SET007 Axioms: SET007+261.ax
%------------------------------------------------------------------------------
% File : SET007+261 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex Spaces
% 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 : complsp1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 177 ( 26 unt; 0 def)
% Number of atoms : 692 ( 135 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 557 ( 42 ~; 6 |; 101 &)
% ( 20 <=>; 388 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 83 ( 83 usr; 19 con; 0-6 aty)
% Number of variables : 404 ( 393 !; 11 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ~ v1_xboole_0(k8_complsp1(A)) ) ).
fof(fc2_complsp1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ~ v3_struct_0(g1_pre_topc(A,B))
& v1_pre_topc(g1_pre_topc(A,B)) ) ) ).
fof(fc3_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v3_struct_0(k23_complsp1(A))
& v1_pre_topc(k23_complsp1(A))
& v2_pre_topc(k23_complsp1(A)) ) ) ).
fof(t1_complsp1,axiom,
$true ).
fof(t2_complsp1,axiom,
$true ).
fof(t3_complsp1,axiom,
r3_binop_1(k2_numbers,k5_complex1,k27_binop_2) ).
fof(t4_complsp1,axiom,
$true ).
fof(t5_complsp1,axiom,
$true ).
fof(t6_complsp1,axiom,
r1_finseqop(k2_numbers,k25_binop_2,k27_binop_2) ).
fof(t7_complsp1,axiom,
v1_finseqop(k27_binop_2,k2_numbers) ).
fof(t8_complsp1,axiom,
k6_finseqop(k2_numbers,k27_binop_2) = k25_binop_2 ).
fof(d1_complsp1,axiom,
$true ).
fof(d2_complsp1,axiom,
$true ).
fof(d3_complsp1,axiom,
k28_binop_2 = k8_finseqop(k2_numbers,k27_binop_2,k6_partfun1(k2_numbers),k25_binop_2) ).
fof(t9_complsp1,axiom,
$true ).
fof(t10_complsp1,axiom,
$true ).
fof(t11_complsp1,axiom,
$true ).
fof(t12_complsp1,axiom,
r3_binop_1(k2_numbers,k6_complex1,k29_binop_2) ).
fof(t13_complsp1,axiom,
k3_binop_1(k2_numbers,k29_binop_2) = k6_complex1 ).
fof(t14_complsp1,axiom,
$true ).
fof(t15_complsp1,axiom,
r6_binop_1(k2_numbers,k29_binop_2,k27_binop_2) ).
fof(d4_complsp1,axiom,
$true ).
fof(d5_complsp1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k1_complsp1(A) = k5_funcop_1(k29_binop_2,A,k6_partfun1(k2_numbers)) ) ).
fof(t16_complsp1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k8_funct_2(k2_numbers,k2_numbers,k1_complsp1(A),B) = k5_binop_2(A,B) ) ) ).
fof(t17_complsp1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> r7_binop_1(k2_numbers,k1_complsp1(A),k27_binop_2) ) ).
fof(d6_complsp1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_numbers,k1_numbers)
& m2_relset_1(A,k2_numbers,k1_numbers) )
=> ( A = k2_complsp1
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k8_funct_2(k2_numbers,k1_numbers,A,B) = k17_complex1(B) ) ) ) ).
fof(d7_complsp1,axiom,
! [A] :
( m2_finseq_1(A,k2_numbers)
=> ! [B] :
( m2_finseq_1(B,k2_numbers)
=> k3_complsp1(A,B) = k1_finseqop(k2_numbers,k2_numbers,k2_numbers,k27_binop_2,A,B) ) ) ).
fof(d8_complsp1,axiom,
! [A] :
( m2_finseq_1(A,k2_numbers)
=> ! [B] :
( m2_finseq_1(B,k2_numbers)
=> k4_complsp1(A,B) = k1_finseqop(k2_numbers,k2_numbers,k2_numbers,k28_binop_2,A,B) ) ) ).
fof(d9_complsp1,axiom,
! [A] :
( m2_finseq_1(A,k2_numbers)
=> k5_complsp1(A) = k5_finseqop(k2_numbers,k2_numbers,A,k25_binop_2) ) ).
fof(d10_complsp1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( m2_finseq_1(B,k2_numbers)
=> k6_complsp1(A,B) = k5_finseqop(k2_numbers,k2_numbers,B,k1_complsp1(A)) ) ) ).
fof(d11_complsp1,axiom,
! [A] :
( m2_finseq_1(A,k2_numbers)
=> k7_complsp1(A) = k5_finseqop(k2_numbers,k1_numbers,A,k2_complsp1) ) ).
fof(d12_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k8_complsp1(A) = k4_finseq_2(A,k2_numbers) ) ).
fof(t18_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k3_finseq_1(B) = A ) ) ).
fof(t19_complsp1,axiom,
! [A] :
( m2_finseq_2(A,k2_numbers,k8_complsp1(np__0))
=> A = k6_finseq_1(k2_numbers) ) ).
fof(t20_complsp1,axiom,
m2_finseq_2(k6_finseq_1(k2_numbers),k2_numbers,k8_complsp1(np__0)) ).
fof(t21_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(B))
=> ( r2_hidden(A,k2_finseq_1(B))
=> r2_hidden(k1_funct_1(C,A),k2_numbers) ) ) ) ) ).
fof(t22_complsp1,axiom,
$true ).
fof(t23_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k2_finseq_1(A))
=> k1_funct_1(B,D) = k1_funct_1(C,D) ) )
=> B = C ) ) ) ) ).
fof(t24_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
=> ! [F] :
( m2_finseq_2(F,k2_numbers,k8_complsp1(B))
=> ( ( r2_hidden(A,k2_finseq_1(B))
& C = k1_funct_1(E,A)
& D = k1_funct_1(F,A) )
=> k1_funct_1(k9_complsp1(B,E,F),A) = k3_binop_2(C,D) ) ) ) ) ) ) ) ).
fof(t25_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k9_complsp1(A,B,C) = k9_complsp1(A,C,B) ) ) ) ).
fof(t26_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k9_complsp1(A,B,k9_complsp1(A,C,D)) = k9_complsp1(A,k9_complsp1(A,B,C),D) ) ) ) ) ).
fof(d13_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k10_complsp1(A) = k4_finseqop(k2_numbers,A,k5_complex1) ) ).
fof(t27_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,k2_finseq_1(B))
=> k1_funct_1(k11_complsp1(B),A) = k5_complex1 ) ) ) ).
fof(t28_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ( k9_complsp1(A,B,k11_complsp1(A)) = B
& B = k9_complsp1(A,k11_complsp1(A),B) ) ) ) ).
fof(t29_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(B))
=> ( ( r2_hidden(A,k2_finseq_1(B))
& C = k1_funct_1(D,A) )
=> k1_funct_1(k12_complsp1(B,D),A) = k1_binop_2(C) ) ) ) ) ) ).
fof(t30_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ( k9_complsp1(A,B,k12_complsp1(A,B)) = k11_complsp1(A)
& k9_complsp1(A,k12_complsp1(A,B),B) = k11_complsp1(A) ) ) ) ).
fof(t31_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( k9_complsp1(A,B,C) = k11_complsp1(A)
=> ( B = k12_complsp1(A,C)
& C = k12_complsp1(A,B) ) ) ) ) ) ).
fof(t32_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k12_complsp1(A,k12_complsp1(A,B)) = B ) ) ).
fof(t33_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( k12_complsp1(A,B) = k12_complsp1(A,C)
=> B = C ) ) ) ) ).
fof(t34_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> ( ( k9_complsp1(A,B,C) = k9_complsp1(A,D,C)
| k9_complsp1(A,B,C) = k9_complsp1(A,C,D) )
=> B = D ) ) ) ) ) ).
fof(t35_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k12_complsp1(A,k9_complsp1(A,B,C)) = k9_complsp1(A,k12_complsp1(A,B),k12_complsp1(A,C)) ) ) ) ).
fof(t36_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
=> ! [F] :
( m2_finseq_2(F,k2_numbers,k8_complsp1(B))
=> ( ( r2_hidden(A,k2_finseq_1(B))
& C = k1_funct_1(E,A)
& D = k1_funct_1(F,A) )
=> k1_funct_1(k13_complsp1(B,E,F),A) = k4_binop_2(C,D) ) ) ) ) ) ) ) ).
fof(t37_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,B,C) = k9_complsp1(A,B,k12_complsp1(A,C)) ) ) ) ).
fof(t38_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,B,k11_complsp1(A)) = B ) ) ).
fof(t39_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,k11_complsp1(A),B) = k12_complsp1(A,B) ) ) ).
fof(t40_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,B,k12_complsp1(A,C)) = k9_complsp1(A,B,C) ) ) ) ).
fof(t41_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k12_complsp1(A,k13_complsp1(A,B,C)) = k13_complsp1(A,C,B) ) ) ) ).
fof(t42_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k12_complsp1(A,k13_complsp1(A,B,C)) = k9_complsp1(A,k12_complsp1(A,B),C) ) ) ) ).
fof(t43_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,B,B) = k11_complsp1(A) ) ) ).
fof(t44_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( k13_complsp1(A,B,C) = k11_complsp1(A)
=> B = C ) ) ) ) ).
fof(t45_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,k13_complsp1(A,B,C),D) = k13_complsp1(A,B,k9_complsp1(A,C,D)) ) ) ) ) ).
fof(t46_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k9_complsp1(A,B,k13_complsp1(A,C,D)) = k13_complsp1(A,k9_complsp1(A,B,C),D) ) ) ) ) ).
fof(t47_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k13_complsp1(A,B,k13_complsp1(A,C,D)) = k9_complsp1(A,k13_complsp1(A,B,C),D) ) ) ) ) ).
fof(t48_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k9_complsp1(A,k13_complsp1(A,B,C),D) = k13_complsp1(A,k9_complsp1(A,B,D),C) ) ) ) ) ).
fof(t49_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> B = k13_complsp1(A,k9_complsp1(A,B,C),C) ) ) ) ).
fof(t50_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k9_complsp1(A,B,k13_complsp1(A,C,B)) = C ) ) ) ).
fof(t51_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> B = k9_complsp1(A,k13_complsp1(A,B,C),C) ) ) ) ).
fof(t52_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
=> ( ( r2_hidden(A,k2_finseq_1(B))
& C = k1_funct_1(E,A) )
=> k1_funct_1(k14_complsp1(B,D,E),A) = k5_binop_2(D,C) ) ) ) ) ) ) ).
fof(t53_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,B,k14_complsp1(A,C,D)) = k14_complsp1(A,k5_binop_2(B,C),D) ) ) ) ) ).
fof(t54_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,k3_binop_2(B,C),D) = k9_complsp1(A,k14_complsp1(A,B,D),k14_complsp1(A,C,D)) ) ) ) ) ).
fof(t55_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,B,k9_complsp1(A,C,D)) = k9_complsp1(A,k14_complsp1(A,B,C),k14_complsp1(A,B,D)) ) ) ) ) ).
fof(t56_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,k6_complex1,B) = B ) ) ).
fof(t57_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,k5_complex1,B) = k11_complsp1(A) ) ) ).
fof(t58_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k14_complsp1(A,k1_binop_2(k6_complex1),B) = k12_complsp1(A,B) ) ) ).
fof(t59_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(B))
=> ( ( r2_hidden(A,k2_finseq_1(B))
& C = k1_funct_1(D,A) )
=> k1_funct_1(k15_complsp1(B,D),A) = k17_complex1(C) ) ) ) ) ) ).
fof(t60_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k15_complsp1(A,k11_complsp1(A)) = k4_finseqop(k1_numbers,A,np__0) ) ).
fof(t61_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k15_complsp1(A,k12_complsp1(A,B)) = k15_complsp1(A,B) ) ) ).
fof(t62_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k15_complsp1(A,k14_complsp1(A,B,C)) = k10_rvsum_1(A,k17_complex1(B),k15_complsp1(A,C)) ) ) ) ).
fof(d14_complsp1,axiom,
! [A] :
( m2_finseq_1(A,k2_numbers)
=> k16_complsp1(A) = k9_square_1(k15_rvsum_1(k11_rvsum_1(k7_complsp1(A)))) ) ).
fof(t63_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k16_complsp1(k11_complsp1(A)) = np__0 ) ).
fof(t64_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ( k16_complsp1(B) = np__0
=> B = k11_complsp1(A) ) ) ) ).
fof(t65_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(np__0,k16_complsp1(B)) ) ) ).
fof(t66_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> k16_complsp1(k12_complsp1(A,B)) = k16_complsp1(B) ) ) ).
fof(t67_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k16_complsp1(k14_complsp1(A,B,C)) = k11_binop_2(k17_complex1(B),k16_complsp1(C)) ) ) ) ).
fof(t68_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(k16_complsp1(k9_complsp1(A,B,C)),k9_binop_2(k16_complsp1(B),k16_complsp1(C))) ) ) ) ).
fof(t69_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(k16_complsp1(k13_complsp1(A,B,C)),k9_binop_2(k16_complsp1(B),k16_complsp1(C))) ) ) ) ).
fof(t70_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(k10_binop_2(k16_complsp1(B),k16_complsp1(C)),k16_complsp1(k9_complsp1(A,B,C))) ) ) ) ).
fof(t71_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(k10_binop_2(k16_complsp1(B),k16_complsp1(C)),k16_complsp1(k13_complsp1(A,B,C))) ) ) ) ).
fof(t72_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( k16_complsp1(k13_complsp1(A,B,C)) = np__0
<=> B = C ) ) ) ) ).
fof(t73_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ~ ( B != C
& r1_xreal_0(k16_complsp1(k13_complsp1(A,B,C)),np__0) ) ) ) ) ).
fof(t74_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> k16_complsp1(k13_complsp1(A,B,C)) = k16_complsp1(k13_complsp1(A,C,B)) ) ) ) ).
fof(t75_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> r1_xreal_0(k16_complsp1(k13_complsp1(A,B,C)),k9_binop_2(k16_complsp1(k13_complsp1(A,B,D)),k16_complsp1(k13_complsp1(A,D,C)))) ) ) ) ) ).
fof(d15_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( v1_complsp1(B,A)
<=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(A))
=> ( ~ r1_xreal_0(D,k16_complsp1(E))
=> r2_hidden(k9_complsp1(A,C,E),B) ) ) ) ) ) ) ) ) ) ).
fof(d16_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( v2_complsp1(B,A)
<=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(A))
=> ~ ( ~ r1_xreal_0(D,k16_complsp1(E))
& r2_hidden(k9_complsp1(A,C,E),B) ) ) ) )
=> r2_hidden(C,B) ) ) ) ) ) ).
fof(t76_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( B = k1_xboole_0
=> v1_complsp1(B,A) ) ) ) ).
fof(t77_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( B = k8_complsp1(A)
=> v1_complsp1(B,A) ) ) ) ).
fof(t78_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k8_complsp1(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( r2_hidden(C,B)
=> v1_complsp1(C,A) ) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( C = k5_setfam_1(k8_complsp1(A),B)
=> v1_complsp1(C,A) ) ) ) ) ) ).
fof(t79_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( ( v1_complsp1(B,A)
& v1_complsp1(C,A) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ( D = k5_subset_1(k8_complsp1(A),B,C)
=> v1_complsp1(D,A) ) ) ) ) ) ) ).
fof(t80_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m2_finseq_2(D,k2_numbers,k8_complsp1(A))
=> ( r2_hidden(C,k17_complsp1(A,D,B))
<=> ~ r1_xreal_0(B,k16_complsp1(k13_complsp1(A,D,C))) ) ) ) ) ) ).
fof(t81_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ( ~ r1_xreal_0(B,np__0)
=> r2_hidden(C,k17_complsp1(A,C,B)) ) ) ) ) ).
fof(t82_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> v1_complsp1(k17_complsp1(A,C,B),A) ) ) ) ).
fof(t83_complsp1,axiom,
$true ).
fof(t84_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> r1_xreal_0(B,C) ) )
=> ( A = k1_xboole_0
| r1_xreal_0(B,k5_seq_4(A)) ) ) ) ) ).
fof(t85_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( C != k1_xboole_0
=> r1_xreal_0(np__0,k18_complsp1(A,B,C)) ) ) ) ) ).
fof(t86_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ( D != k1_xboole_0
=> r1_xreal_0(k18_complsp1(A,k9_complsp1(A,B,C),D),k9_binop_2(k18_complsp1(A,B,D),k16_complsp1(C))) ) ) ) ) ) ).
fof(t87_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( r2_hidden(B,C)
=> k18_complsp1(A,B,C) = np__0 ) ) ) ) ).
fof(t88_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ~ ( ~ r2_hidden(B,C)
& C != k1_xboole_0
& v2_complsp1(C,A)
& r1_xreal_0(k18_complsp1(A,B,C),np__0) ) ) ) ) ).
fof(t89_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ( D != k1_xboole_0
=> r1_xreal_0(k18_complsp1(A,B,D),k9_binop_2(k16_complsp1(k13_complsp1(A,B,C)),k18_complsp1(A,C,D))) ) ) ) ) ) ).
fof(t90_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ( r2_hidden(C,k19_complsp1(A,D,B))
<=> ~ r1_xreal_0(B,k18_complsp1(A,C,D)) ) ) ) ) ) ).
fof(t91_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_2(C,k2_numbers,k8_complsp1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ( r2_hidden(C,D)
=> ( r1_xreal_0(B,np__0)
| r2_hidden(C,k19_complsp1(A,D,B)) ) ) ) ) ) ) ).
fof(t92_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( ~ r1_xreal_0(B,np__0)
=> r1_tarski(C,k19_complsp1(A,C,B)) ) ) ) ) ).
fof(t93_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( C != k1_xboole_0
=> v1_complsp1(k19_complsp1(A,C,B),A) ) ) ) ) ).
fof(t94_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ~ ( A != k1_xboole_0
& B != k1_xboole_0
& k21_complsp1(A,B) = k1_xboole_0 ) ) ) ).
fof(t95_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( ( v2_seq_4(A)
& v2_seq_4(B) )
=> v2_seq_4(k21_complsp1(A,B)) ) ) ) ).
fof(t96_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( ( v2_seq_4(A)
& v2_seq_4(B) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| k5_seq_4(k21_complsp1(A,B)) = k9_binop_2(k5_seq_4(A),k5_seq_4(B)) ) ) ) ) ).
fof(t97_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( ( v2_seq_4(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( r2_hidden(C,A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r2_hidden(D,B)
& r1_xreal_0(D,C) ) ) ) ) )
=> ( A = k1_xboole_0
| r1_xreal_0(k5_seq_4(B),k5_seq_4(A)) ) ) ) ) ).
fof(t98_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ~ ( B != k1_xboole_0
& C != k1_xboole_0
& ~ r1_xreal_0(np__0,k20_complsp1(A,B,C)) ) ) ) ) ).
fof(t99_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> k20_complsp1(A,B,C) = k20_complsp1(A,C,B) ) ) ) ).
fof(t100_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_complsp1(A)))
=> ~ ( C != k1_xboole_0
& D != k1_xboole_0
& ~ r1_xreal_0(k20_complsp1(A,C,D),k9_binop_2(k18_complsp1(A,B,C),k18_complsp1(A,B,D))) ) ) ) ) ) ).
fof(t101_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( ~ r1_xboole_0(B,C)
=> k20_complsp1(A,B,C) = np__0 ) ) ) ) ).
fof(t102_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( r2_hidden(B,k22_complsp1(A))
<=> v1_complsp1(B,A) ) ) ) ).
fof(d23_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k23_complsp1(A) = g1_pre_topc(k8_complsp1(A),k22_complsp1(A)) ) ).
fof(t103_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> u1_pre_topc(k23_complsp1(A)) = k22_complsp1(A) ) ).
fof(t104_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> u1_struct_0(k23_complsp1(A)) = k8_complsp1(A) ) ).
fof(t105_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k23_complsp1(A)))
=> m2_finseq_2(B,k2_numbers,k8_complsp1(A)) ) ) ).
fof(t106_complsp1,axiom,
$true ).
fof(t107_complsp1,axiom,
$true ).
fof(t108_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k23_complsp1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( C = B
=> ( v1_complsp1(C,A)
<=> v3_pre_topc(B,k23_complsp1(A)) ) ) ) ) ) ).
fof(t109_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ( v2_complsp1(B,A)
<=> v1_complsp1(k3_subset_1(k8_complsp1(A),B),A) ) ) ) ).
fof(t110_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k23_complsp1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ( C = B
=> ( v2_complsp1(C,A)
<=> v4_pre_topc(B,k23_complsp1(A)) ) ) ) ) ) ).
fof(t111_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> v3_compts_1(k23_complsp1(A)) ) ).
fof(t112_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> v4_compts_1(k23_complsp1(A)) ) ).
fof(dt_k1_complsp1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( v1_funct_1(k1_complsp1(A))
& v1_funct_2(k1_complsp1(A),k2_numbers,k2_numbers)
& m2_relset_1(k1_complsp1(A),k2_numbers,k2_numbers) ) ) ).
fof(dt_k2_complsp1,axiom,
( v1_funct_1(k2_complsp1)
& v1_funct_2(k2_complsp1,k2_numbers,k1_numbers)
& m2_relset_1(k2_complsp1,k2_numbers,k1_numbers) ) ).
fof(dt_k3_complsp1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k2_numbers)
& m1_finseq_1(B,k2_numbers) )
=> m2_finseq_1(k3_complsp1(A,B),k2_numbers) ) ).
fof(dt_k4_complsp1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k2_numbers)
& m1_finseq_1(B,k2_numbers) )
=> m2_finseq_1(k4_complsp1(A,B),k2_numbers) ) ).
fof(dt_k5_complsp1,axiom,
! [A] :
( m1_finseq_1(A,k2_numbers)
=> m2_finseq_1(k5_complsp1(A),k2_numbers) ) ).
fof(dt_k6_complsp1,axiom,
! [A,B] :
( ( v1_xcmplx_0(A)
& m1_finseq_1(B,k2_numbers) )
=> m2_finseq_1(k6_complsp1(A,B),k2_numbers) ) ).
fof(dt_k7_complsp1,axiom,
! [A] :
( m1_finseq_1(A,k2_numbers)
=> m2_finseq_1(k7_complsp1(A),k1_numbers) ) ).
fof(dt_k8_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k8_complsp1(A))
& m1_finseq_2(k8_complsp1(A),k2_numbers) ) ) ).
fof(dt_k9_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k8_complsp1(A)) )
=> m2_finseq_2(k9_complsp1(A,B,C),k2_numbers,k8_complsp1(A)) ) ).
fof(redefinition_k9_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k8_complsp1(A)) )
=> k9_complsp1(A,B,C) = k3_complsp1(B,C) ) ).
fof(dt_k10_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_1(k10_complsp1(A),k2_numbers) ) ).
fof(dt_k11_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_2(k11_complsp1(A),k2_numbers,k8_complsp1(A)) ) ).
fof(redefinition_k11_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> k11_complsp1(A) = k10_complsp1(A) ) ).
fof(dt_k12_complsp1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A)) )
=> m2_finseq_2(k12_complsp1(A,B),k2_numbers,k8_complsp1(A)) ) ).
fof(redefinition_k12_complsp1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A)) )
=> k12_complsp1(A,B) = k5_complsp1(B) ) ).
fof(dt_k13_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k8_complsp1(A)) )
=> m2_finseq_2(k13_complsp1(A,B,C),k2_numbers,k8_complsp1(A)) ) ).
fof(redefinition_k13_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k8_complsp1(A)) )
=> k13_complsp1(A,B,C) = k4_complsp1(B,C) ) ).
fof(dt_k14_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k2_numbers)
& m1_subset_1(C,k8_complsp1(A)) )
=> m2_finseq_2(k14_complsp1(A,B,C),k2_numbers,k8_complsp1(A)) ) ).
fof(redefinition_k14_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k2_numbers)
& m1_subset_1(C,k8_complsp1(A)) )
=> k14_complsp1(A,B,C) = k6_complsp1(B,C) ) ).
fof(dt_k15_complsp1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A)) )
=> m2_finseq_2(k15_complsp1(A,B),k1_numbers,k4_finseq_2(A,k1_numbers)) ) ).
fof(redefinition_k15_complsp1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A)) )
=> k15_complsp1(A,B) = k7_complsp1(B) ) ).
fof(dt_k16_complsp1,axiom,
! [A] :
( m1_finseq_1(A,k2_numbers)
=> m1_subset_1(k16_complsp1(A),k1_numbers) ) ).
fof(dt_k17_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k17_complsp1(A,B,C),k1_zfmisc_1(k8_complsp1(A))) ) ).
fof(dt_k18_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k8_complsp1(A))
& m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A))) )
=> m1_subset_1(k18_complsp1(A,B,C),k1_numbers) ) ).
fof(dt_k19_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k19_complsp1(A,B,C),k1_zfmisc_1(k8_complsp1(A))) ) ).
fof(dt_k20_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
& m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A))) )
=> m1_subset_1(k20_complsp1(A,B,C),k1_numbers) ) ).
fof(dt_k21_complsp1,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> m1_subset_1(k21_complsp1(A,B),k1_zfmisc_1(k1_numbers)) ) ).
fof(dt_k22_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k22_complsp1(A),k1_zfmisc_1(k1_zfmisc_1(k8_complsp1(A)))) ) ).
fof(dt_k23_complsp1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_pre_topc(k23_complsp1(A))
& v2_pre_topc(k23_complsp1(A))
& l1_pre_topc(k23_complsp1(A)) ) ) ).
fof(d17_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k17_complsp1(A,B,C) = a_3_0_complsp1(A,B,C) ) ) ) ).
fof(d18_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k2_numbers,k8_complsp1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( D = k18_complsp1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_numbers))
=> ( E = a_3_1_complsp1(A,B,C)
=> D = k5_seq_4(E) ) ) ) ) ) ) ) ).
fof(d19_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k19_complsp1(A,B,C) = a_3_2_complsp1(A,B,C) ) ) ) ).
fof(d20_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k8_complsp1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( D = k20_complsp1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_numbers))
=> ( E = a_3_3_complsp1(A,B,C)
=> D = k5_seq_4(E) ) ) ) ) ) ) ) ).
fof(d21_complsp1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> k21_complsp1(A,B) = a_2_0_complsp1(A,B) ) ) ).
fof(d22_complsp1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k22_complsp1(A) = a_1_0_complsp1(A) ) ).
fof(s1_complsp1,axiom,
m1_subset_1(a_0_0_complsp1,k1_zfmisc_1(f2_s1_complsp1)) ).
fof(s2_complsp1,axiom,
m1_subset_1(a_0_1_complsp1,k1_zfmisc_1(f3_s2_complsp1)) ).
fof(fraenkel_a_3_0_complsp1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_finseq_2(C,k2_numbers,k8_complsp1(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_0_complsp1(B,C,D))
<=> ? [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
& A = E
& ~ r1_xreal_0(D,k16_complsp1(k13_complsp1(B,E,C))) ) ) ) ).
fof(fraenkel_a_3_1_complsp1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_finseq_2(C,k2_numbers,k8_complsp1(B))
& m1_subset_1(D,k1_zfmisc_1(k8_complsp1(B))) )
=> ( r2_hidden(A,a_3_1_complsp1(B,C,D))
<=> ? [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
& A = k16_complsp1(k13_complsp1(B,C,E))
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_2_complsp1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(k8_complsp1(B)))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_2_complsp1(B,C,D))
<=> ? [E] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
& A = E
& ~ r1_xreal_0(D,k18_complsp1(B,E,C)) ) ) ) ).
fof(fraenkel_a_3_3_complsp1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(k8_complsp1(B)))
& m1_subset_1(D,k1_zfmisc_1(k8_complsp1(B))) )
=> ( r2_hidden(A,a_3_3_complsp1(B,C,D))
<=> ? [E,F] :
( m2_finseq_2(E,k2_numbers,k8_complsp1(B))
& m2_finseq_2(F,k2_numbers,k8_complsp1(B))
& A = k16_complsp1(k13_complsp1(B,E,F))
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_2_0_complsp1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
& m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
=> ( r2_hidden(A,a_2_0_complsp1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k9_binop_2(D,E)
& r2_hidden(D,B)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_1_0_complsp1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_0_complsp1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k8_complsp1(B)))
& A = C
& v1_complsp1(C,B) ) ) ) ).
fof(fraenkel_a_0_0_complsp1,axiom,
! [A] :
( r2_hidden(A,a_0_0_complsp1)
<=> ? [B] :
( m1_subset_1(B,f1_s1_complsp1)
& A = f3_s1_complsp1(B)
& p1_s1_complsp1(B) ) ) ).
fof(fraenkel_a_0_1_complsp1,axiom,
! [A] :
( r2_hidden(A,a_0_1_complsp1)
<=> ? [B,C] :
( m1_subset_1(B,f1_s2_complsp1)
& m1_subset_1(C,f2_s2_complsp1)
& A = f4_s2_complsp1(B,C)
& p1_s2_complsp1(B,C) ) ) ).
%------------------------------------------------------------------------------