ).
fof(t3_rlsub_1,axiom,
$true ).
fof(t4_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ( B = k1_xboole_0
| r2_hidden(k1_rlvect_1(A),B) ) ) ) ) ).
fof(t5_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) ) ).
fof(t6_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) ).
fof(t7_rlsub_1,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_rlsub_1(k1_struct_0(A,k1_rlvect_1(A)),A) ) ).
fof(t8_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( u1_struct_0(A) = B
=> v1_rlsub_1(B,A) ) ) ) ).
fof(t10_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_rlsub_1(B,A)
& v1_rlsub_1(C,A) )
=> v1_rlsub_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d2_rlsub_1,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ( m1_rlsub_1(B,A)
<=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& u2_struct_0(B) = u2_struct_0(A)
& u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
& u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) ) ) ) ) ).
fof(t11_rlsub_1,axiom,
$true ).
fof(t12_rlsub_1,axiom,
$true ).
fof(t13_rlsub_1,axiom,
$true ).
fof(t14_rlsub_1,axiom,
$true ).
fof(t15_rlsub_1,axiom,
$true ).
fof(t16_rlsub_1,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,C] :
( m1_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( ( r1_rlvect_1(C,B)
& m1_rlsub_1(C,D) )
=> r1_rlvect_1(D,B) ) ) ) ) ).
fof(t17_rlsub_1,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,C] :
( m1_rlsub_1(C,A)
=> ( r1_rlvect_1(C,B)
=> r1_rlvect_1(A,B) ) ) ) ).
fof(t18_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t19_rlsub_1,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_rlsub_1(B,A)
=> k1_rlvect_1(B) = k1_rlvect_1(A) ) ) ).
fof(t20_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) ).
fof(t21_rlsub_1,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_rlsub_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( ( E = B
& F = C )
=> k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C) ) ) ) ) ) ) ) ).
fof(t22_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ( E = B
=> k3_rlvect_1(D,E,C) = k3_rlvect_1(A,B,C) ) ) ) ) ) ) ).
fof(t23_rlsub_1,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_rlsub_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( D = B
=> k5_rlvect_1(A,B) = k5_rlvect_1(C,D) ) ) ) ) ) ).
fof(t24_rlsub_1,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_rlsub_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( ( E = B
& F = C )
=> k6_rlvect_1(D,E,F) = k6_rlvect_1(A,B,C) ) ) ) ) ) ) ) ).
fof(t25_rlsub_1,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_rlsub_1(B,A)
=> r1_rlvect_1(B,k1_rlvect_1(A)) ) ) ).
fof(t26_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) ).
fof(t27_rlsub_1,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_rlsub_1(B,A)
=> r1_rlvect_1(A,k1_rlvect_1(B)) ) ) ).
fof(t28_rlsub_1,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_rlsub_1(D,A)
=> ( ( r1_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k4_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t29_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( r1_rlvect_1(D,B)
=> r1_rlvect_1(D,k3_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t30_rlsub_1,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_rlsub_1(C,A)
=> ( r1_rlvect_1(C,B)
=> r1_rlvect_1(C,k5_rlvect_1(A,B)) ) ) ) ) ).
fof(t31_rlsub_1,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_rlsub_1(D,A)
=> ( ( r1_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t32_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,C),C)
& m2_relset_1(E,k2_zfmisc_1(C,C),C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C)
& m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) )
=> ( ( B = C
& D = k1_rlvect_1(A)
& E = k1_realset1(u1_rlvect_1(A),B)
& F = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) )
=> m1_rlsub_1(g2_rlvect_1(C,D,E,F),A) ) ) ) ) ) ) ) ).
fof(t33_rlsub_1,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) )
=> m1_rlsub_1(A,A) ) ).
fof(t34_rlsub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(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] :
( ( ~ v3_struct_0(B)
& v2_rlvect_1(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ( ( m1_rlsub_1(A,B)
& m1_rlsub_1(B,A) )
=> A = B ) ) ) ).
fof(t35_rlsub_1,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& l2_rlvect_1(C) )
=> ( ( m1_rlsub_1(A,B)
& m1_rlsub_1(B,C) )
=> m1_rlsub_1(A,C) ) ) ) ) ).
fof(t36_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_rlsub_1(B,C) ) ) ) ) ).
fof(t37_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
=> r1_rlvect_1(C,D) ) )
=> m1_rlsub_1(B,C) ) ) ) ) ).
fof(t38_rlsub_1,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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ( u1_struct_0(B) = u1_struct_0(C)
=> B = C ) ) ) ) ).
fof(t39_rlsub_1,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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
<=> r1_rlvect_1(C,D) ) )
=> B = C ) ) ) ) ).
fof(t40_rlsub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ( u1_struct_0(B) = u1_struct_0(A)
=> B = A ) ) ) ).
fof(t41_rlsub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> r1_rlvect_1(A,C) ) )
=> B = A ) ) ) ).
fof(t42_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_rlsub_1(C,A)
=> ( u1_struct_0(C) = B
=> v1_rlsub_1(B,A) ) ) ) ) ).
fof(t43_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( B != k1_xboole_0
& v1_rlsub_1(B,A)
& ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(d3_rlsub_1,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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ( B = k1_rlsub_1(A)
<=> u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ) ).
fof(d4_rlsub_1,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) )
=> k2_rlsub_1(A) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ).
fof(t44_rlsub_1,axiom,
$true ).
fof(t45_rlsub_1,axiom,
$true ).
fof(t46_rlsub_1,axiom,
$true ).
fof(t47_rlsub_1,axiom,
$true ).
fof(t48_rlsub_1,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_rlsub_1(B,A)
=> k1_rlsub_1(B) = k1_rlsub_1(A) ) ) ).
fof(t49_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> k1_rlsub_1(B) = k1_rlsub_1(C) ) ) ) ).
fof(t50_rlsub_1,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_rlsub_1(B,A)
=> m1_rlsub_1(k1_rlsub_1(B),A) ) ) ).
fof(t51_rlsub_1,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_rlsub_1(B,A)
=> m1_rlsub_1(k1_rlsub_1(A),B) ) ) ).
fof(t52_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> m1_rlsub_1(k1_rlsub_1(B),C) ) ) ) ).
fof(t53_rlsub_1,axiom,
$true ).
fof(t54_rlsub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(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) )
=> m1_rlsub_1(A,k2_rlsub_1(A)) ) ).
fof(d6_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_rlsub_1(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k3_rlsub_1(A,D,B) ) ) ) ) ) ).
fof(t55_rlsub_1,axiom,
$true ).
fof(t56_rlsub_1,axiom,
$true ).
fof(t57_rlsub_1,axiom,
$true ).
fof(t58_rlsub_1,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_rlsub_1(C,A)
=> ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t59_rlsub_1,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_rlsub_1(C,A)
=> r2_hidden(B,k3_rlsub_1(A,B,C)) ) ) ) ).
fof(t60_rlsub_1,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_rlsub_1(B,A)
=> k3_rlsub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) ).
fof(t61_rlsub_1,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))
=> k3_rlsub_1(A,B,k1_rlsub_1(A)) = k1_struct_0(A,B) ) ) ).
fof(t62_rlsub_1,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))
=> k3_rlsub_1(A,B,k2_rlsub_1(A)) = u1_struct_0(A) ) ) ).
fof(t63_rlsub_1,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_rlsub_1(C,A)
=> ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
<=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) ).
fof(t64_rlsub_1,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_rlsub_1(C,A)
=> ( r1_rlvect_1(C,B)
<=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) ).
fof(t65_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( r1_rlvect_1(D,B)
=> k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D) ) ) ) ) ) ).
fof(t66_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D)
=> ( C = np__0
| r1_rlvect_1(D,B) ) ) ) ) ) ) ).
fof(t67_rlsub_1,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_rlsub_1(C,A)
=> ( r1_rlvect_1(C,B)
<=> k3_rlsub_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C) ) ) ) ) ).
fof(t68_rlsub_1,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_rlsub_1(D,A)
=> ( r1_rlvect_1(D,B)
<=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k4_rlvect_1(A,C,B),D) ) ) ) ) ) ).
fof(t69_rlsub_1,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_rlsub_1(D,A)
=> ( r1_rlvect_1(D,B)
<=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k6_rlvect_1(A,C,B),D) ) ) ) ) ) ).
fof(t70_rlsub_1,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_rlsub_1(D,A)
=> ( r2_hidden(B,k3_rlsub_1(A,C,D))
<=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) ).
fof(t71_rlsub_1,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_rlsub_1(C,A)
=> ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,k5_rlvect_1(A,B),C)
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t72_rlsub_1,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_rlsub_1(E,A)
=> ( ( r2_hidden(B,k3_rlsub_1(A,C,E))
& r2_hidden(B,k3_rlsub_1(A,D,E)) )
=> k3_rlsub_1(A,C,E) = k3_rlsub_1(A,D,E) ) ) ) ) ) ) ).
fof(t73_rlsub_1,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_rlsub_1(D,A)
=> ( ( r2_hidden(B,k3_rlsub_1(A,C,D))
& r2_hidden(B,k3_rlsub_1(A,k5_rlvect_1(A,C),D)) )
=> r1_rlvect_1(D,C) ) ) ) ) ) ).
fof(t74_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
=> ( C = np__1
| r1_rlvect_1(D,B) ) ) ) ) ) ) ).
fof(t75_rlsub_1,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,k1_numbers)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( r1_rlvect_1(D,B)
=> r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) ).
fof(t76_rlsub_1,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_rlsub_1(C,A)
=> ( r2_hidden(k5_rlvect_1(A,B),k3_rlsub_1(A,B,C))
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t77_rlsub_1,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_rlsub_1(D,A)
=> ( r2_hidden(k4_rlvect_1(A,B,C),k3_rlsub_1(A,C,D))
<=> r1_rlvect_1(D,B) ) ) ) ) ) ).
fof(t78_rlsub_1,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_rlsub_1(D,A)
=> ( r2_hidden(k6_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
<=> r1_rlvect_1(D,C) ) ) ) ) ) ).
fof(t79_rlsub_1,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_rlsub_1(D,A)
=> ( r2_hidden(B,k3_rlsub_1(A,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(D,E)
& B = k4_rlvect_1(A,C,E) ) ) ) ) ) ) ).
fof(t80_rlsub_1,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_rlsub_1(D,A)
=> ( r2_hidden(B,k3_rlsub_1(A,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(D,E)
& B = k6_rlvect_1(A,C,E) ) ) ) ) ) ) ).
fof(t81_rlsub_1,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_rlsub_1(D,A)
=> ( ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r2_hidden(B,k3_rlsub_1(A,E,D))
& r2_hidden(C,k3_rlsub_1(A,E,D)) )
<=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t82_rlsub_1,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_rlsub_1(D,A)
=> ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,E)
& k4_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ).
fof(t83_rlsub_1,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_rlsub_1(D,A)
=> ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,E)
& k6_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ).
fof(t84_rlsub_1,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] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ! [D] :
( ( v2_rlvect_1(D)
& m1_rlsub_1(D,A) )
=> ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,B,D)
<=> C = D ) ) ) ) ) ).
fof(t85_rlsub_1,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] :
( ( v2_rlvect_1(D)
& m1_rlsub_1(D,A) )
=> ! [E] :
( ( v2_rlvect_1(E)
& m1_rlsub_1(E,A) )
=> ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,E)
=> D = E ) ) ) ) ) ) ).
fof(t86_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m2_rlsub_1(C,A,B)
=> ( v1_rlsub_1(C,A)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t87_rlsub_1,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] :
( ( v2_rlvect_1(B)
& m1_rlsub_1(B,A) )
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ! [D] :
( m2_rlsub_1(D,A,B)
=> ! [E] :
( m2_rlsub_1(E,A,C)
=> ( D = E
=> B = C ) ) ) ) ) ) ).
fof(t88_rlsub_1,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))
=> m2_rlsub_1(k1_struct_0(A,B),A,k1_rlsub_1(A)) ) ) ).
fof(t89_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( m2_rlsub_1(B,A,k1_rlsub_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B != k1_struct_0(A,C) ) ) ) ) ).
fof(t90_rlsub_1,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_rlsub_1(B,A)
=> m2_rlsub_1(u1_struct_0(B),A,B) ) ) ).
fof(t91_rlsub_1,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) )
=> m2_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)) ) ).
fof(t92_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_rlsub_1(B,A,k2_rlsub_1(A))
=> B = u1_struct_0(A) ) ) ) ).
fof(t93_rlsub_1,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_rlsub_1(B,A)
=> ! [C] :
( m2_rlsub_1(C,A,B)
=> ( r2_hidden(k1_rlvect_1(A),C)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t94_rlsub_1,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_rlsub_1(C,A)
=> ! [D] :
( m2_rlsub_1(D,A,C)
=> ( r2_hidden(B,D)
<=> D = k3_rlsub_1(A,B,C) ) ) ) ) ) ).
fof(t95_rlsub_1,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_rlsub_1(D,A)
=> ! [E] :
( m2_rlsub_1(E,A,D)
=> ~ ( r2_hidden(B,E)
& r2_hidden(C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,F)
& k4_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ).
fof(t96_rlsub_1,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_rlsub_1(D,A)
=> ! [E] :
( m2_rlsub_1(E,A,D)
=> ~ ( r2_hidden(B,E)
& r2_hidden(C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,F)
& k6_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ).
fof(t97_rlsub_1,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_rlsub_1(D,A)
=> ( ? [E] :
( m2_rlsub_1(E,A,D)
& r2_hidden(B,E)
& r2_hidden(C,E) )
<=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t98_rlsub_1,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_rlsub_1(C,A)
=> ! [D] :
( m2_rlsub_1(D,A,C)
=> ! [E] :
( m2_rlsub_1(E,A,C)
=> ( ( r2_hidden(B,D)
& r2_hidden(B,E) )
=> D = E ) ) ) ) ) ) ).
fof(dt_m1_rlsub_1,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_rlsub_1(B,A)
=> ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) ) ) ) ).
fof(existence_m1_rlsub_1,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_rlsub_1(B,A) ) ).
fof(dt_m2_rlsub_1,axiom,
! [A,B] :
( ( ~ 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)
& m1_rlsub_1(B,A) )
=> ! [C] :
( m2_rlsub_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m2_rlsub_1,axiom,
! [A,B] :
( ( ~ 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)
& m1_rlsub_1(B,A) )
=> ? [C] : m2_rlsub_1(C,A,B) ) ).
fof(dt_k1_rlsub_1,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) )
=> ( v2_rlvect_1(k1_rlsub_1(A))
& m1_rlsub_1(k1_rlsub_1(A),A) ) ) ).
fof(dt_k2_rlsub_1,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) )
=> ( v2_rlvect_1(k2_rlsub_1(A))
& m1_rlsub_1(k2_rlsub_1(A),A) ) ) ).
fof(dt_k3_rlsub_1,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(B,u1_struct_0(A))
& m1_rlsub_1(C,A) )
=> m1_subset_1(k3_rlsub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(t9_rlsub_1,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_rlsub_1(B,A)
& v1_rlsub_1(C,A)
& D = a_3_0_rlsub_1(A,B,C) )
=> v1_rlsub_1(D,A) ) ) ) ) ) ).
fof(d5_rlsub_1,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_rlsub_1(C,A)
=> k3_rlsub_1(A,B,C) = a_3_1_rlsub_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_rlsub_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_rlsub_1(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k4_rlvect_1(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_3_1_rlsub_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_rlsub_1(D,B) )
=> ( r2_hidden(A,a_3_1_rlsub_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_rlvect_1(B,C,E)
& r1_rlvect_1(D,E) ) ) ) ).
%------------------------------------------------------------------------------