SET007 Axioms: SET007+694.ax
%------------------------------------------------------------------------------
% File : SET007+694 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Turing Machines
% 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 : turing_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 136 ( 10 unt; 0 def)
% Number of atoms : 730 ( 191 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 656 ( 62 ~; 3 |; 256 &)
% ( 15 <=>; 320 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-4 aty)
% Number of functors : 96 ( 96 usr; 19 con; 0-6 aty)
% Number of variables : 379 ( 362 !; 17 ?)
% 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_turing_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ( ~ v1_xboole_0(k3_turing_1(A))
& v1_finset_1(k3_turing_1(A)) ) ) ).
fof(rc1_turing_1,axiom,
? [A] :
( l1_turing_1(A)
& v1_turing_1(A) ) ).
fof(t1_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,k3_turing_1(B))
<=> r1_xreal_0(A,B) ) ) ) ).
fof(t2_turing_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E,F] :
( E != B
=> k1_funct_1(k1_funct_4(A,k3_cqc_lang(k4_tarski(B,C),D)),k4_tarski(E,F)) = k1_funct_1(A,k4_tarski(E,F)) ) ) ).
fof(t3_turing_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E,F] :
( F != C
=> k1_funct_1(k1_funct_4(A,k3_cqc_lang(k4_tarski(B,C),D)),k4_tarski(E,F)) = k1_funct_1(A,k4_tarski(E,F)) ) ) ).
fof(t4_turing_1,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> k2_gr_cy_1(k2_finseq_4(k4_numbers,A,B)) = k2_xcmplx_0(A,B) ) ) ).
fof(t5_turing_1,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> ! [C] :
( m1_subset_1(C,k4_numbers)
=> k2_gr_cy_1(k3_finseq_4(k4_numbers,A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ).
fof(t6_turing_1,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> ! [C] :
( m1_subset_1(C,k4_numbers)
=> ! [D] :
( m1_subset_1(D,k4_numbers)
=> k2_gr_cy_1(k3_scmpds_1(k4_numbers,A,B,C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) ) ) ) ) ).
fof(d2_turing_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_turing_1(A,B) = k7_relat_1(A,k2_finseq_1(B)) ) ) ).
fof(t7_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k2_gr_cy_1(k4_turing_1(k2_finseq_4(k5_numbers,A,B),np__1)) = A
& k2_gr_cy_1(k4_turing_1(k2_finseq_4(k5_numbers,A,B),np__2)) = k1_nat_1(A,B) ) ) ) ).
fof(t8_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k2_gr_cy_1(k4_turing_1(k3_finseq_4(k5_numbers,A,B,C),np__1)) = A
& k2_gr_cy_1(k4_turing_1(k3_finseq_4(k5_numbers,A,B,C),np__2)) = k1_nat_1(A,B)
& k2_gr_cy_1(k4_turing_1(k3_finseq_4(k5_numbers,A,B,C),np__3)) = k1_nat_1(k1_nat_1(A,B),C) ) ) ) ) ).
fof(d3_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_subset_1(D,u1_turing_1(A))
=> k5_turing_1(A,B,C,D) = k1_funct_4(B,k3_cqc_lang(C,D)) ) ) ) ) ).
fof(d4_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
=> k6_turing_1(A,B) = k7_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),B) ) ) ).
fof(d5_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> k7_turing_1(A,B) = k6_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B) ) ) ).
fof(d6_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> k8_turing_1(A,B) = k1_funct_1(u3_turing_1(A),k4_tarski(k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B),k1_funct_1(k7_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B),k7_turing_1(A,B)))) ) ) ).
fof(d7_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ( ( k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B) != u5_turing_1(A)
=> k9_turing_1(A,B) = k3_mcart_1(k5_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k8_turing_1(A,B)),k2_xcmplx_0(k7_turing_1(A,B),k6_turing_1(A,k8_turing_1(A,B))),k5_turing_1(A,k7_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B),k7_turing_1(A,B),k6_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k8_turing_1(A,B)))) )
& ( k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B) = u5_turing_1(A)
=> k9_turing_1(A,B) = B ) ) ) ) ).
fof(d8_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
& m2_relset_1(C,k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> ( C = k10_turing_1(A,B)
<=> ( k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),C,np__0) = B
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),C,k1_nat_1(D,np__1)) = k9_turing_1(A,k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),C,D)) ) ) ) ) ) ) ).
fof(t9_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ( k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B) = u5_turing_1(A)
=> B = k9_turing_1(A,B) ) ) ) ).
fof(t10_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),np__0) = B ) ) ).
fof(t11_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B))))
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B))),k10_turing_1(B,C),k1_nat_1(A,np__1)) = k9_turing_1(B,k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B))),k10_turing_1(B,C),A)) ) ) ) ).
fof(t12_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),np__1) = k9_turing_1(A,B) ) ) ).
fof(t13_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( l1_turing_1(C)
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))))
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),k1_nat_1(A,B)) = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A)),B) ) ) ) ) ).
fof(t14_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( l1_turing_1(C)
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))))
=> ( ( r1_xreal_0(A,B)
& k9_turing_1(C,k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A)) = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A) )
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),B) = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A) ) ) ) ) ) ).
fof(t15_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( l1_turing_1(C)
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))))
=> ( ( r1_xreal_0(A,B)
& k5_mcart_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C)),k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A)) = u5_turing_1(C) )
=> k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),B) = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(C))),k10_turing_1(C,D),A) ) ) ) ) ) ).
fof(d9_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ( v2_turing_1(B,A)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),C)) = u5_turing_1(A) ) ) ) ) ).
fof(d10_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ( v2_turing_1(B,A)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ( C = k11_turing_1(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& C = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),D)
& k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),D)) = u5_turing_1(A) ) ) ) ) ) ) ).
fof(t16_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ~ ( v2_turing_1(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),C)) = u5_turing_1(A)
& k11_turing_1(A,B) = k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,D)
& k5_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k8_funct_2(k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))),k10_turing_1(A,B),D)) = u5_turing_1(A) ) ) ) ) ) ) ) ).
fof(d11_turing_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( r2_hidden(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(A,B))
& m2_relset_1(D,A,k2_zfmisc_1(A,B)) )
=> ( D = k12_turing_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k8_funct_2(A,k2_zfmisc_1(A,B),D,E) = k4_tarski(E,C) ) ) ) ) ) ) ).
fof(d12_turing_1,axiom,
k13_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__5),k7_domain_1(k5_numbers,np__0,np__1)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),np__0),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__0,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__0),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__3,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__4,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__1,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__4,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__5,np__0,np__0))) ).
fof(t17_turing_1,axiom,
( k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__0,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__0,np__0,np__1)
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__0,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1)
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__1,np__1)
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1)
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1)
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1))
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__3,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__0,k1_real_1(np__1))
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__4,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__1,k1_real_1(np__1))
& k1_funct_1(k13_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__4,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__5,np__0,np__0) ) ).
fof(d13_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_turing_1(A,B,C,D)
<=> ( k1_funct_1(B,C) = np__0
& k1_funct_1(B,D) = np__0
& ! [E] :
( v1_int_1(E)
=> ~ ( ~ r1_xreal_0(E,C)
& ~ r1_xreal_0(D,E)
& k1_funct_1(B,E) != np__1 ) ) ) ) ) ) ) ) ).
fof(d14_turing_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m2_fraenkel(C,k4_numbers,u1_turing_1(B),k1_fraenkel(k4_numbers,u1_turing_1(B)))
=> ( r2_turing_1(A,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,D)
=> ( r1_xreal_0(k3_finseq_1(A),D)
| r1_turing_1(B,C,k2_xcmplx_0(k2_gr_cy_1(k4_turing_1(A,D)),k4_real_1(np__2,k5_real_1(D,np__1))),k2_xcmplx_0(k2_gr_cy_1(k4_turing_1(A,k1_nat_1(D,np__1))),k2_nat_1(np__2,D))) ) ) ) ) ) ) ) ).
fof(t18_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_turing_1(k2_finseq_4(k5_numbers,C,D),A,B)
=> r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),np__2)) ) ) ) ) ) ).
fof(t19_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),np__2))
=> r2_turing_1(k2_finseq_4(k5_numbers,C,D),A,B) ) ) ) ) ) ).
fof(t20_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_turing_1(k2_finseq_4(k5_numbers,C,D),A,B)
=> ( k1_funct_1(B,C) = np__0
& k1_funct_1(B,k1_nat_1(k1_nat_1(C,D),np__2)) = np__0
& ! [E] :
( v1_int_1(E)
=> ~ ( ~ r1_xreal_0(E,C)
& ~ r1_xreal_0(k1_nat_1(k1_nat_1(C,D),np__2),E)
& k1_funct_1(B,E) != np__1 ) ) ) ) ) ) ) ) ).
fof(t21_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_turing_1(k3_finseq_4(k5_numbers,C,D,E),A,B)
=> ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),np__2))
& r1_turing_1(A,B,k1_nat_1(k1_nat_1(C,D),np__2),k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),np__4)) ) ) ) ) ) ) ) ).
fof(t22_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_turing_1(k3_finseq_4(k5_numbers,C,D,E),A,B)
=> ( k1_funct_1(B,C) = np__0
& k1_funct_1(B,k1_nat_1(k1_nat_1(C,D),np__2)) = np__0
& k1_funct_1(B,k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),np__4)) = np__0
& ! [F] :
( v1_int_1(F)
=> ~ ( ~ r1_xreal_0(F,C)
& ~ r1_xreal_0(k1_nat_1(k1_nat_1(C,D),np__2),F)
& k1_funct_1(B,F) != np__1 ) )
& ! [F] :
( v1_int_1(F)
=> ~ ( ~ r1_xreal_0(F,k1_nat_1(k1_nat_1(C,D),np__2))
& ~ r1_xreal_0(k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),np__4),F)
& k1_funct_1(B,F) != np__1 ) ) ) ) ) ) ) ) ) ).
fof(t23_turing_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,k3_finseq_1(A))
=> ( k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__1)) = B
& k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__2)) = k1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,np__1)) ) ) ) ) ).
fof(t24_turing_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__3,k3_finseq_1(A))
=> ( k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__1)) = B
& k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__2)) = k1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,np__1))
& k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__3)) = k1_nat_1(k1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,np__1)),k4_finseq_4(k5_numbers,k5_numbers,A,np__2))
& k2_gr_cy_1(k4_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,B),A),np__4)) = k1_nat_1(k1_nat_1(k1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,np__1)),k4_finseq_4(k5_numbers,k5_numbers,A,np__2)),k4_finseq_4(k5_numbers,k5_numbers,A,np__3)) ) ) ) ) ).
fof(t25_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( r1_xreal_0(np__1,k3_finseq_1(D))
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,C),D),A,B) )
=> r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),np__2)) ) ) ) ) ) ).
fof(t26_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( r1_xreal_0(np__3,k3_finseq_1(D))
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,C),D),A,B) )
=> ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),np__2))
& r1_turing_1(A,B,k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),np__2),k1_nat_1(k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),k4_finseq_4(k5_numbers,k5_numbers,D,np__2)),np__4))
& r1_turing_1(A,B,k1_nat_1(k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),k4_finseq_4(k5_numbers,k5_numbers,D,np__2)),np__4),k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),k4_finseq_4(k5_numbers,k5_numbers,D,np__2)),k4_finseq_4(k5_numbers,k5_numbers,D,np__3)),np__6)) ) ) ) ) ) ) ).
fof(d15_turing_1,axiom,
! [A] :
( ( v1_turing_1(A)
& l1_turing_1(A) )
=> ( A = k14_turing_1
<=> ( u1_turing_1(A) = k7_domain_1(k5_numbers,np__0,np__1)
& u2_turing_1(A) = k3_turing_1(np__5)
& u3_turing_1(A) = k13_turing_1
& u4_turing_1(A) = np__0
& u5_turing_1(A) = np__5 ) ) ) ).
fof(t27_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ! [C,D,E] :
( B = k3_mcart_1(C,D,E)
=> k7_turing_1(A,B) = D ) ) ) ).
fof(t28_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_subset_1(D,u1_turing_1(A))
=> ( k1_funct_1(B,C) = D
=> k5_turing_1(A,B,C,D) = B ) ) ) ) ) ).
fof(t29_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ! [C,D,E] :
( B = k3_mcart_1(C,D,E)
=> ( C = u5_turing_1(A)
| k9_turing_1(A,B) = k3_mcart_1(k5_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k8_turing_1(A,B)),k2_xcmplx_0(k7_turing_1(A,B),k6_turing_1(A,k8_turing_1(A,B))),k5_turing_1(A,k7_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),B),k7_turing_1(A,B),k6_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k8_turing_1(A,B)))) ) ) ) ) ).
fof(t30_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_subset_1(D,u1_turing_1(A))
=> ! [E] :
( k1_funct_1(k5_turing_1(A,B,C,D),C) = D
& ( E != C
=> k1_funct_1(k5_turing_1(A,B,C,D),E) = k1_funct_1(B,E) ) ) ) ) ) ) ).
fof(t31_turing_1,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(u2_turing_1(k14_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k14_turing_1))))
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(k14_turing_1),k1_fraenkel(k4_numbers,u1_turing_1(k14_turing_1)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( A = k4_domain_1(k5_numbers,k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k14_turing_1)),np__0,C,B)
& r2_turing_1(k3_finseq_4(k5_numbers,C,D,E),k14_turing_1,B) )
=> ( v2_turing_1(A,k14_turing_1)
& k6_mcart_1(u2_turing_1(k14_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k14_turing_1)),k11_turing_1(k14_turing_1,A)) = k1_nat_1(np__1,C)
& r2_turing_1(k2_finseq_4(k5_numbers,k1_nat_1(np__1,C),k1_nat_1(D,E)),k14_turing_1,k7_mcart_1(u2_turing_1(k14_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k14_turing_1)),k11_turing_1(k14_turing_1,A))) ) ) ) ) ) ) ) ).
fof(d16_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r3_turing_1(A,B)
<=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ! [D] :
( m2_fraenkel(D,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ( ( r2_hidden(F,k1_relat_1(B))
& C = k4_domain_1(u2_turing_1(A),k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),u4_turing_1(A),E,D)
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,E),F),A,D) )
=> ( v2_turing_1(C,A)
& ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& ? [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
& k6_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k11_turing_1(A,C)) = G
& H = k1_funct_1(B,F)
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,G),k12_finseq_1(k5_numbers,H)),A,k7_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k11_turing_1(A,C))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_turing_1,axiom,
r1_tarski(k1_relat_1(k17_comput_1),k4_finseq_2(np__2,k5_numbers)) ).
fof(t33_turing_1,axiom,
r3_turing_1(k14_turing_1,k17_comput_1) ).
fof(d17_turing_1,axiom,
k15_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),np__0),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__0),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__3,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__1,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__3,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__4,np__0,np__0))) ).
fof(t34_turing_1,axiom,
( k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__0,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1)
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__1,np__1)
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1)
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1))
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1))
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__3,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__1,k1_real_1(np__1))
& k1_funct_1(k15_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__3,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__4,np__0,np__0) ) ).
fof(d18_turing_1,axiom,
! [A] :
( ( v1_turing_1(A)
& l1_turing_1(A) )
=> ( A = k16_turing_1
<=> ( u1_turing_1(A) = k7_domain_1(k5_numbers,np__0,np__1)
& u2_turing_1(A) = k3_turing_1(np__4)
& u3_turing_1(A) = k15_turing_1
& u4_turing_1(A) = np__0
& u5_turing_1(A) = np__4 ) ) ) ).
fof(t35_turing_1,axiom,
$true ).
fof(t36_turing_1,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(u2_turing_1(k16_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k16_turing_1))))
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(k16_turing_1),k1_fraenkel(k4_numbers,u1_turing_1(k16_turing_1)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( A = k4_domain_1(k5_numbers,k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k16_turing_1)),np__0,C,B)
& r2_turing_1(k2_finseq_4(k5_numbers,C,D),k16_turing_1,B) )
=> ( v2_turing_1(A,k16_turing_1)
& k6_mcart_1(u2_turing_1(k16_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k16_turing_1)),k11_turing_1(k16_turing_1,A)) = C
& r2_turing_1(k2_finseq_4(k5_numbers,C,k1_nat_1(D,np__1)),k16_turing_1,k7_mcart_1(u2_turing_1(k16_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k16_turing_1)),k11_turing_1(k16_turing_1,A))) ) ) ) ) ) ) ).
fof(t37_turing_1,axiom,
r3_turing_1(k16_turing_1,k7_comput_1(np__1,np__1)) ).
fof(d19_turing_1,axiom,
k17_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),np__1),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__0),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1)))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k1_numbers),k1_domain_1(k5_numbers,k5_numbers,np__3,np__1),k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__1,k1_real_1(np__1)))) ).
fof(t38_turing_1,axiom,
( k1_funct_1(k17_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__0,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1)
& k1_funct_1(k17_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__1,np__1)
& k1_funct_1(k17_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1))
& k1_funct_1(k17_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__3,np__0,k1_real_1(np__1))
& k1_funct_1(k17_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__3,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k1_numbers,np__4,np__1,k1_real_1(np__1)) ) ).
fof(d20_turing_1,axiom,
! [A] :
( ( v1_turing_1(A)
& l1_turing_1(A) )
=> ( A = k18_turing_1
<=> ( u1_turing_1(A) = k7_domain_1(k5_numbers,np__0,np__1)
& u2_turing_1(A) = k3_turing_1(np__4)
& u3_turing_1(A) = k17_turing_1
& u4_turing_1(A) = np__0
& u5_turing_1(A) = np__4 ) ) ) ).
fof(t39_turing_1,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(u2_turing_1(k18_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1))))
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(k18_turing_1),k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( r1_xreal_0(np__1,k3_finseq_1(D))
& A = k4_domain_1(k5_numbers,k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)),np__0,C,B)
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,C),D),k18_turing_1,B) )
=> ( v2_turing_1(A,k18_turing_1)
& k6_mcart_1(u2_turing_1(k18_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)),k11_turing_1(k18_turing_1,A)) = C
& r2_turing_1(k2_finseq_4(k5_numbers,C,np__0),k18_turing_1,k7_mcart_1(u2_turing_1(k18_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)),k11_turing_1(k18_turing_1,A))) ) ) ) ) ) ) ).
fof(t40_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> r3_turing_1(k18_turing_1,k6_comput_1(A,np__0)) ) ) ).
fof(d21_turing_1,axiom,
k19_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__3),k7_domain_1(k5_numbers,np__0,np__1)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),np__0),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__1),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__0,np__1))),k2_turing_1(k2_zfmisc_1(k5_numbers,k5_numbers),k3_zfmisc_1(k5_numbers,k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__2,np__0),k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__3,np__0,np__0))) ).
fof(t41_turing_1,axiom,
( k1_funct_1(k19_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__0,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1)
& k1_funct_1(k19_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__1,np__0,np__1)
& k1_funct_1(k19_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__1,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__0,np__1)
& k1_funct_1(k19_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__1)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__2,np__0,np__1)
& k1_funct_1(k19_turing_1,k1_domain_1(k5_numbers,k5_numbers,np__2,np__0)) = k4_domain_1(k5_numbers,k5_numbers,k5_numbers,np__3,np__0,np__0) ) ).
fof(d22_turing_1,axiom,
! [A] :
( ( v1_turing_1(A)
& l1_turing_1(A) )
=> ( A = k20_turing_1
<=> ( u1_turing_1(A) = k7_domain_1(k5_numbers,np__0,np__1)
& u2_turing_1(A) = k3_turing_1(np__3)
& u3_turing_1(A) = k19_turing_1
& u4_turing_1(A) = np__0
& u5_turing_1(A) = np__3 ) ) ) ).
fof(t42_turing_1,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(u2_turing_1(k20_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k20_turing_1))))
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(k20_turing_1),k1_fraenkel(k4_numbers,u1_turing_1(k20_turing_1)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( r1_xreal_0(np__3,k3_finseq_1(D))
& A = k4_domain_1(k5_numbers,k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k20_turing_1)),np__0,C,B)
& r2_turing_1(k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,C),D),k20_turing_1,B) )
=> ( v2_turing_1(A,k20_turing_1)
& k6_mcart_1(u2_turing_1(k20_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k20_turing_1)),k11_turing_1(k20_turing_1,A)) = k1_nat_1(k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),k4_finseq_4(k5_numbers,k5_numbers,D,np__2)),np__4)
& r2_turing_1(k2_finseq_4(k5_numbers,k1_nat_1(k1_nat_1(k1_nat_1(C,k4_finseq_4(k5_numbers,k5_numbers,D,np__1)),k4_finseq_4(k5_numbers,k5_numbers,D,np__2)),np__4),k4_finseq_4(k5_numbers,k5_numbers,D,np__3)),k20_turing_1,k7_mcart_1(u2_turing_1(k20_turing_1),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k20_turing_1)),k11_turing_1(k20_turing_1,A))) ) ) ) ) ) ) ).
fof(t43_turing_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__3,A)
=> r3_turing_1(k20_turing_1,k8_comput_1(A,np__3)) ) ) ).
fof(d23_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> k21_turing_1(A,B) = k2_xboole_0(k2_zfmisc_1(u2_turing_1(A),k6_domain_1(u2_turing_1(B),u4_turing_1(B))),k2_zfmisc_1(k6_domain_1(u2_turing_1(A),u5_turing_1(A)),u2_turing_1(B))) ) ) ).
fof(t44_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ( r2_hidden(k1_domain_1(u2_turing_1(A),u2_turing_1(B),u4_turing_1(A),u4_turing_1(B)),k21_turing_1(A,B))
& r2_hidden(k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),u5_turing_1(B)),k21_turing_1(A,B)) ) ) ) ).
fof(t45_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,u2_turing_1(A))
=> r2_hidden(k1_domain_1(u2_turing_1(A),u2_turing_1(B),C,u4_turing_1(B)),k21_turing_1(A,B)) ) ) ) ).
fof(t46_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,u2_turing_1(B))
=> r2_hidden(k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),C),k21_turing_1(A,B)) ) ) ) ).
fof(t47_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k21_turing_1(A,B))
=> ? [D] :
( m1_subset_1(D,u2_turing_1(A))
& ? [E] :
( m1_subset_1(E,u2_turing_1(B))
& C = k1_domain_1(u2_turing_1(A),u2_turing_1(B),D,E) ) ) ) ) ) ).
fof(d24_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
=> k22_turing_1(A,B,C) = k4_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),k5_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),u4_turing_1(B)),k6_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),k7_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)) ) ) ) ).
fof(d25_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
=> k23_turing_1(A,B,C) = k4_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),k5_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)),k6_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),k7_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)) ) ) ) ).
fof(d26_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))))
=> k26_turing_1(A,B,C) = k24_turing_1(A,B,k2_domain_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),C)) ) ) ) ).
fof(d27_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))))
=> k27_turing_1(A,B,C) = k25_turing_1(A,B,k2_domain_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),C)) ) ) ) ).
fof(d28_turing_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C)))
=> ( ? [E,F] :
( m1_subset_1(F,B)
& D = k4_tarski(E,F) )
=> k28_turing_1(A,B,C,D) = k3_domain_1(A,k2_xboole_0(B,C),D) ) ) ) ) ) ).
fof(d29_turing_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C)))
=> ( ? [E,F] :
( m1_subset_1(F,C)
& D = k4_tarski(E,F) )
=> k29_turing_1(A,B,C,D) = k3_domain_1(A,k2_xboole_0(B,C),D) ) ) ) ) ) ).
fof(d30_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))))
=> ( ( ? [D] :
( m1_subset_1(D,u2_turing_1(A))
& ? [E] :
( m1_subset_1(E,u1_turing_1(A))
& C = k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(A),k1_domain_1(u2_turing_1(A),u2_turing_1(B),D,u4_turing_1(B)),E)
& D != u5_turing_1(A) ) )
=> k30_turing_1(A,B,C) = k22_turing_1(A,B,k8_funct_2(k2_zfmisc_1(u2_turing_1(A),u1_turing_1(A)),k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)),u3_turing_1(A),k1_domain_1(u2_turing_1(A),u1_turing_1(A),k26_turing_1(A,B,C),k28_turing_1(k21_turing_1(A,B),u1_turing_1(A),u1_turing_1(B),C)))) )
& ( ? [D] :
( m1_subset_1(D,u2_turing_1(B))
& ? [E] :
( m1_subset_1(E,u1_turing_1(B))
& C = k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(B),k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),D),E) ) )
=> k30_turing_1(A,B,C) = k23_turing_1(A,B,k8_funct_2(k2_zfmisc_1(u2_turing_1(B),u1_turing_1(B)),k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)),u3_turing_1(B),k1_domain_1(u2_turing_1(B),u1_turing_1(B),k27_turing_1(A,B,C),k29_turing_1(k21_turing_1(A,B),u1_turing_1(A),u1_turing_1(B),C)))) )
& ( ( ! [D] :
( m1_subset_1(D,u2_turing_1(A))
=> ! [E] :
( m1_subset_1(E,u1_turing_1(A))
=> ~ ( C = k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(A),k1_domain_1(u2_turing_1(A),u2_turing_1(B),D,u4_turing_1(B)),E)
& D != u5_turing_1(A) ) ) )
& ! [D] :
( m1_subset_1(D,u2_turing_1(B))
=> ! [E] :
( m1_subset_1(E,u1_turing_1(B))
=> C != k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(B),k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),D),E) ) ) )
=> k30_turing_1(A,B,C) = k4_domain_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k1_numbers,k2_domain_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),C),k3_domain_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),C),k1_real_1(np__1)) ) ) ) ) ) ).
fof(d31_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) )
=> ( C = k31_turing_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))))
=> k8_funct_2(k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)),C,D) = k30_turing_1(A,B,D) ) ) ) ) ) ).
fof(d32_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( ( v1_turing_1(C)
& l1_turing_1(C) )
=> ( C = k32_turing_1(A,B)
<=> ( u1_turing_1(C) = k2_xboole_0(u1_turing_1(A),u1_turing_1(B))
& u2_turing_1(C) = k21_turing_1(A,B)
& u3_turing_1(C) = k31_turing_1(A,B)
& u4_turing_1(C) = k1_domain_1(u2_turing_1(A),u2_turing_1(B),u4_turing_1(A),u4_turing_1(B))
& u5_turing_1(C) = k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),u5_turing_1(B)) ) ) ) ) ) ).
fof(t48_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
=> ! [D] :
( m1_subset_1(D,u2_turing_1(A))
=> ! [E] :
( m1_subset_1(E,u1_turing_1(A))
=> ( C = k8_funct_2(k2_zfmisc_1(u2_turing_1(A),u1_turing_1(A)),k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)),u3_turing_1(A),k1_domain_1(u2_turing_1(A),u1_turing_1(A),D,E))
=> ( D = u5_turing_1(A)
| k1_funct_1(u3_turing_1(k32_turing_1(A,B)),k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(A),k1_domain_1(u2_turing_1(A),u2_turing_1(B),D,u4_turing_1(B)),E)) = k4_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),k5_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),u4_turing_1(B)),k6_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),k7_mcart_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)) ) ) ) ) ) ) ) ).
fof(t49_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
=> ! [D] :
( m1_subset_1(D,u2_turing_1(B))
=> ! [E] :
( m1_subset_1(E,u1_turing_1(B))
=> ( C = k8_funct_2(k2_zfmisc_1(u2_turing_1(B),u1_turing_1(B)),k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)),u3_turing_1(B),k1_domain_1(u2_turing_1(B),u1_turing_1(B),D,E))
=> k1_funct_1(u3_turing_1(k32_turing_1(A,B)),k1_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(B),k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),D),E)) = k4_domain_1(k2_zfmisc_1(u2_turing_1(A),u2_turing_1(B)),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),u5_turing_1(A),k5_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)),k6_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C),k7_mcart_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1),C)) ) ) ) ) ) ) ).
fof(t50_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_fraenkel(E,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ! [F] :
( m1_subset_1(F,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B))))
=> ! [G] :
( m1_subset_1(G,k3_zfmisc_1(u2_turing_1(k32_turing_1(A,B)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(A,B)))))
=> ( ( v2_turing_1(C,A)
& C = k4_domain_1(u2_turing_1(A),k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),u4_turing_1(A),D,E)
& v2_turing_1(F,B)
& F = k4_domain_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),u4_turing_1(B),k6_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k11_turing_1(A,C)),k7_mcart_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),k11_turing_1(A,C)))
& G = k4_domain_1(u2_turing_1(k32_turing_1(A,B)),k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)),u4_turing_1(k32_turing_1(A,B)),D,E) )
=> ( v2_turing_1(G,k32_turing_1(A,B))
& k6_mcart_1(u2_turing_1(k32_turing_1(A,B)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(A,B))),k11_turing_1(k32_turing_1(A,B),G)) = k6_mcart_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B)),k11_turing_1(B,F))
& k7_mcart_1(u2_turing_1(k32_turing_1(A,B)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(A,B))),k11_turing_1(k32_turing_1(A,B),G)) = k7_mcart_1(u2_turing_1(B),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(B)),k11_turing_1(B,F)) ) ) ) ) ) ) ) ) ) ).
fof(t51_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m2_fraenkel(C,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
=> ( u1_turing_1(A) = u1_turing_1(B)
=> m2_fraenkel(C,k4_numbers,u1_turing_1(k32_turing_1(A,B)),k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(A,B)))) ) ) ) ) ).
fof(t52_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( m2_fraenkel(C,k4_numbers,u1_turing_1(k32_turing_1(A,B)),k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(A,B))))
=> ( u1_turing_1(A) = u1_turing_1(B)
=> ( m2_fraenkel(C,k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A)))
& m2_fraenkel(C,k4_numbers,u1_turing_1(B),k1_fraenkel(k4_numbers,u1_turing_1(B))) ) ) ) ) ) ).
fof(t53_turing_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( l1_turing_1(B)
=> ! [C] :
( l1_turing_1(C)
=> ! [D] :
( m2_fraenkel(D,k4_numbers,u1_turing_1(B),k1_fraenkel(k4_numbers,u1_turing_1(B)))
=> ! [E] :
( m2_fraenkel(E,k4_numbers,u1_turing_1(C),k1_fraenkel(k4_numbers,u1_turing_1(C)))
=> ( ( D = E
& r2_turing_1(A,B,D) )
=> r2_turing_1(A,C,E) ) ) ) ) ) ) ).
fof(t54_turing_1,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(u2_turing_1(k32_turing_1(k18_turing_1,k16_turing_1)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(k18_turing_1,k16_turing_1)))))
=> ! [B] :
( m2_fraenkel(B,k4_numbers,u1_turing_1(k18_turing_1),k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( A = k4_domain_1(k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k18_turing_1)),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),C,B)
& r2_turing_1(k2_finseq_4(k5_numbers,C,D),k18_turing_1,B) )
=> ( v2_turing_1(A,k32_turing_1(k18_turing_1,k16_turing_1))
& k6_mcart_1(u2_turing_1(k32_turing_1(k18_turing_1,k16_turing_1)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(k18_turing_1,k16_turing_1))),k11_turing_1(k32_turing_1(k18_turing_1,k16_turing_1),A)) = C
& r2_turing_1(k2_finseq_4(k5_numbers,C,np__1),k32_turing_1(k18_turing_1,k16_turing_1),k7_mcart_1(u2_turing_1(k32_turing_1(k18_turing_1,k16_turing_1)),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(k32_turing_1(k18_turing_1,k16_turing_1))),k11_turing_1(k32_turing_1(k18_turing_1,k16_turing_1),A))) ) ) ) ) ) ) ).
fof(dt_l1_turing_1,axiom,
$true ).
fof(existence_l1_turing_1,axiom,
? [A] : l1_turing_1(A) ).
fof(abstractness_v1_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ( v1_turing_1(A)
=> A = g1_turing_1(u1_turing_1(A),u2_turing_1(A),u3_turing_1(A),u4_turing_1(A),u5_turing_1(A)) ) ) ).
fof(dt_k1_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& v1_funct_1(D)
& m1_relset_1(D,A,B) )
=> ( v1_funct_1(k1_turing_1(A,B,C,D))
& v1_funct_2(k1_turing_1(A,B,C,D),A,B)
& m2_relset_1(k1_turing_1(A,B,C,D),A,B) ) ) ).
fof(idempotence_k1_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& v1_funct_1(D)
& m1_relset_1(D,A,B) )
=> k1_turing_1(A,B,C,C) = C ) ).
fof(redefinition_k1_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& v1_funct_1(D)
& m1_relset_1(D,A,B) )
=> k1_turing_1(A,B,C,D) = k1_funct_4(C,D) ) ).
fof(dt_k2_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A)
& m1_subset_1(D,B) )
=> ( v1_funct_1(k2_turing_1(A,B,C,D))
& m2_relset_1(k2_turing_1(A,B,C,D),A,B) ) ) ).
fof(redefinition_k2_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A)
& m1_subset_1(D,B) )
=> k2_turing_1(A,B,C,D) = k3_cqc_lang(C,D) ) ).
fof(dt_k3_turing_1,axiom,
! [A] :
( v4_ordinal2(A)
=> m1_subset_1(k3_turing_1(A),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k4_turing_1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_1(k4_turing_1(A,B),k4_numbers) ) ).
fof(dt_k5_turing_1,axiom,
! [A,B,C,D] :
( ( l1_turing_1(A)
& m1_subset_1(B,k1_fraenkel(k4_numbers,u1_turing_1(A)))
& v1_int_1(C)
& m1_subset_1(D,u1_turing_1(A)) )
=> m2_fraenkel(k5_turing_1(A,B,C,D),k4_numbers,u1_turing_1(A),k1_fraenkel(k4_numbers,u1_turing_1(A))) ) ).
fof(dt_k6_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) )
=> v1_int_1(k6_turing_1(A,B)) ) ).
fof(dt_k7_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> v1_int_1(k7_turing_1(A,B)) ) ).
fof(dt_k8_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> m1_subset_1(k8_turing_1(A,B),k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k9_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> m1_subset_1(k9_turing_1(A,B),k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) ) ).
fof(dt_k10_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> ( v1_funct_1(k10_turing_1(A,B))
& v1_funct_2(k10_turing_1(A,B),k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A))))
& m2_relset_1(k10_turing_1(A,B),k5_numbers,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) ) ) ).
fof(dt_k11_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) )
=> m1_subset_1(k11_turing_1(A,B),k3_zfmisc_1(u2_turing_1(A),k4_numbers,k1_fraenkel(k4_numbers,u1_turing_1(A)))) ) ).
fof(dt_k12_turing_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ( v1_funct_1(k12_turing_1(A,B,C))
& v1_funct_2(k12_turing_1(A,B,C),A,k2_zfmisc_1(A,B))
& m2_relset_1(k12_turing_1(A,B,C),A,k2_zfmisc_1(A,B)) ) ) ).
fof(dt_k13_turing_1,axiom,
( v1_funct_1(k13_turing_1)
& v1_funct_2(k13_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__5),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__5),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(k13_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__5),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__5),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k14_turing_1,axiom,
( v1_turing_1(k14_turing_1)
& l1_turing_1(k14_turing_1) ) ).
fof(dt_k15_turing_1,axiom,
( v1_funct_1(k15_turing_1)
& v1_funct_2(k15_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(k15_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k16_turing_1,axiom,
( v1_turing_1(k16_turing_1)
& l1_turing_1(k16_turing_1) ) ).
fof(dt_k17_turing_1,axiom,
( v1_funct_1(k17_turing_1)
& v1_funct_2(k17_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(k17_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__4),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k18_turing_1,axiom,
( v1_turing_1(k18_turing_1)
& l1_turing_1(k18_turing_1) ) ).
fof(dt_k19_turing_1,axiom,
( v1_funct_1(k19_turing_1)
& v1_funct_2(k19_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__3),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__3),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(k19_turing_1,k12_mcart_1(k5_numbers,k5_numbers,k3_turing_1(np__3),k7_domain_1(k5_numbers,np__0,np__1)),k13_mcart_1(k5_numbers,k5_numbers,k1_numbers,k3_turing_1(np__3),k7_domain_1(k5_numbers,np__0,np__1),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k20_turing_1,axiom,
( v1_turing_1(k20_turing_1)
& l1_turing_1(k20_turing_1) ) ).
fof(dt_k21_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& l1_turing_1(B) )
=> ( ~ v1_xboole_0(k21_turing_1(A,B))
& v1_finset_1(k21_turing_1(A,B)) ) ) ).
fof(dt_k22_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) )
=> m1_subset_1(k22_turing_1(A,B,C),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k23_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) )
=> m1_subset_1(k23_turing_1(A,B,C),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k24_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k21_turing_1(A,B)) )
=> m1_subset_1(k24_turing_1(A,B,C),u2_turing_1(A)) ) ).
fof(redefinition_k24_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k21_turing_1(A,B)) )
=> k24_turing_1(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k25_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k21_turing_1(A,B)) )
=> m1_subset_1(k25_turing_1(A,B,C),u2_turing_1(B)) ) ).
fof(redefinition_k25_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k21_turing_1(A,B)) )
=> k25_turing_1(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k26_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)))) )
=> m1_subset_1(k26_turing_1(A,B,C),u2_turing_1(A)) ) ).
fof(dt_k27_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)))) )
=> m1_subset_1(k27_turing_1(A,B,C),u2_turing_1(B)) ) ).
fof(dt_k28_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C))) )
=> m1_subset_1(k28_turing_1(A,B,C,D),B) ) ).
fof(dt_k29_turing_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C))) )
=> m1_subset_1(k29_turing_1(A,B,C,D),C) ) ).
fof(dt_k30_turing_1,axiom,
! [A,B,C] :
( ( l1_turing_1(A)
& l1_turing_1(B)
& m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)))) )
=> m1_subset_1(k30_turing_1(A,B,C),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ).
fof(dt_k31_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& l1_turing_1(B) )
=> ( v1_funct_1(k31_turing_1(A,B))
& v1_funct_2(k31_turing_1(A,B),k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(k31_turing_1(A,B),k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B))),k3_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ) ).
fof(dt_k32_turing_1,axiom,
! [A,B] :
( ( l1_turing_1(A)
& l1_turing_1(B) )
=> ( v1_turing_1(k32_turing_1(A,B))
& l1_turing_1(k32_turing_1(A,B)) ) ) ).
fof(dt_u1_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ( ~ v1_xboole_0(u1_turing_1(A))
& v1_finset_1(u1_turing_1(A)) ) ) ).
fof(dt_u2_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ( ~ v1_xboole_0(u2_turing_1(A))
& v1_finset_1(u2_turing_1(A)) ) ) ).
fof(dt_u3_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> ( v1_funct_1(u3_turing_1(A))
& v1_funct_2(u3_turing_1(A),k2_zfmisc_1(u2_turing_1(A),u1_turing_1(A)),k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m2_relset_1(u3_turing_1(A),k2_zfmisc_1(u2_turing_1(A),u1_turing_1(A)),k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1))) ) ) ).
fof(dt_u4_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> m1_subset_1(u4_turing_1(A),u2_turing_1(A)) ) ).
fof(dt_u5_turing_1,axiom,
! [A] :
( l1_turing_1(A)
=> m1_subset_1(u5_turing_1(A),u2_turing_1(A)) ) ).
fof(dt_g1_turing_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m1_relset_1(C,k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m1_subset_1(D,B)
& m1_subset_1(E,B) )
=> ( v1_turing_1(g1_turing_1(A,B,C,D,E))
& l1_turing_1(g1_turing_1(A,B,C,D,E)) ) ) ).
fof(free_g1_turing_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m1_relset_1(C,k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k8_domain_1(k1_numbers,k1_real_1(np__1),np__0,np__1)))
& m1_subset_1(D,B)
& m1_subset_1(E,B) )
=> ! [F,G,H,I,J] :
( g1_turing_1(A,B,C,D,E) = g1_turing_1(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(d1_turing_1,axiom,
! [A] :
( v4_ordinal2(A)
=> k3_turing_1(A) = a_1_0_turing_1(A) ) ).
fof(fraenkel_a_1_0_turing_1,axiom,
! [A,B] :
( v4_ordinal2(B)
=> ( r2_hidden(A,a_1_0_turing_1(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = C
& r1_xreal_0(C,B) ) ) ) ).
%------------------------------------------------------------------------------