SET007 Axioms: SET007+224.ax
%------------------------------------------------------------------------------
% File : SET007+224 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Linear Combinations 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 171 ( 37 unt; 0 def)
% Number of atoms : 1255 ( 118 equ)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1218 ( 134 ~; 1 |; 730 &)
% ( 19 <=>; 334 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 1 prp; 0-4 aty)
% Number of functors : 71 ( 71 usr; 5 con; 0-6 aty)
% Number of variables : 384 ( 375 !; 9 ?)
% 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_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B) ) ) ).
fof(rc2_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(fc1_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ~ v1_xboole_0(k18_rlvect_2(A)) ) ).
fof(fc2_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k23_rlvect_2(A))
& v2_rlvect_1(k23_rlvect_2(A))
& v3_rlvect_1(k23_rlvect_2(A))
& v4_rlvect_1(k23_rlvect_2(A))
& v5_rlvect_1(k23_rlvect_2(A))
& v6_rlvect_1(k23_rlvect_2(A))
& v7_rlvect_1(k23_rlvect_2(A)) ) ) ).
fof(d1_rlvect_2,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( r1_rlvect_1(A,B)
=> k1_rlvect_2(A,B) = B ) ) ).
fof(t1_rlvect_2,axiom,
$true ).
fof(t2_rlvect_2,axiom,
$true ).
fof(t3_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_rlvect_2(A,B) = B ) ) ).
fof(t4_rlvect_2,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))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& k3_finseq_1(B) = k3_finseq_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k1_relat_1(B))
=> k1_funct_1(D,E) = k4_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) ) ) )
=> k9_rlvect_1(A,D) = k4_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) ) ) ).
fof(t5_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( ( k3_finseq_1(C) = k3_finseq_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k1_relat_1(C))
=> k1_funct_1(D,E) = k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E),B) ) ) )
=> k9_rlvect_1(A,D) = k3_rlvect_1(A,k9_rlvect_1(A,C),B) ) ) ) ) ) ).
fof(t6_rlvect_2,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)
=> ( r2_hidden(D,k1_relat_1(B))
=> k1_funct_1(C,D) = k5_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,D)) ) ) )
=> k9_rlvect_1(A,C) = k5_rlvect_1(A,k9_rlvect_1(A,B)) ) ) ) ) ).
fof(t7_rlvect_2,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))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& k3_finseq_1(B) = k3_finseq_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k1_relat_1(B))
=> k1_funct_1(D,E) = k6_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) ) ) )
=> k9_rlvect_1(A,D) = k6_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) ) ) ).
fof(t8_rlvect_2,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))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_relat_1(B),k1_relat_1(B))
& v3_funct_2(D,k1_relat_1(B),k1_relat_1(B))
& m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) )
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k1_relat_1(C))
=> k1_funct_1(C,E) = k1_funct_1(B,k1_funct_1(D,E)) ) ) )
=> k9_rlvect_1(A,B) = k9_rlvect_1(A,C) ) ) ) ) ) ).
fof(t9_rlvect_2,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))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_relat_1(B),k1_relat_1(B))
& v3_funct_2(D,k1_relat_1(B),k1_relat_1(B))
& m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) )
=> ( C = k5_relat_1(D,B)
=> k9_rlvect_1(A,B) = k9_rlvect_1(A,C) ) ) ) ) ) ).
fof(d2_rlvect_2,axiom,
$true ).
fof(d3_rlvect_2,axiom,
$true ).
fof(d4_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k6_rlvect_2(A,B)
<=> ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& k2_relat_1(D) = B
& v2_funct_1(D)
& C = k9_rlvect_1(A,D) ) ) ) ) ) ) ).
fof(t10_rlvect_2,axiom,
$true ).
fof(t11_rlvect_2,axiom,
$true ).
fof(t12_rlvect_2,axiom,
$true ).
fof(t13_rlvect_2,axiom,
$true ).
fof(t14_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> k6_rlvect_2(A,k1_pre_topc(A)) = k1_rlvect_1(A) ) ).
fof(t15_rlvect_2,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))
=> k6_rlvect_2(A,k7_rlvect_2(A,B)) = B ) ) ).
fof(t16_rlvect_2,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))
=> ( B != C
=> k6_rlvect_2(A,k8_rlvect_2(A,B,C)) = k4_rlvect_1(A,B,C) ) ) ) ) ).
fof(t17_rlvect_2,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))
=> ~ ( B != C
& C != D
& B != D
& k6_rlvect_2(A,k9_rlvect_2(A,B,C,D)) != k4_rlvect_1(A,k4_rlvect_1(A,B,C),D) ) ) ) ) ) ).
fof(t18_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_xboole_0(C,B)
=> k6_rlvect_2(A,k2_rlvect_2(A,C,B)) = k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)) ) ) ) ) ).
fof(t19_rlvect_2,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k2_rlvect_2(A,C,B)) = k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))) ) ) ) ).
fof(t20_rlvect_2,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k3_rlvect_2(A,C,B)) = k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k2_rlvect_2(A,C,B))) ) ) ) ).
fof(t21_rlvect_2,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k4_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,B)) ) ) ) ).
fof(t22_rlvect_2,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k4_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,k3_rlvect_2(A,C,B))) ) ) ) ).
fof(t23_rlvect_2,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k5_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))) ) ) ) ).
fof(t24_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_rlvect_2(A,k5_rlvect_2(A,C,B)) = k4_rlvect_1(A,k6_rlvect_2(A,k4_rlvect_2(A,C,B)),k6_rlvect_2(A,k4_rlvect_2(A,B,C))) ) ) ) ).
fof(d5_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers))
=> ( m1_rlvect_2(B,A)
<=> ? [C] :
( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ~ r2_hidden(D,C)
=> k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = np__0 ) ) ) ) ) ) ).
fof(t25_rlvect_2,axiom,
$true ).
fof(t26_rlvect_2,axiom,
$true ).
fof(t27_rlvect_2,axiom,
$true ).
fof(t28_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),k1_numbers,B,C) = np__0
<=> ~ r2_hidden(C,k10_rlvect_2(A,B)) ) ) ) ) ).
fof(d7_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ( B = k11_rlvect_2(A)
<=> k10_rlvect_2(A,B) = k1_xboole_0 ) ) ) ).
fof(t29_rlvect_2,axiom,
$true ).
fof(t30_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,k11_rlvect_2(A),B) = np__0 ) ) ).
fof(d8_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( m2_rlvect_2(C,A,B)
<=> r1_tarski(k10_rlvect_2(A,C),B) ) ) ) ) ).
fof(t31_rlvect_2,axiom,
$true ).
fof(t32_rlvect_2,axiom,
$true ).
fof(t33_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m2_rlvect_2(D,A,B)
=> ( r1_tarski(B,C)
=> m2_rlvect_2(D,A,C) ) ) ) ) ) ).
fof(t34_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> m2_rlvect_2(k11_rlvect_2(A),A,B) ) ) ).
fof(t35_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A)))
=> B = k11_rlvect_2(A) ) ) ).
fof(d9_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k12_rlvect_2(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k1_relat_1(D))
=> k1_funct_1(D,E) = k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E))) ) ) ) ) ) ) ) ) ).
fof(t36_rlvect_2,axiom,
$true ).
fof(t37_rlvect_2,axiom,
$true ).
fof(t38_rlvect_2,axiom,
$true ).
fof(t39_rlvect_2,axiom,
$true ).
fof(t40_rlvect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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] :
( m2_finseq_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),k1_numbers)
& m2_relset_1(E,u1_struct_0(B),k1_numbers) )
=> ( ( r2_hidden(A,k1_relat_1(D))
& C = k1_funct_1(D,A) )
=> k1_funct_1(k12_rlvect_2(B,D,E),A) = k3_rlvect_1(B,C,k8_funct_2(u1_struct_0(B),k1_numbers,E,C)) ) ) ) ) ) ) ).
fof(t41_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> k12_rlvect_2(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) ).
fof(t42_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> k12_rlvect_2(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B))) ) ) ) ).
fof(t43_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k1_numbers)
& m2_relset_1(D,u1_struct_0(A),k1_numbers) )
=> k12_rlvect_2(A,k2_finseq_4(u1_struct_0(A),B,C),D) = k2_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ).
fof(t44_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),k1_numbers)
& m2_relset_1(E,u1_struct_0(A),k1_numbers) )
=> k12_rlvect_2(A,k3_finseq_4(u1_struct_0(A),B,C,D),E) = k3_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C)),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))) ) ) ) ) ) ).
fof(d10_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k13_rlvect_2(A,B)
<=> ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& v2_funct_1(D)
& k2_relat_1(D) = k10_rlvect_2(A,B)
& C = k9_rlvect_1(A,k12_rlvect_2(A,D,B)) ) ) ) ) ) ).
fof(t45_rlvect_2,axiom,
$true ).
fof(t46_rlvect_2,axiom,
$true ).
fof(t47_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B != k1_xboole_0
& v1_rlsub_1(B,A) )
<=> ! [C] :
( m2_rlvect_2(C,A,B)
=> r2_hidden(k13_rlvect_2(A,C),B) ) ) ) ) ).
fof(t48_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> k13_rlvect_2(A,k11_rlvect_2(A)) = k1_rlvect_1(A) ) ).
fof(t49_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A)))
=> k13_rlvect_2(A,B) = k1_rlvect_1(A) ) ) ).
fof(t50_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_rlvect_2(C,A,k7_rlvect_2(A,B))
=> k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ).
fof(t51_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != C
=> ! [D] :
( m2_rlvect_2(D,A,k8_rlvect_2(A,B,C))
=> k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ).
fof(t52_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ( k10_rlvect_2(A,B) = k1_xboole_0
=> k13_rlvect_2(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(t53_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( k10_rlvect_2(A,C) = k7_rlvect_2(A,B)
=> k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ) ).
fof(t54_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( k10_rlvect_2(A,D) = k8_rlvect_2(A,B,C)
=> ( B = C
| k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) ).
fof(d11_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( r1_rlvect_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = k8_funct_2(u1_struct_0(A),k1_numbers,C,D) ) ) ) ) ) ).
fof(d12_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( D = k14_rlvect_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) ).
fof(t55_rlvect_2,axiom,
$true ).
fof(t56_rlvect_2,axiom,
$true ).
fof(t57_rlvect_2,axiom,
$true ).
fof(t58_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> r1_tarski(k10_rlvect_2(A,k14_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))) ) ) ) ).
fof(t59_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( ( m2_rlvect_2(C,A,B)
& m2_rlvect_2(D,A,B) )
=> m2_rlvect_2(k14_rlvect_2(A,C,D),A,B) ) ) ) ) ) ).
fof(t60_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> r1_rlvect_2(A,k14_rlvect_2(A,B,C),k14_rlvect_2(A,C,B)) ) ) ) ).
fof(t61_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> r1_rlvect_2(A,k14_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k14_rlvect_2(A,B,C),D)) ) ) ) ) ).
fof(t62_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ( r1_rlvect_2(A,k14_rlvect_2(A,B,k11_rlvect_2(A)),B)
& r1_rlvect_2(A,k14_rlvect_2(A,k11_rlvect_2(A),B),B) ) ) ) ).
fof(d13_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( D = k15_rlvect_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,D,E) = k4_real_1(B,k8_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) ).
fof(t63_rlvect_2,axiom,
$true ).
fof(t64_rlvect_2,axiom,
$true ).
fof(t65_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( B != np__0
=> k10_rlvect_2(A,k15_rlvect_2(A,B,C)) = k10_rlvect_2(A,C) ) ) ) ) ).
fof(t66_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> r1_rlvect_2(A,k15_rlvect_2(A,np__0,B),k11_rlvect_2(A)) ) ) ).
fof(t67_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( m2_rlvect_2(D,A,C)
=> m2_rlvect_2(k15_rlvect_2(A,B,D),A,C) ) ) ) ) ) ).
fof(t68_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_rlvect_2(D,A)
=> r1_rlvect_2(A,k15_rlvect_2(A,k3_real_1(B,C),D),k14_rlvect_2(A,k15_rlvect_2(A,B,D),k15_rlvect_2(A,C,D))) ) ) ) ) ).
fof(t69_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> r1_rlvect_2(A,k15_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k15_rlvect_2(A,B,C),k15_rlvect_2(A,B,D))) ) ) ) ) ).
fof(t70_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_rlvect_2(D,A)
=> r1_rlvect_2(A,k15_rlvect_2(A,B,k15_rlvect_2(A,C,D)),k15_rlvect_2(A,k4_real_1(B,C),D)) ) ) ) ) ).
fof(t71_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> r1_rlvect_2(A,k15_rlvect_2(A,np__1,B),B) ) ) ).
fof(d14_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k16_rlvect_2(A,B) = k15_rlvect_2(A,k1_real_1(np__1),B) ) ) ).
fof(t72_rlvect_2,axiom,
$true ).
fof(t73_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rlvect_2(C,A)
=> k8_funct_2(u1_struct_0(A),k1_numbers,k16_rlvect_2(A,C),B) = k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ).
fof(t74_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( r1_rlvect_2(A,k14_rlvect_2(A,B,C),k11_rlvect_2(A))
=> r1_rlvect_2(A,C,k16_rlvect_2(A,B)) ) ) ) ) ).
fof(t75_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k10_rlvect_2(A,k16_rlvect_2(A,B)) = k10_rlvect_2(A,B) ) ) ).
fof(t76_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( m2_rlvect_2(C,A,B)
=> m2_rlvect_2(k16_rlvect_2(A,C),A,B) ) ) ) ) ).
fof(t77_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> r1_rlvect_2(A,k16_rlvect_2(A,k16_rlvect_2(A,B)),B) ) ) ).
fof(d15_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k17_rlvect_2(A,B,C) = k14_rlvect_2(A,B,k16_rlvect_2(A,C)) ) ) ) ).
fof(t78_rlvect_2,axiom,
$true ).
fof(t79_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> k8_funct_2(u1_struct_0(A),k1_numbers,k17_rlvect_2(A,C,D),B) = k5_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,B)) ) ) ) ) ).
fof(t80_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> r1_tarski(k10_rlvect_2(A,k17_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))) ) ) ) ).
fof(t81_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( ( m2_rlvect_2(C,A,B)
& m2_rlvect_2(D,A,B) )
=> m2_rlvect_2(k17_rlvect_2(A,C,D),A,B) ) ) ) ) ) ).
fof(t82_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> r1_rlvect_2(A,k17_rlvect_2(A,B,B),k11_rlvect_2(A)) ) ) ).
fof(d16_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( B = k18_rlvect_2(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> m1_rlvect_2(C,A) ) ) ) ).
fof(d17_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k18_rlvect_2(A))
=> k19_rlvect_2(A,B) = B ) ) ).
fof(d18_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k20_rlvect_2(A,B) = B ) ) ).
fof(d19_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A))
& m2_relset_1(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) )
=> ( B = k21_rlvect_2(A)
<=> ! [C] :
( m1_subset_1(C,k18_rlvect_2(A))
=> ! [D] :
( m1_subset_1(D,k18_rlvect_2(A))
=> k2_binop_1(k18_rlvect_2(A),k18_rlvect_2(A),k18_rlvect_2(A),B,C,D) = k14_rlvect_2(A,k19_rlvect_2(A,C),k19_rlvect_2(A,D)) ) ) ) ) ) ).
fof(d20_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A))
& m2_relset_1(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) )
=> ( B = k22_rlvect_2(A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k18_rlvect_2(A))
=> k1_funct_1(B,k4_tarski(C,D)) = k15_rlvect_2(A,C,k19_rlvect_2(A,D)) ) ) ) ) ) ).
fof(d21_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> k23_rlvect_2(A) = g2_rlvect_1(k18_rlvect_2(A),k20_rlvect_2(A,k11_rlvect_2(A)),k21_rlvect_2(A),k22_rlvect_2(A)) ) ).
fof(t83_rlvect_2,axiom,
$true ).
fof(t84_rlvect_2,axiom,
$true ).
fof(t85_rlvect_2,axiom,
$true ).
fof(t86_rlvect_2,axiom,
$true ).
fof(t87_rlvect_2,axiom,
$true ).
fof(t88_rlvect_2,axiom,
$true ).
fof(t89_rlvect_2,axiom,
$true ).
fof(t90_rlvect_2,axiom,
$true ).
fof(t91_rlvect_2,axiom,
$true ).
fof(t92_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> u1_struct_0(k23_rlvect_2(A)) = k18_rlvect_2(A) ) ).
fof(t93_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> u2_struct_0(k23_rlvect_2(A)) = k11_rlvect_2(A) ) ).
fof(t94_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> u1_rlvect_1(k23_rlvect_2(A)) = k21_rlvect_2(A) ) ).
fof(t95_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> u2_rlvect_1(k23_rlvect_2(A)) = k22_rlvect_2(A) ) ).
fof(t96_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k4_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)) = k14_rlvect_2(A,B,C) ) ) ) ).
fof(t97_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k3_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),C),B) = k15_rlvect_2(A,B,C) ) ) ) ).
fof(t98_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k5_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B)) = k16_rlvect_2(A,B) ) ) ).
fof(t99_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k6_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)) = k17_rlvect_2(A,B,C) ) ) ) ).
fof(dt_m1_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)) ) ) ).
fof(existence_m1_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ? [B] : m1_rlvect_2(B,A) ) ).
fof(dt_m2_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_rlvect_2(C,A,B)
=> m1_rlvect_2(C,A) ) ) ).
fof(existence_m2_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] : m2_rlvect_2(C,A,B) ) ).
fof(symmetry_r1_rlvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_rlvect_2(B,A)
& m1_rlvect_2(C,A) )
=> ( r1_rlvect_2(A,B,C)
=> r1_rlvect_2(A,C,B) ) ) ).
fof(reflexivity_r1_rlvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_rlvect_2(B,A)
& m1_rlvect_2(C,A) )
=> r1_rlvect_2(A,B,B) ) ).
fof(redefinition_r1_rlvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_rlvect_2(B,A)
& m1_rlvect_2(C,A) )
=> ( r1_rlvect_2(A,B,C)
<=> B = C ) ) ).
fof(dt_k1_rlvect_2,axiom,
! [A,B] :
( l1_struct_0(A)
=> m1_subset_1(k1_rlvect_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k2_rlvect_2(A,B,C))
& m1_subset_1(k2_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(commutativity_k2_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_rlvect_2(A,B,C) = k2_rlvect_2(A,C,B) ) ).
fof(idempotence_k2_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_rlvect_2(A,B,B) = B ) ).
fof(redefinition_k2_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_rlvect_2(A,B,C) = k2_xboole_0(B,C) ) ).
fof(dt_k3_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k3_rlvect_2(A,B,C))
& m1_subset_1(k3_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(commutativity_k3_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_rlvect_2(A,B,C) = k3_rlvect_2(A,C,B) ) ).
fof(idempotence_k3_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_rlvect_2(A,B,B) = B ) ).
fof(redefinition_k3_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_rlvect_2(A,B,C) = k3_xboole_0(B,C) ) ).
fof(dt_k4_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k4_rlvect_2(A,B,C))
& m1_subset_1(k4_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k4_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_rlvect_2(A,B,C) = k4_xboole_0(B,C) ) ).
fof(dt_k5_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k5_rlvect_2(A,B,C))
& m1_subset_1(k5_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(commutativity_k5_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k5_rlvect_2(A,B,C) = k5_rlvect_2(A,C,B) ) ).
fof(redefinition_k5_rlvect_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k5_rlvect_2(A,B,C) = k5_xboole_0(B,C) ) ).
fof(dt_k6_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k6_rlvect_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k7_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_finset_1(k7_rlvect_2(A,B))
& m1_subset_1(k7_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k7_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k7_rlvect_2(A,B) = k1_tarski(B) ) ).
fof(dt_k8_rlvect_2,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)) )
=> ( v1_finset_1(k8_rlvect_2(A,B,C))
& m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(commutativity_k8_rlvect_2,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)) )
=> k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B) ) ).
fof(redefinition_k8_rlvect_2,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)) )
=> k8_rlvect_2(A,B,C) = k2_tarski(B,C) ) ).
fof(dt_k9_rlvect_2,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)) )
=> ( v1_finset_1(k9_rlvect_2(A,B,C,D))
& m1_subset_1(k9_rlvect_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k9_rlvect_2,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)) )
=> k9_rlvect_2(A,B,C,D) = k1_enumset1(B,C,D) ) ).
fof(dt_k10_rlvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_rlvect_2(B,A) )
=> ( v1_finset_1(k10_rlvect_2(A,B))
& m1_subset_1(k10_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(dt_k11_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> m1_rlvect_2(k11_rlvect_2(A),A) ) ).
fof(dt_k12_rlvect_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)
& l2_rlvect_1(A)
& m1_finseq_1(B,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m1_relset_1(C,u1_struct_0(A),k1_numbers) )
=> m2_finseq_1(k12_rlvect_2(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k13_rlvect_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)
& l2_rlvect_1(A)
& m1_rlvect_2(B,A) )
=> m1_subset_1(k13_rlvect_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k14_rlvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_rlvect_2(B,A)
& m1_rlvect_2(C,A) )
=> m1_rlvect_2(k14_rlvect_2(A,B,C),A) ) ).
fof(dt_k15_rlvect_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)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_numbers)
& m1_rlvect_2(C,A) )
=> m1_rlvect_2(k15_rlvect_2(A,B,C),A) ) ).
fof(dt_k16_rlvect_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)
& l2_rlvect_1(A)
& m1_rlvect_2(B,A) )
=> m1_rlvect_2(k16_rlvect_2(A,B),A) ) ).
fof(dt_k17_rlvect_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)
& l2_rlvect_1(A)
& m1_rlvect_2(B,A)
& m1_rlvect_2(C,A) )
=> m1_rlvect_2(k17_rlvect_2(A,B,C),A) ) ).
fof(dt_k18_rlvect_2,axiom,
$true ).
fof(dt_k19_rlvect_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)
& l2_rlvect_1(A)
& m1_subset_1(B,k18_rlvect_2(A)) )
=> m1_rlvect_2(k19_rlvect_2(A,B),A) ) ).
fof(dt_k20_rlvect_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)
& l2_rlvect_1(A)
& m1_rlvect_2(B,A) )
=> m1_subset_1(k20_rlvect_2(A,B),k18_rlvect_2(A)) ) ).
fof(dt_k21_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( v1_funct_1(k21_rlvect_2(A))
& v1_funct_2(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A))
& m2_relset_1(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) ) ) ).
fof(dt_k22_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( v1_funct_1(k22_rlvect_2(A))
& v1_funct_2(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A))
& m2_relset_1(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) ) ) ).
fof(dt_k23_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k23_rlvect_2(A))
& v3_rlvect_1(k23_rlvect_2(A))
& v4_rlvect_1(k23_rlvect_2(A))
& v5_rlvect_1(k23_rlvect_2(A))
& v6_rlvect_1(k23_rlvect_2(A))
& v7_rlvect_1(k23_rlvect_2(A))
& l2_rlvect_1(k23_rlvect_2(A)) ) ) ).
fof(dt_k24_rlvect_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)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_rlvect_1(k24_rlvect_2(A,B))
& m1_rlsub_1(k24_rlvect_2(A,B),k23_rlvect_2(A)) ) ) ).
fof(d6_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k10_rlvect_2(A,B) = a_2_0_rlvect_2(A,B) ) ) ).
fof(d22_rlvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,k23_rlvect_2(A)) )
=> ( C = k24_rlvect_2(A,B)
<=> u1_struct_0(C) = a_2_1_rlvect_2(A,B) ) ) ) ) ).
fof(fraenkel_a_2_0_rlvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B)
& m1_rlvect_2(C,B) )
=> ( r2_hidden(A,a_2_0_rlvect_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& k8_funct_2(u1_struct_0(B),k1_numbers,C,D) != np__0 ) ) ) ).
fof(fraenkel_a_2_1_rlvect_2,axiom,
! [A,B,C] :
( ( ~ 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))) )
=> ( r2_hidden(A,a_2_1_rlvect_2(B,C))
<=> ? [D] :
( m2_rlvect_2(D,B,C)
& A = D ) ) ) ).
%------------------------------------------------------------------------------