SET007 Axioms: SET007+741.ax
%------------------------------------------------------------------------------
% File : SET007+741 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Operations on Subspaces in Real Unitary 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 : rusub_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 84 ( 1 unt; 0 def)
% Number of atoms : 1076 ( 75 equ)
% Maximal formula atoms : 25 ( 12 avg)
% Number of connectives : 1088 ( 96 ~; 3 |; 721 &)
% ( 18 <=>; 250 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 0 con; 1-6 aty)
% Number of variables : 266 ( 250 !; 16 ?)
% 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_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ~ v1_xboole_0(k3_rusub_2(A)) ) ).
fof(rc1_rusub_2,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ? [C] :
( m1_rusub_2(C,A,B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v1_bhsp_1(C)
& v2_bhsp_1(C) ) ) ).
fof(fc2_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ~ v3_struct_0(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v3_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v4_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v5_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v6_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v7_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v8_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v9_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v10_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ) ).
fof(fc3_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ~ v3_struct_0(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v3_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v4_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v5_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v6_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v7_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v8_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v9_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v10_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v12_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v13_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v14_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v15_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v16_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ) ).
fof(d2_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( ( v1_bhsp_1(D)
& m1_rusub_1(D,A) )
=> ( D = k2_rusub_2(A,B,C)
<=> u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ).
fof(t1_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( r1_rlvect_1(k1_rusub_2(A,B,C),D)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r1_rlvect_1(B,E)
& r1_rlvect_1(C,F)
& D = k4_rlvect_1(A,E,F) ) ) ) ) ) ) ).
fof(t2_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_rlvect_1(B,D)
| r1_rlvect_1(C,D) )
=> r1_rlvect_1(k1_rusub_2(A,B,C),D) ) ) ) ) ) ).
fof(t3_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( r1_rlvect_1(k2_rusub_2(A,B,C),D)
<=> ( r1_rlvect_1(B,D)
& r1_rlvect_1(C,D) ) ) ) ) ) ).
fof(t4_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> k1_rusub_2(A,B,B) = B ) ) ).
fof(t5_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> k1_rusub_2(A,B,C) = k1_rusub_2(A,C,B) ) ) ) ).
fof(t6_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> k1_rusub_2(A,B,k1_rusub_2(A,C,D)) = k1_rusub_2(A,k1_rusub_2(A,B,C),D) ) ) ) ) ).
fof(t7_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( m1_rusub_1(B,k1_rusub_2(A,B,C))
& m1_rusub_1(C,k1_rusub_2(A,B,C)) ) ) ) ) ).
fof(t8_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( m1_rusub_1(B,C)
<=> k1_rusub_2(A,B,C) = C ) ) ) ) ).
fof(t9_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( k1_rusub_2(A,k1_rusub_1(A),B) = B
& k1_rusub_2(A,B,k1_rusub_1(A)) = B ) ) ) ).
fof(t10_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( k1_rusub_2(A,k1_rusub_1(A),k2_rusub_1(A)) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A))
& k1_rusub_2(A,k2_rusub_1(A),k1_rusub_1(A)) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ).
fof(t11_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ( k1_rusub_2(A,k2_rusub_1(A),B) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A))
& k1_rusub_2(A,B,k2_rusub_1(A)) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ) ).
fof(t12_rusub_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_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k1_rusub_2(A,k2_rusub_1(A),k2_rusub_1(A)) = A ) ).
fof(t13_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> k2_rusub_2(A,B,B) = B ) ) ).
fof(t14_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> k2_rusub_2(A,B,C) = k2_rusub_2(A,C,B) ) ) ) ).
fof(t15_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> k2_rusub_2(A,B,k2_rusub_2(A,C,D)) = k2_rusub_2(A,k2_rusub_2(A,B,C),D) ) ) ) ) ).
fof(t16_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( m1_rusub_1(k2_rusub_2(A,B,C),B)
& m1_rusub_1(k2_rusub_2(A,B,C),C) ) ) ) ) ).
fof(t17_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( m1_rusub_1(C,B)
<=> k2_rusub_2(A,C,B) = C ) ) ) ) ).
fof(t18_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ( k2_rusub_2(A,k1_rusub_1(A),B) = k1_rusub_1(A)
& k2_rusub_2(A,B,k1_rusub_1(A)) = k1_rusub_1(A) ) ) ) ).
fof(t19_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( k2_rusub_2(A,k1_rusub_1(A),k2_rusub_1(A)) = k1_rusub_1(A)
& k2_rusub_2(A,k2_rusub_1(A),k1_rusub_1(A)) = k1_rusub_1(A) ) ) ).
fof(t20_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( k2_rusub_2(A,k2_rusub_1(A),B) = B
& k2_rusub_2(A,B,k2_rusub_1(A)) = B ) ) ) ).
fof(t21_rusub_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_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k2_rusub_2(A,k2_rusub_1(A),k2_rusub_1(A)) = A ) ).
fof(t22_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> m1_rusub_1(k2_rusub_2(A,B,C),k1_rusub_2(A,B,C)) ) ) ) ).
fof(t23_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> k1_rusub_2(A,k2_rusub_2(A,B,C),C) = C ) ) ) ).
fof(t24_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> k2_rusub_2(A,C,k1_rusub_2(A,C,B)) = C ) ) ) ).
fof(t25_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> m1_rusub_1(k1_rusub_2(A,k2_rusub_2(A,B,C),k2_rusub_2(A,C,D)),k2_rusub_2(A,C,k1_rusub_2(A,B,D))) ) ) ) ) ).
fof(t26_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( m1_rusub_1(B,C)
=> k2_rusub_2(A,C,k1_rusub_2(A,B,D)) = k1_rusub_2(A,k2_rusub_2(A,B,C),k2_rusub_2(A,C,D)) ) ) ) ) ) ).
fof(t27_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> m1_rusub_1(k1_rusub_2(A,C,k2_rusub_2(A,B,D)),k2_rusub_2(A,k1_rusub_2(A,B,C),k1_rusub_2(A,C,D))) ) ) ) ) ).
fof(t28_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( m1_rusub_1(B,C)
=> k1_rusub_2(A,C,k2_rusub_2(A,B,D)) = k2_rusub_2(A,k1_rusub_2(A,B,C),k1_rusub_2(A,C,D)) ) ) ) ) ) ).
fof(t29_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( ( v1_bhsp_1(B)
& m1_rusub_1(B,D) )
=> k1_rusub_2(A,B,k2_rusub_2(A,C,D)) = k2_rusub_2(A,k1_rusub_2(A,B,C),D) ) ) ) ) ) ).
fof(t30_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( k1_rusub_2(A,B,C) = C
<=> k2_rusub_2(A,B,C) = B ) ) ) ) ).
fof(t31_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ! [D] :
( ( v1_bhsp_1(D)
& m1_rusub_1(D,A) )
=> ( m1_rusub_1(B,C)
=> m1_rusub_1(k1_rusub_2(A,B,D),k1_rusub_2(A,C,D)) ) ) ) ) ) ).
fof(t32_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( ~ ( ? [D] :
( m1_rusub_1(D,A)
& u1_struct_0(D) = k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) )
& ~ m1_rusub_1(B,C)
& ~ m1_rusub_1(C,B) )
& ~ ( ( m1_rusub_1(B,C)
| m1_rusub_1(C,B) )
& ! [D] :
( m1_rusub_1(D,A)
=> u1_struct_0(D) != k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(d3_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( B = k3_rusub_2(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v1_bhsp_1(C)
& m1_rusub_1(C,A) ) ) ) ) ).
fof(t33_rusub_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_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> r2_hidden(A,k3_rusub_2(A)) ) ).
fof(d4_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( r1_rusub_2(A,B,C)
<=> ( g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) = k1_rusub_2(A,B,C)
& k2_rusub_2(A,B,C) = k1_rusub_1(A) ) ) ) ) ) ).
fof(d5_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( m1_rusub_2(C,A,B)
<=> r1_rusub_2(A,C,B) ) ) ) ) ).
fof(t34_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( r1_rusub_2(A,B,C)
=> m1_rusub_2(C,A,B) ) ) ) ) ).
fof(t35_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ( r1_rusub_2(A,C,B)
& r1_rusub_2(A,B,C) ) ) ) ) ).
fof(t36_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ( k1_rusub_2(A,B,C) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A))
& k1_rusub_2(A,C,B) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ) ) ).
fof(t37_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ( k2_rusub_2(A,B,C) = k1_rusub_1(A)
& k2_rusub_2(A,C,B) = k1_rusub_1(A) ) ) ) ) ).
fof(t38_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( r1_rusub_2(A,B,C)
=> r1_rusub_2(A,C,B) ) ) ) ) ).
fof(t39_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( r1_rusub_2(A,k1_rusub_1(A),k2_rusub_1(A))
& r1_rusub_2(A,k2_rusub_1(A),k1_rusub_1(A)) ) ) ).
fof(t40_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> m1_rusub_2(B,A,C) ) ) ) ).
fof(t41_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( m1_rusub_2(k1_rusub_1(A),A,k2_rusub_1(A))
& m1_rusub_2(k2_rusub_1(A),A,k1_rusub_1(A)) ) ) ).
fof(t42_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m2_rusub_1(D,A,B)
=> ! [E] :
( m2_rusub_1(E,A,C)
=> ( ~ r1_xboole_0(D,E)
=> m2_rusub_1(k5_subset_1(u1_struct_0(A),D,E),A,k2_rusub_2(A,B,C)) ) ) ) ) ) ) ).
fof(t43_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( r1_rusub_2(A,B,C)
<=> ! [D] :
( m2_rusub_1(D,A,B)
=> ! [E] :
( m2_rusub_1(E,A,C)
=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& k5_subset_1(u1_struct_0(A),D,E) = k6_domain_1(u1_struct_0(A),F) ) ) ) ) ) ) ) ).
fof(t44_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( k1_rusub_2(A,B,C) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(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_rlvect_1(B,E)
& r1_rlvect_1(C,F)
& D = k4_rlvect_1(A,E,F) ) ) ) ) ) ) ) ).
fof(t45_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,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_rusub_2(A,B,C)
& D = k4_rlvect_1(A,E,F)
& D = k4_rlvect_1(A,G,H)
& r1_rlvect_1(B,E)
& r1_rlvect_1(B,G)
& r1_rlvect_1(C,F)
& r1_rlvect_1(C,H) )
=> ( E = G
& F = H ) ) ) ) ) ) ) ) ) ) ).
fof(t46_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( A = k1_rusub_2(A,B,C)
=> ( ! [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))
& D = k4_rlvect_1(A,E,F)
& D = k4_rlvect_1(A,G,H)
& r1_rlvect_1(B,E)
& r1_rlvect_1(B,G)
& r1_rlvect_1(C,F)
& r1_rlvect_1(C,H)
& ~ ( E = G
& F = H ) ) ) ) ) )
| r1_rusub_2(A,B,C) ) ) ) ) ) ).
fof(d6_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( r1_rusub_2(A,C,D)
=> ! [E] :
( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( E = k4_rusub_2(A,B,C,D)
<=> ( B = k4_rlvect_1(A,k2_domain_1(u1_struct_0(A),u1_struct_0(A),E),k3_domain_1(u1_struct_0(A),u1_struct_0(A),E))
& r1_rlvect_1(C,k2_domain_1(u1_struct_0(A),u1_struct_0(A),E))
& r1_rlvect_1(D,k3_domain_1(u1_struct_0(A),u1_struct_0(A),E)) ) ) ) ) ) ) ) ) ).
fof(t47_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( r1_rusub_2(A,C,D)
=> k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,B,C,D)) = k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,B,D,C)) ) ) ) ) ) ).
fof(t48_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( m1_rusub_1(D,A)
=> ( r1_rusub_2(A,C,D)
=> k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,B,C,D)) = k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,B,D,C)) ) ) ) ) ) ).
fof(t49_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( ( k4_rlvect_1(A,k2_domain_1(u1_struct_0(A),u1_struct_0(A),E),k3_domain_1(u1_struct_0(A),u1_struct_0(A),E)) = D
& r1_rlvect_1(B,k2_domain_1(u1_struct_0(A),u1_struct_0(A),E))
& r1_rlvect_1(C,k3_domain_1(u1_struct_0(A),u1_struct_0(A),E)) )
=> E = k4_rusub_2(A,D,B,C) ) ) ) ) ) ) ).
fof(t50_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k4_rlvect_1(A,k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C)),k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C))) = D ) ) ) ) ).
fof(t51_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C)))
& r1_rlvect_1(C,k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C))) ) ) ) ) ) ).
fof(t52_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C)) = k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,C,B)) ) ) ) ) ).
fof(t53_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,B,C)) = k2_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rusub_2(A,D,C,B)) ) ) ) ) ).
fof(d7_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A))
& m2_relset_1(B,k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A)) )
=> ( B = k5_rusub_2(A)
<=> ! [C] :
( m1_subset_1(C,k3_rusub_2(A))
=> ! [D] :
( m1_subset_1(D,k3_rusub_2(A))
=> ! [E] :
( m1_rusub_1(E,A)
=> ! [F] :
( m1_rusub_1(F,A)
=> ( ( C = E
& D = F )
=> k2_binop_1(k3_rusub_2(A),k3_rusub_2(A),k3_rusub_2(A),B,C,D) = k1_rusub_2(A,E,F) ) ) ) ) ) ) ) ) ).
fof(d8_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A))
& m2_relset_1(B,k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A)) )
=> ( B = k6_rusub_2(A)
<=> ! [C] :
( m1_subset_1(C,k3_rusub_2(A))
=> ! [D] :
( m1_subset_1(D,k3_rusub_2(A))
=> ! [E] :
( m1_rusub_1(E,A)
=> ! [F] :
( m1_rusub_1(F,A)
=> ( ( C = E
& D = F )
=> k2_binop_1(k3_rusub_2(A),k3_rusub_2(A),k3_rusub_2(A),B,C,D) = k2_rusub_2(A,E,F) ) ) ) ) ) ) ) ) ).
fof(t54_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ~ v3_struct_0(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v10_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& l3_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ) ).
fof(t55_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> v13_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ).
fof(t56_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> v14_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ).
fof(t57_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ~ v3_struct_0(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v10_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& v15_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A)))
& l3_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ) ).
fof(t58_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> v12_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ).
fof(t59_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> v16_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) ).
fof(t60_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ! [D] :
( ( v1_bhsp_1(D)
& m1_rusub_1(D,A) )
=> ( m1_rusub_1(B,C)
=> m1_rusub_1(k2_rusub_2(A,B,D),k2_rusub_2(A,C,D)) ) ) ) ) ) ).
fof(t61_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_rlvect_1(B,C) )
=> B = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ) ).
fof(t62_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m2_rusub_1(D,A,B)
& r2_hidden(C,D) ) ) ) ) ).
fof(t63_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k3_rusub_1(A,C,B))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(B,E)
& D = k4_rlvect_1(A,C,E) ) ) ) ) ) ).
fof(dt_m1_rusub_2,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ! [C] :
( m1_rusub_2(C,A,B)
=> m1_rusub_1(C,A) ) ) ).
fof(existence_m1_rusub_2,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ? [C] : m1_rusub_2(C,A,B) ) ).
fof(dt_k1_rusub_2,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A)
& m1_rusub_1(C,A) )
=> ( v1_bhsp_1(k1_rusub_2(A,B,C))
& m1_rusub_1(k1_rusub_2(A,B,C),A) ) ) ).
fof(dt_k2_rusub_2,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A)
& m1_rusub_1(C,A) )
=> ( v1_bhsp_1(k2_rusub_2(A,B,C))
& m1_rusub_1(k2_rusub_2(A,B,C),A) ) ) ).
fof(dt_k3_rusub_2,axiom,
$true ).
fof(dt_k4_rusub_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_rusub_1(C,A)
& m1_rusub_1(D,A) )
=> m1_subset_1(k4_rusub_2(A,B,C,D),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k5_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( v1_funct_1(k5_rusub_2(A))
& v1_funct_2(k5_rusub_2(A),k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A))
& m2_relset_1(k5_rusub_2(A),k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A)) ) ) ).
fof(dt_k6_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( v1_funct_1(k6_rusub_2(A))
& v1_funct_2(k6_rusub_2(A),k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A))
& m2_relset_1(k6_rusub_2(A),k2_zfmisc_1(k3_rusub_2(A),k3_rusub_2(A)),k3_rusub_2(A)) ) ) ).
fof(d1_rusub_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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( ( v1_bhsp_1(D)
& m1_rusub_1(D,A) )
=> ( D = k1_rusub_2(A,B,C)
<=> u1_struct_0(D) = a_3_0_rusub_2(A,B,C) ) ) ) ) ) ).
fof(fraenkel_a_3_0_rusub_2,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)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_rusub_1(C,B)
& m1_rusub_1(D,B) )
=> ( r2_hidden(A,a_3_0_rusub_2(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)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ).
%------------------------------------------------------------------------------