SET007 Axioms: SET007+210.ax
%------------------------------------------------------------------------------
% File : SET007+210 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Vectors 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 : rlvect_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 142 ( 20 unt; 0 def)
% Number of atoms : 1008 ( 165 equ)
% Maximal formula atoms : 35 ( 7 avg)
% Number of connectives : 979 ( 113 ~; 6 |; 501 &)
% ( 9 <=>; 350 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 6 con; 0-6 aty)
% Number of variables : 379 ( 366 !; 13 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_rlvect_1,axiom,
? [A] :
( l1_rlvect_1(A)
& v1_rlvect_1(A) ) ).
fof(rc2_rlvect_1,axiom,
? [A] :
( l2_rlvect_1(A)
& v2_rlvect_1(A) ) ).
fof(rc3_rlvect_1,axiom,
? [A] :
( l2_rlvect_1(A)
& ~ v3_struct_0(A) ) ).
fof(rc4_rlvect_1,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& v1_rlvect_1(A) ) ).
fof(fc1_rlvect_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
=> ( ~ v3_struct_0(g2_rlvect_1(A,B,C,D))
& v2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ).
fof(rc5_rlvect_1,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) ) ).
fof(rc6_rlvect_1,axiom,
? [A] :
( l2_rlvect_1(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) ) ).
fof(d1_rlvect_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( r1_rlvect_1(A,B)
<=> r2_hidden(B,u1_struct_0(A)) ) ) ).
fof(t1_rlvect_1,axiom,
$true ).
fof(t2_rlvect_1,axiom,
$true ).
fof(t3_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_rlvect_1(A,B) ) ) ).
fof(d2_rlvect_1,axiom,
! [A] :
( l2_struct_0(A)
=> k1_rlvect_1(A) = u2_struct_0(A) ) ).
fof(d3_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ).
fof(d4_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) ).
fof(t4_rlvect_1,axiom,
$true ).
fof(t5_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ).
fof(d5_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v3_rlvect_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) ) ) ) ).
fof(d6_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v4_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))
=> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(d7_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v5_rlvect_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) ).
fof(d8_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v6_rlvect_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ).
fof(d9_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ( v7_rlvect_1(A)
<=> ( ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_rlvect_1(A,B,np__1) = B ) ) ) ) ).
fof(t6_rlvect_1,axiom,
$true ).
fof(t7_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ( ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_rlvect_1(A,B,np__1) = 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) ) ) ) ).
fof(t8_rlvect_1,axiom,
$true ).
fof(t9_rlvect_1,axiom,
$true ).
fof(t10_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
& k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ).
fof(d10_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k5_rlvect_1(A,B)
<=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(d11_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) ).
fof(t11_rlvect_1,axiom,
$true ).
fof(t12_rlvect_1,axiom,
$true ).
fof(t13_rlvect_1,axiom,
$true ).
fof(t14_rlvect_1,axiom,
$true ).
fof(t15_rlvect_1,axiom,
$true ).
fof(t16_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
& k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) ).
fof(t17_rlvect_1,axiom,
$true ).
fof(t18_rlvect_1,axiom,
$true ).
fof(t19_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k2_rlvect_1(A,B,C) = k1_rlvect_1(A)
=> B = k5_rlvect_1(A,C) ) ) ) ) ).
fof(t20_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
& k2_rlvect_1(A,B,D) = C ) ) ) ) ).
fof(t21_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
| k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
=> D = E ) ) ) ) ) ) ).
fof(t22_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( k2_rlvect_1(A,B,C) = B
| k2_rlvect_1(A,C,B) = B )
=> C = k1_rlvect_1(A) ) ) ) ) ).
fof(t23_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> ( ( A = np__0
| C = k1_rlvect_1(B) )
=> k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) ).
fof(t24_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> ~ ( k3_rlvect_1(B,C,A) = k1_rlvect_1(B)
& A != np__0
& C != k1_rlvect_1(B) ) ) ) ) ).
fof(t25_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k5_rlvect_1(A,k1_rlvect_1(A)) = k1_rlvect_1(A) ) ).
fof(t26_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ).
fof(t27_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B) ) ) ).
fof(t28_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ).
fof(t29_rlvect_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))
=> k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(np__1)) ) ) ).
fof(t30_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B ) ) ).
fof(t31_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k5_rlvect_1(A,B) = k5_rlvect_1(A,C)
=> B = C ) ) ) ) ).
fof(t32_rlvect_1,axiom,
$true ).
fof(t33_rlvect_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))
=> ( B = k5_rlvect_1(A,B)
=> B = k1_rlvect_1(A) ) ) ) ).
fof(t34_rlvect_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))
=> ( k4_rlvect_1(A,B,B) = k1_rlvect_1(A)
=> B = k1_rlvect_1(A) ) ) ) ).
fof(t35_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
=> B = C ) ) ) ) ).
fof(t36_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
& k6_rlvect_1(A,C,D) = B ) ) ) ) ).
fof(t37_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t38_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) ).
fof(t39_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)) ) ) ) ).
fof(t40_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)) = k3_rlvect_1(B,C,A) ) ) ) ).
fof(t41_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) ).
fof(t42_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(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))
=> k6_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) ) ) ) ) ).
fof(t43_rlvect_1,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) )
=> ! [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))
=> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) ) ) ) ) ).
fof(t44_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) ).
fof(t45_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) ) ) ) ).
fof(t46_rlvect_1,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) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k6_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) ).
fof(t47_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)) ) ) ) ).
fof(t48_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) ) ) ) ) ).
fof(t49_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [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) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) ) ) ) ) ).
fof(t50_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( k3_rlvect_1(B,C,A) = k3_rlvect_1(B,D,A)
=> ( A = np__0
| C = D ) ) ) ) ) ) ).
fof(t51_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [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) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( k3_rlvect_1(C,D,A) = k3_rlvect_1(C,D,B)
=> ( D = k1_rlvect_1(C)
| A = B ) ) ) ) ) ) ).
fof(d12_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k9_rlvect_1(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A))
& C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B))
& k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) = k1_rlvect_1(A)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( F = k1_funct_1(B,k1_nat_1(E,np__1))
=> ( r1_xreal_0(k3_finseq_1(B),E)
| k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ) ).
fof(t52_rlvect_1,axiom,
$true ).
fof(t53_rlvect_1,axiom,
$true ).
fof(t54_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k2_finseq_1(D))
& k3_finseq_1(B) = D )
=> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A)) ) ) ) ) ) ).
fof(t55_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1)
& C = k7_relat_1(B,k4_finseq_1(C))
& D = k1_funct_1(B,k3_finseq_1(B)) )
=> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D) ) ) ) ) ) ).
fof(t56_rlvect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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] :
( m2_finseq_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ( ( k3_finseq_1(C) = k3_finseq_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r2_hidden(E,k4_finseq_1(C))
& F = k1_funct_1(D,E) )
=> k1_funct_1(C,E) = k3_rlvect_1(B,F,A) ) ) ) )
=> k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A) ) ) ) ) ) ).
fof(t57_rlvect_1,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) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,k4_finseq_1(B))
& E = k1_funct_1(C,D) )
=> k1_funct_1(B,D) = k5_rlvect_1(A,E) ) ) ) )
=> k9_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,C)) ) ) ) ) ).
fof(t58_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) ).
fof(t59_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( ( k2_relat_1(B) = k2_relat_1(C)
& v2_funct_1(B)
& v2_funct_1(C) )
=> k9_rlvect_1(A,B) = k9_rlvect_1(A,C) ) ) ) ) ).
fof(t60_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A) ) ).
fof(t61_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) ).
fof(t62_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,B,C) ) ) ) ).
fof(t63_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) ) ) ) ) ).
fof(t64_rlvect_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_numbers)
=> k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A) ) ) ).
fof(t65_rlvect_1,axiom,
$true ).
fof(t66_rlvect_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_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) ) ) ).
fof(t67_rlvect_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_numbers)
=> ! [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))
=> k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B) = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) ) ) ) ) ) ).
fof(t68_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A) ) ).
fof(t69_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))) = k5_rlvect_1(A,B) ) ) ).
fof(t70_rlvect_1,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) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))) = k6_rlvect_1(A,k5_rlvect_1(A,B),C) ) ) ) ).
fof(t71_rlvect_1,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) )
=> ! [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))
=> k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))) = k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D) ) ) ) ) ).
fof(t72_rlvect_1,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) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k9_rlvect_1(A,k7_rlvect_1(A,C,B)) ) ) ) ).
fof(t73_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))) ) ) ) ).
fof(t74_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A) ) ).
fof(t75_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)) = B
& k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B ) ) ) ).
fof(t76_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) = k1_rlvect_1(A)
& k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)) = k1_rlvect_1(A) ) ) ) ).
fof(t77_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))) = k6_rlvect_1(A,B,C) ) ) ) ).
fof(t78_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)) ) ) ) ).
fof(t79_rlvect_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))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2) ) ) ).
fof(t80_rlvect_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))
=> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)) ) ) ).
fof(t81_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) ) ) ) ) ).
fof(t82_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(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))
=> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) ) ) ) ) ).
fof(t83_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C) ) ) ) ) ).
fof(t84_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) ) ) ) ) ).
fof(t85_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) ) ) ) ) ).
fof(t86_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) ) ) ) ) ).
fof(t87_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) ) ) ) ) ).
fof(t88_rlvect_1,axiom,
$true ).
fof(t89_rlvect_1,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) )
=> ! [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))
=> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)) ) ) ) ) ).
fof(t90_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A) ) ).
fof(t91_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)) = B
& k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))) = B
& k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) = B ) ) ) ).
fof(t92_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) = k2_rlvect_1(A,B,C)
& k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) = k2_rlvect_1(A,B,C)
& k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C) ) ) ) ) ).
fof(t93_rlvect_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))
=> k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)) = k3_rlvect_1(A,B,np__3) ) ) ).
fof(t94_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ( k3_finseq_1(B) = np__0
=> k9_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(t95_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ( k3_finseq_1(B) = np__1
=> k9_rlvect_1(A,B) = k1_funct_1(B,np__1) ) ) ) ).
fof(t96_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = np__2
& C = k1_funct_1(B,np__1)
& D = k1_funct_1(B,np__2) )
=> k9_rlvect_1(A,B) = k2_rlvect_1(A,C,D) ) ) ) ) ) ).
fof(t97_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_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))
=> ( ( k3_finseq_1(B) = np__3
& C = k1_funct_1(B,np__1)
& D = k1_funct_1(B,np__2)
& E = k1_funct_1(B,np__3) )
=> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E) ) ) ) ) ) ) ).
fof(d13_rlvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v8_rlvect_1(B,A)
<=> B != k1_rlvect_1(A) ) ) ) ).
fof(dt_l1_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ) ).
fof(existence_l1_rlvect_1,axiom,
? [A] : l1_rlvect_1(A) ).
fof(dt_l2_rlvect_1,axiom,
! [A] :
( l2_rlvect_1(A)
=> l1_rlvect_1(A) ) ).
fof(existence_l2_rlvect_1,axiom,
? [A] : l2_rlvect_1(A) ).
fof(abstractness_v1_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> ( v1_rlvect_1(A)
=> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) ).
fof(abstractness_v2_rlvect_1,axiom,
! [A] :
( l2_rlvect_1(A)
=> ( v2_rlvect_1(A)
=> A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ).
fof(dt_k1_rlvect_1,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ).
fof(dt_k2_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k4_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k4_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ).
fof(redefinition_k4_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ).
fof(dt_k5_rlvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ).
fof(dt_k6_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k7_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k7_rlvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C) ) ).
fof(dt_k8_rlvect_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)) ) ).
fof(redefinition_k8_rlvect_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D) ) ).
fof(dt_k9_rlvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_finseq_1(B,u1_struct_0(A)) )
=> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)) ) ).
fof(dt_u1_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> ( v1_funct_1(u1_rlvect_1(A))
& v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u2_rlvect_1,axiom,
! [A] :
( l2_rlvect_1(A)
=> ( v1_funct_1(u2_rlvect_1(A))
& v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_g1_rlvect_1,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_subset_1(C,A) )
=> ( v1_rlvect_1(g1_rlvect_1(A,B,C))
& l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ).
fof(free_g1_rlvect_1,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_subset_1(C,A) )
=> ! [D,E,F] :
( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g2_rlvect_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
=> ( v2_rlvect_1(g2_rlvect_1(A,B,C,D))
& l2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ).
fof(free_g2_rlvect_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
=> ! [E,F,G,H] :
( g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
%------------------------------------------------------------------------------