SET007 Axioms: SET007+808.ax
%------------------------------------------------------------------------------
% File : SET007+808 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex Linear Space and Complex Normed 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 : clvect_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 178 ( 3 unt; 0 def)
% Number of atoms : 2063 ( 164 equ)
% Maximal formula atoms : 35 ( 11 avg)
% Number of connectives : 2079 ( 194 ~; 6 |;1262 &)
% ( 37 <=>; 580 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 8 con; 0-5 aty)
% Number of variables : 588 ( 565 !; 23 ?)
% 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_clvect_1,axiom,
? [A] :
( l1_clvect_1(A)
& v1_clvect_1(A) ) ).
fof(rc2_clvect_1,axiom,
? [A] :
( l1_clvect_1(A)
& ~ v3_struct_0(A) ) ).
fof(fc1_clvect_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(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A) )
=> ( ~ v3_struct_0(g1_clvect_1(A,B,C,D))
& v1_clvect_1(g1_clvect_1(A,B,C,D)) ) ) ).
fof(rc3_clvect_1,axiom,
? [A] :
( l1_clvect_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_clvect_1(A)
& v2_clvect_1(A) ) ).
fof(rc4_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ? [B] :
( m1_clvect_1(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_clvect_1(B)
& v2_clvect_1(B) ) ) ).
fof(rc5_clvect_1,axiom,
? [A] :
( l2_clvect_1(A)
& v4_clvect_1(A) ) ).
fof(rc6_clvect_1,axiom,
? [A] :
( l2_clvect_1(A)
& ~ v3_struct_0(A) ) ).
fof(rc7_clvect_1,axiom,
? [A] :
( l2_clvect_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v4_clvect_1(A)
& v5_clvect_1(A) ) ).
fof(d1_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k1_clvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A),u1_clvect_1(A),k1_domain_1(k2_numbers,u1_struct_0(A),C,B)) ) ) ) ).
fof(d2_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clvect_1(A) )
=> ( v2_clvect_1(A)
<=> ( ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_clvect_1(A,C,B),k1_clvect_1(A,D,B)) ) ) )
& ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,D,k8_complex1(B,C)) = k2_rlvect_1(A,k1_clvect_1(A,D,B),k1_clvect_1(A,D,C)) ) ) )
& ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,D,k9_complex1(B,C)) = k1_clvect_1(A,k1_clvect_1(A,D,C),B) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_clvect_1(A,B,k6_complex1) = B ) ) ) ) ).
fof(t1_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clvect_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,k2_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_clvect_1(A,C,B),k1_clvect_1(A,D,B)) ) ) )
& ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,D,k8_complex1(B,C)) = k2_rlvect_1(A,k1_clvect_1(A,D,B),k1_clvect_1(A,D,C)) ) ) )
& ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,D,k9_complex1(B,C)) = k1_clvect_1(A,k1_clvect_1(A,D,C),B) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_clvect_1(A,B,k6_complex1) = B ) )
=> ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) ) ) ) ).
fof(t2_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( ( C = np__0
| B = k1_rlvect_1(A) )
=> k1_clvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ).
fof(t3_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ~ ( k1_clvect_1(A,B,C) = k1_rlvect_1(A)
& C != np__0
& B != k1_rlvect_1(A) ) ) ) ) ).
fof(t4_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_rlvect_1(A,B) = k1_clvect_1(A,B,k10_complex1(k6_complex1)) ) ) ).
fof(t5_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k5_rlvect_1(A,B)
=> B = k1_rlvect_1(A) ) ) ) ).
fof(t6_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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(t7_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k1_clvect_1(A,k5_rlvect_1(A,B),C) = k1_clvect_1(A,B,k10_complex1(C)) ) ) ) ).
fof(t8_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k1_clvect_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k1_clvect_1(A,B,C)) ) ) ) ).
fof(t9_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k1_clvect_1(A,k5_rlvect_1(A,B),k10_complex1(C)) = k1_clvect_1(A,B,C) ) ) ) ).
fof(t10_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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,k2_numbers)
=> k1_clvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_clvect_1(A,B,D),k1_clvect_1(A,C,D)) ) ) ) ) ).
fof(t11_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k1_clvect_1(A,B,k11_complex1(C,D)) = k6_rlvect_1(A,k1_clvect_1(A,B,C),k1_clvect_1(A,B,D)) ) ) ) ) ).
fof(t12_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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,k2_numbers)
=> ( k1_clvect_1(A,B,D) = k1_clvect_1(A,C,D)
=> ( D = np__0
| B = C ) ) ) ) ) ) ).
fof(t13_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( k1_clvect_1(A,B,C) = k1_clvect_1(A,B,D)
=> ( B = k1_rlvect_1(A)
| C = D ) ) ) ) ) ) ).
fof(t14_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_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)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(E,k4_finseq_1(C))
& F = k1_funct_1(D,E) )
=> k1_funct_1(C,E) = k1_clvect_1(A,F,B) ) ) ) )
=> k9_rlvect_1(A,C) = k1_clvect_1(A,k9_rlvect_1(A,D),B) ) ) ) ) ) ).
fof(t15_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k1_clvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A) ) ) ).
fof(t16_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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,k2_numbers)
=> k1_clvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) = k4_rlvect_1(A,k1_clvect_1(A,B,D),k1_clvect_1(A,C,D)) ) ) ) ) ).
fof(t17_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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,k2_numbers)
=> k1_clvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)),E) = k4_rlvect_1(A,k4_rlvect_1(A,k1_clvect_1(A,B,E),k1_clvect_1(A,C,E)),k1_clvect_1(A,D,E)) ) ) ) ) ) ).
fof(t18_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k1_clvect_1(A,B,k5_arytm_0(np__2,np__0)) ) ) ).
fof(t19_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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))) = k1_clvect_1(A,B,k5_arytm_0(k1_real_1(np__2),np__0)) ) ) ).
fof(t20_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)) = k1_clvect_1(A,B,k5_arytm_0(np__3,np__0)) ) ) ).
fof(d3_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_rlvect_1(A,C,D),B) ) ) )
& ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r2_hidden(k1_clvect_1(A,D,C),B) ) ) ) ) ) ) ) ).
fof(t21_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ( B = k1_xboole_0
| r2_hidden(k1_rlvect_1(A),B) ) ) ) ) ).
fof(t22_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) ) ).
fof(t23_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) ).
fof(t24_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> v3_clvect_1(k1_struct_0(A,k1_rlvect_1(A)),A) ) ).
fof(t25_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( u1_struct_0(A) = B
=> v3_clvect_1(B,A) ) ) ) ).
fof(t27_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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)))
=> ( ( v3_clvect_1(B,A)
& v3_clvect_1(C,A) )
=> v3_clvect_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d4_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B) )
=> ( m1_clvect_1(B,A)
<=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& u2_struct_0(B) = u2_struct_0(A)
& u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
& u1_clvect_1(B) = k2_partfun1(k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A),u1_clvect_1(A),k2_zfmisc_1(k2_numbers,u1_struct_0(B))) ) ) ) ) ).
fof(t28_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> ! [D] :
( ( r1_rlvect_1(B,D)
& m1_clvect_1(B,C) )
=> r1_rlvect_1(C,D) ) ) ) ) ).
fof(t29_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( r1_rlvect_1(B,C)
=> r1_rlvect_1(A,C) ) ) ) ).
fof(t30_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t31_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> k1_rlvect_1(B) = k1_rlvect_1(A) ) ) ).
fof(t32_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) ).
fof(t33_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( ( E = B
& F = C )
=> k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C) ) ) ) ) ) ) ) ).
fof(t34_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ( E = B
=> k1_clvect_1(D,E,C) = k1_clvect_1(A,B,C) ) ) ) ) ) ) ).
fof(t35_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( D = B
=> k5_rlvect_1(A,B) = k5_rlvect_1(C,D) ) ) ) ) ) ).
fof(t36_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( ( E = B
& F = C )
=> k6_rlvect_1(D,E,F) = k6_rlvect_1(A,B,C) ) ) ) ) ) ) ) ).
fof(t37_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> r1_rlvect_1(B,k1_rlvect_1(A)) ) ) ).
fof(t38_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) ).
fof(t39_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> r1_rlvect_1(A,k1_rlvect_1(B)) ) ) ).
fof(t40_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( ( r1_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k4_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t41_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r1_rlvect_1(D,B)
=> r1_rlvect_1(D,k1_clvect_1(A,B,C)) ) ) ) ) ) ).
fof(t42_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r1_rlvect_1(C,B)
=> r1_rlvect_1(C,k5_rlvect_1(A,B)) ) ) ) ) ).
fof(t43_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( ( r1_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t44_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,C),C)
& m2_relset_1(E,k2_zfmisc_1(C,C),C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(k2_numbers,C),C)
& m2_relset_1(F,k2_zfmisc_1(k2_numbers,C),C) )
=> ( ( B = C
& D = k1_rlvect_1(A)
& E = k1_realset1(u1_rlvect_1(A),B)
& F = k2_partfun1(k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A),u1_clvect_1(A),k2_zfmisc_1(k2_numbers,B)) )
=> m1_clvect_1(g1_clvect_1(C,D,E,F),A) ) ) ) ) ) ) ) ).
fof(t45_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> m1_clvect_1(A,A) ) ).
fof(t46_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_clvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_clvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B) )
=> ( ( m1_clvect_1(A,B)
& m1_clvect_1(B,A) )
=> A = B ) ) ) ).
fof(t47_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& l1_clvect_1(C) )
=> ( ( m1_clvect_1(A,B)
& m1_clvect_1(B,C) )
=> m1_clvect_1(A,C) ) ) ) ) ).
fof(t48_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_clvect_1(B,C) ) ) ) ) ).
fof(t49_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
=> r1_rlvect_1(C,D) ) )
=> m1_clvect_1(B,C) ) ) ) ) ).
fof(t50_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ! [C] :
( ( v1_clvect_1(C)
& m1_clvect_1(C,A) )
=> ( u1_struct_0(B) = u1_struct_0(C)
=> B = C ) ) ) ) ).
fof(t51_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ! [C] :
( ( v1_clvect_1(C)
& m1_clvect_1(C,A) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
<=> r1_rlvect_1(C,D) ) )
=> B = C ) ) ) ) ).
fof(t52_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_clvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ( u1_struct_0(B) = u1_struct_0(A)
=> B = A ) ) ) ).
fof(t53_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_clvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> r1_rlvect_1(A,C) ) )
=> B = A ) ) ) ).
fof(t54_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( u1_struct_0(C) = B
=> v3_clvect_1(B,A) ) ) ) ) ).
fof(t55_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( B != k1_xboole_0
& v3_clvect_1(B,A)
& ! [C] :
( ( v1_clvect_1(C)
& m1_clvect_1(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(d5_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ( B = k2_clvect_1(A)
<=> u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ) ).
fof(d6_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> k3_clvect_1(A) = g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)) ) ).
fof(t56_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> k2_clvect_1(B) = k2_clvect_1(A) ) ) ).
fof(t57_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> k2_clvect_1(B) = k2_clvect_1(C) ) ) ) ).
fof(t58_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> m1_clvect_1(k2_clvect_1(B),A) ) ) ).
fof(t59_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> m1_clvect_1(k2_clvect_1(A),B) ) ) ).
fof(t60_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_clvect_1(C,A)
=> m1_clvect_1(k2_clvect_1(B),C) ) ) ) ).
fof(t61_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_clvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> m1_clvect_1(A,k3_clvect_1(A)) ) ).
fof(d8_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_clvect_1(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k4_clvect_1(A,D,B) ) ) ) ) ) ).
fof(t62_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r2_hidden(k1_rlvect_1(A),k4_clvect_1(A,B,C))
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t63_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> r2_hidden(B,k4_clvect_1(A,B,C)) ) ) ) ).
fof(t64_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> k4_clvect_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) ).
fof(t65_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_clvect_1(A,B,k2_clvect_1(A)) = k1_struct_0(A,B) ) ) ).
fof(t66_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_clvect_1(A,B,k3_clvect_1(A)) = u1_struct_0(A) ) ) ).
fof(t67_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r2_hidden(k1_rlvect_1(A),k4_clvect_1(A,B,C))
<=> k4_clvect_1(A,B,C) = u1_struct_0(C) ) ) ) ) ).
fof(t68_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r1_rlvect_1(C,B)
<=> k4_clvect_1(A,B,C) = u1_struct_0(C) ) ) ) ) ).
fof(t69_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r1_rlvect_1(D,B)
=> k4_clvect_1(A,k1_clvect_1(A,B,C),D) = u1_struct_0(D) ) ) ) ) ) ).
fof(t70_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ( k4_clvect_1(A,k1_clvect_1(A,B,C),D) = u1_struct_0(D)
=> ( C = np__0
| r1_rlvect_1(D,B) ) ) ) ) ) ) ).
fof(t71_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r1_rlvect_1(C,B)
<=> k4_clvect_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C) ) ) ) ) ).
fof(t72_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r1_rlvect_1(D,B)
<=> k4_clvect_1(A,C,D) = k4_clvect_1(A,k4_rlvect_1(A,C,B),D) ) ) ) ) ) ).
fof(t73_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r1_rlvect_1(D,B)
<=> k4_clvect_1(A,C,D) = k4_clvect_1(A,k6_rlvect_1(A,C,B),D) ) ) ) ) ) ).
fof(t74_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(B,k4_clvect_1(A,C,D))
<=> k4_clvect_1(A,C,D) = k4_clvect_1(A,B,D) ) ) ) ) ) ).
fof(t75_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( k4_clvect_1(A,B,C) = k4_clvect_1(A,k5_rlvect_1(A,B),C)
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t76_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_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_clvect_1(E,A)
=> ( ( r2_hidden(B,k4_clvect_1(A,C,E))
& r2_hidden(B,k4_clvect_1(A,D,E)) )
=> k4_clvect_1(A,C,E) = k4_clvect_1(A,D,E) ) ) ) ) ) ) ).
fof(t77_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( ( r2_hidden(B,k4_clvect_1(A,C,D))
& r2_hidden(B,k4_clvect_1(A,k5_rlvect_1(A,C),D)) )
=> r1_rlvect_1(D,C) ) ) ) ) ) ).
fof(t78_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(k1_clvect_1(A,B,C),k4_clvect_1(A,B,D))
=> ( C = k6_complex1
| r1_rlvect_1(D,B) ) ) ) ) ) ) ).
fof(t79_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r1_rlvect_1(D,B)
=> r2_hidden(k1_clvect_1(A,B,C),k4_clvect_1(A,B,D)) ) ) ) ) ) ).
fof(t80_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ( r2_hidden(k5_rlvect_1(A,B),k4_clvect_1(A,B,C))
<=> r1_rlvect_1(C,B) ) ) ) ) ).
fof(t81_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(k4_rlvect_1(A,B,C),k4_clvect_1(A,C,D))
<=> r1_rlvect_1(D,B) ) ) ) ) ) ).
fof(t82_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(k6_rlvect_1(A,B,C),k4_clvect_1(A,B,D))
<=> r1_rlvect_1(D,C) ) ) ) ) ) ).
fof(t83_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(B,k4_clvect_1(A,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(D,E)
& B = k4_rlvect_1(A,C,E) ) ) ) ) ) ) ).
fof(t84_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( r2_hidden(B,k4_clvect_1(A,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(D,E)
& B = k6_rlvect_1(A,C,E) ) ) ) ) ) ) ).
fof(t85_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r2_hidden(B,k4_clvect_1(A,E,D))
& r2_hidden(C,k4_clvect_1(A,E,D)) )
<=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t86_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ~ ( k4_clvect_1(A,B,D) = k4_clvect_1(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,E)
& k4_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ).
fof(t87_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ~ ( k4_clvect_1(A,B,D) = k4_clvect_1(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,E)
& k6_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ).
fof(t88_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_clvect_1(C)
& m1_clvect_1(C,A) )
=> ! [D] :
( ( v1_clvect_1(D)
& m1_clvect_1(D,A) )
=> ( k4_clvect_1(A,B,C) = k4_clvect_1(A,B,D)
<=> C = D ) ) ) ) ) ).
fof(t89_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_clvect_1(D)
& m1_clvect_1(D,A) )
=> ! [E] :
( ( v1_clvect_1(E)
& m1_clvect_1(E,A) )
=> ( k4_clvect_1(A,B,D) = k4_clvect_1(A,C,E)
=> D = E ) ) ) ) ) ) ).
fof(t90_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m2_clvect_1(C,A,B)
=> ( v3_clvect_1(C,A)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t91_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_clvect_1(B)
& m1_clvect_1(B,A) )
=> ! [C] :
( ( v1_clvect_1(C)
& m1_clvect_1(C,A) )
=> ! [D] :
( m2_clvect_1(D,A,B)
=> ! [E] :
( m2_clvect_1(E,A,C)
=> ( D = E
=> B = C ) ) ) ) ) ) ).
fof(t92_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m2_clvect_1(k1_struct_0(A,B),A,k2_clvect_1(A)) ) ) ).
fof(t93_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( m2_clvect_1(B,A,k2_clvect_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B != k1_struct_0(A,C) ) ) ) ) ).
fof(t94_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> m2_clvect_1(u1_struct_0(B),A,B) ) ) ).
fof(t95_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> m2_clvect_1(u1_struct_0(A),A,k3_clvect_1(A)) ) ).
fof(t96_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_clvect_1(B,A,k3_clvect_1(A))
=> B = u1_struct_0(A) ) ) ) ).
fof(t97_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ! [C] :
( m2_clvect_1(C,A,B)
=> ( r2_hidden(k1_rlvect_1(A),C)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t98_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ! [D] :
( m2_clvect_1(D,A,C)
=> ( r2_hidden(B,D)
<=> D = k4_clvect_1(A,B,C) ) ) ) ) ) ).
fof(t99_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ! [E] :
( m2_clvect_1(E,A,D)
=> ~ ( r2_hidden(B,E)
& r2_hidden(C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,F)
& k4_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ).
fof(t100_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ! [E] :
( m2_clvect_1(E,A,D)
=> ~ ( r2_hidden(B,E)
& r2_hidden(C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(D,F)
& k6_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ).
fof(t101_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_clvect_1(D,A)
=> ( ? [E] :
( m2_clvect_1(E,A,D)
& r2_hidden(B,E)
& r2_hidden(C,E) )
<=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ).
fof(t102_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> ! [D] :
( m2_clvect_1(D,A,C)
=> ! [E] :
( m2_clvect_1(E,A,C)
=> ( ( r2_hidden(B,D)
& r2_hidden(B,E) )
=> D = E ) ) ) ) ) ) ).
fof(d9_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_clvect_1(A,B) = k2_seq_1(u1_struct_0(A),k1_numbers,u2_clvect_1(A),B) ) ) ).
fof(d10_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_clvect_1(A) )
=> ( v5_clvect_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,k2_numbers)
=> ( ( k5_clvect_1(A,B) = np__0
=> B = k1_rlvect_1(A) )
& ( B = k1_rlvect_1(A)
=> k5_clvect_1(A,B) = np__0 )
& k5_clvect_1(A,k1_clvect_1(A,B,D)) = k4_real_1(k17_complex1(D),k5_clvect_1(A,B))
& r1_xreal_0(k5_clvect_1(A,k2_rlvect_1(A,B,C)),k3_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C))) ) ) ) ) ) ) ).
fof(t103_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k5_clvect_1(A,k1_rlvect_1(A)) = np__0 ) ).
fof(t104_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_clvect_1(A,k5_rlvect_1(A,B)) = k5_clvect_1(A,B) ) ) ).
fof(t105_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k5_clvect_1(A,k6_rlvect_1(A,B,C)),k3_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C))) ) ) ) ).
fof(t106_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_xreal_0(np__0,k5_clvect_1(A,B)) ) ) ).
fof(t107_clvect_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v5_clvect_1(C)
& l2_clvect_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> r1_xreal_0(k5_clvect_1(C,k4_rlvect_1(C,k1_clvect_1(C,D,A),k1_clvect_1(C,E,B))),k3_real_1(k4_real_1(k17_complex1(A),k5_clvect_1(C,D)),k4_real_1(k17_complex1(B),k5_clvect_1(C,E)))) ) ) ) ) ) ).
fof(t108_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k5_clvect_1(A,k6_rlvect_1(A,B,C)) = np__0
<=> B = C ) ) ) ) ).
fof(t109_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_clvect_1(A,k6_rlvect_1(A,B,C)) = k5_clvect_1(A,k6_rlvect_1(A,C,B)) ) ) ) ).
fof(t110_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k5_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C)),k5_clvect_1(A,k6_rlvect_1(A,B,C))) ) ) ) ).
fof(t111_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k18_complex1(k5_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C))),k5_clvect_1(A,k6_rlvect_1(A,B,C))) ) ) ) ).
fof(t112_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k5_clvect_1(A,k6_rlvect_1(A,B,C)),k3_real_1(k5_clvect_1(A,k6_rlvect_1(A,B,D)),k5_clvect_1(A,k6_rlvect_1(A,D,C)))) ) ) ) ) ).
fof(t113_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& k5_clvect_1(A,k6_rlvect_1(A,B,C)) = np__0 ) ) ) ) ).
fof(d11_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [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)) )
=> ( D = k6_clvect_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k4_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,C,E)) ) ) ) ) ) ) ).
fof(d12_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [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)) )
=> ( D = k7_clvect_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,C,E)) ) ) ) ) ) ) ).
fof(d13_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [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)) )
=> ( D = k8_clvect_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k6_rlvect_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(d14_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [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)) )
=> ( D = k9_clvect_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k1_clvect_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(d15_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v6_clvect_1(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k5_clvect_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ).
fof(t114_clvect_1,axiom,
$true ).
fof(t115_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v6_clvect_1(B,A)
& v6_clvect_1(C,A) )
=> v6_clvect_1(k6_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t116_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v6_clvect_1(B,A)
& v6_clvect_1(C,A) )
=> v6_clvect_1(k7_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t117_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v6_clvect_1(C,A)
=> v6_clvect_1(k8_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t118_clvect_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ( v6_clvect_1(C,B)
=> v6_clvect_1(k9_clvect_1(B,C,A),B) ) ) ) ) ).
fof(d16_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( C = k10_clvect_1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k5_clvect_1(A,k2_normsp_1(A,B,D)) ) ) ) ) ) ).
fof(t119_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v6_clvect_1(B,A)
=> v4_seq_2(k10_clvect_1(A,B)) ) ) ) ).
fof(d17_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v6_clvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k11_clvect_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k5_clvect_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ) ).
fof(t120_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v6_clvect_1(C,A)
& k11_clvect_1(A,C) = B )
=> ( v4_seq_2(k10_clvect_1(A,k8_clvect_1(A,C,B)))
& k2_seq_2(k10_clvect_1(A,k8_clvect_1(A,C,B))) = np__0 ) ) ) ) ) ).
fof(t121_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v6_clvect_1(B,A)
& v6_clvect_1(C,A) )
=> k11_clvect_1(A,k6_clvect_1(A,B,C)) = k4_rlvect_1(A,k11_clvect_1(A,B),k11_clvect_1(A,C)) ) ) ) ) ).
fof(t122_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v6_clvect_1(B,A)
& v6_clvect_1(C,A) )
=> k11_clvect_1(A,k7_clvect_1(A,B,C)) = k6_rlvect_1(A,k11_clvect_1(A,B),k11_clvect_1(A,C)) ) ) ) ) ).
fof(t123_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v6_clvect_1(C,A)
=> k11_clvect_1(A,k8_clvect_1(A,C,B)) = k6_rlvect_1(A,k11_clvect_1(A,C),B) ) ) ) ) ).
fof(t124_clvect_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ( v6_clvect_1(C,B)
=> k11_clvect_1(B,k9_clvect_1(B,C,A)) = k1_clvect_1(B,k11_clvect_1(B,C),A) ) ) ) ) ).
fof(dt_m1_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_clvect_1(B,A)
=> ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B) ) ) ) ).
fof(existence_m1_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ? [B] : m1_clvect_1(B,A) ) ).
fof(dt_m2_clvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_clvect_1(B,A) )
=> ! [C] :
( m2_clvect_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m2_clvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_clvect_1(B,A) )
=> ? [C] : m2_clvect_1(C,A,B) ) ).
fof(dt_l1_clvect_1,axiom,
! [A] :
( l1_clvect_1(A)
=> l1_rlvect_1(A) ) ).
fof(existence_l1_clvect_1,axiom,
? [A] : l1_clvect_1(A) ).
fof(dt_l2_clvect_1,axiom,
! [A] :
( l2_clvect_1(A)
=> l1_clvect_1(A) ) ).
fof(existence_l2_clvect_1,axiom,
? [A] : l2_clvect_1(A) ).
fof(abstractness_v1_clvect_1,axiom,
! [A] :
( l1_clvect_1(A)
=> ( v1_clvect_1(A)
=> A = g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)) ) ) ).
fof(abstractness_v4_clvect_1,axiom,
! [A] :
( l2_clvect_1(A)
=> ( v4_clvect_1(A)
=> A = g2_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A),u2_clvect_1(A)) ) ) ).
fof(dt_k1_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_clvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k2_numbers) )
=> m1_subset_1(k1_clvect_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ( v1_clvect_1(k2_clvect_1(A))
& m1_clvect_1(k2_clvect_1(A),A) ) ) ).
fof(dt_k3_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ( v1_clvect_1(k3_clvect_1(A))
& m1_clvect_1(k3_clvect_1(A),A) ) ) ).
fof(dt_k4_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_clvect_1(C,A) )
=> m1_subset_1(k4_clvect_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_clvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_clvect_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k5_clvect_1(A,B),k1_numbers) ) ).
fof(dt_k6_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k6_clvect_1(A,B,C))
& v1_funct_2(k6_clvect_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k6_clvect_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k7_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k7_clvect_1(A,B,C))
& v1_funct_2(k7_clvect_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k7_clvect_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k8_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_funct_1(k8_clvect_1(A,B,C))
& v1_funct_2(k8_clvect_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k8_clvect_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k9_clvect_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k2_numbers) )
=> ( v1_funct_1(k9_clvect_1(A,B,C))
& v1_funct_2(k9_clvect_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k9_clvect_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k10_clvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k10_clvect_1(A,B))
& v1_funct_2(k10_clvect_1(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k10_clvect_1(A,B),k5_numbers,k1_numbers) ) ) ).
fof(dt_k11_clvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v5_clvect_1(A)
& l2_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> m1_subset_1(k11_clvect_1(A,B),u1_struct_0(A)) ) ).
fof(dt_u1_clvect_1,axiom,
! [A] :
( l1_clvect_1(A)
=> ( v1_funct_1(u1_clvect_1(A))
& v1_funct_2(u1_clvect_1(A),k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u1_clvect_1(A),k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u2_clvect_1,axiom,
! [A] :
( l2_clvect_1(A)
=> ( v1_funct_1(u2_clvect_1(A))
& v1_funct_2(u2_clvect_1(A),u1_struct_0(A),k1_numbers)
& m2_relset_1(u2_clvect_1(A),u1_struct_0(A),k1_numbers) ) ) ).
fof(dt_g1_clvect_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(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A) )
=> ( v1_clvect_1(g1_clvect_1(A,B,C,D))
& l1_clvect_1(g1_clvect_1(A,B,C,D)) ) ) ).
fof(free_g1_clvect_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(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A) )
=> ! [E,F,G,H] :
( g1_clvect_1(A,B,C,D) = g1_clvect_1(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(dt_g2_clvect_1,axiom,
! [A,B,C,D,E] :
( ( 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(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& v1_funct_1(E)
& v1_funct_2(E,A,k1_numbers)
& m1_relset_1(E,A,k1_numbers) )
=> ( v4_clvect_1(g2_clvect_1(A,B,C,D,E))
& l2_clvect_1(g2_clvect_1(A,B,C,D,E)) ) ) ).
fof(free_g2_clvect_1,axiom,
! [A,B,C,D,E] :
( ( 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(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& v1_funct_1(E)
& v1_funct_2(E,A,k1_numbers)
& m1_relset_1(E,A,k1_numbers) )
=> ! [F,G,H,I,J] :
( g2_clvect_1(A,B,C,D,E) = g2_clvect_1(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(t26_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_clvect_1(B,A)
& v3_clvect_1(C,A)
& D = a_3_0_clvect_1(A,B,C) )
=> v3_clvect_1(D,A) ) ) ) ) ) ).
fof(d7_clvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_clvect_1(C,A)
=> k4_clvect_1(A,B,C) = a_3_1_clvect_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_clvect_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_clvect_1(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k4_rlvect_1(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_3_1_clvect_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_clvect_1(D,B) )
=> ( r2_hidden(A,a_3_1_clvect_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_rlvect_1(B,C,E)
& r1_rlvect_1(D,E) ) ) ) ).
%------------------------------------------------------------------------------