% Mizar problem: t27_turing_1,turing_1,876,11 
fof(t27_turing_1,conjecture,(
    ! [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 ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,t1_subset,existence_m1_fraenkel,dt_k1_funct_2,dt_m1_fraenkel,fc5_subset_1,rc1_funct_1,cc1_funct_1,rc2_funct_1,cc2_funct_1,rc3_funct_1,rc4_funct_1,rc2_int_1,cc4_int_1,rc1_finset_1,cc1_finset_1,fc15_finset_1,rc1_xboole_0,rc2_xboole_0,rc4_comput_1,rc9_comput_1,t2_subset,t7_boole,t8_boole,existence_l1_turing_1,existence_m1_subset_1,redefinition_k1_fraenkel,dt_k1_fraenkel,dt_k1_xboole_0,dt_k3_mcart_1,dt_k3_zfmisc_1,dt_k4_numbers,dt_k5_mcart_1,dt_k6_mcart_1,dt_k7_mcart_1,dt_k7_turing_1,dt_l1_turing_1,dt_m1_subset_1,dt_u1_turing_1,dt_u2_turing_1,cc1_int_1,fc1_xboole_0,fc2_comput_1,fc5_comput_1,fc4_numbers,t6_boole,d5_turing_1,t68_mcart_1]),
    [file(turing_1,t27_turing_1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(fc5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) )
     => ~ v1_xboole_0(k3_zfmisc_1(A,B,C)) ) ),
    file(subset_1,fc5_subset_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

fof(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(fc15_finset_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B)
        & v1_finset_1(C) )
     => v1_finset_1(k3_zfmisc_1(A,B,C)) ) ),
    file(finset_1,fc15_finset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc4_comput_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v4_comput_1(A) ) ),
    file(comput_1,rc4_comput_1),
    []).

fof(rc9_comput_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v5_comput_1(A) ) ),
    file(comput_1,rc9_comput_1),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(existence_l1_turing_1,axiom,(
    ? [A] : l1_turing_1(A) ),
    file(turing_1,l1_turing_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_numbers,axiom,(
    $true ),
    file(numbers,k4_numbers),
    []).

fof(dt_k5_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k5_mcart_1(A,B,C,D),A) ) ),
    file(mcart_1,k5_mcart_1),
    []).

fof(dt_k6_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k6_mcart_1(A,B,C,D),B) ) ),
    file(mcart_1,k6_mcart_1),
    []).

fof(dt_k7_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k7_mcart_1(A,B,C,D),C) ) ),
    file(mcart_1,k7_mcart_1),
    []).

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)) ) ),
    file(turing_1,k7_turing_1),
    []).

fof(dt_l1_turing_1,axiom,(
    $true ),
    file(turing_1,l1_turing_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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)) ) ) ),
    file(turing_1,u1_turing_1),
    []).

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)) ) ) ),
    file(turing_1,u2_turing_1),
    []).

fof(cc1_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k4_numbers)
     => v1_int_1(A) ) ),
    file(int_1,cc1_int_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_comput_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_funct_7(k1_xboole_0)
    & v4_comput_1(k1_xboole_0) ),
    file(comput_1,fc2_comput_1),
    []).

fof(fc5_comput_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_funct_7(k1_xboole_0)
    & v4_comput_1(k1_xboole_0)
    & v5_comput_1(k1_xboole_0) ),
    file(comput_1,fc5_comput_1),
    []).

fof(fc4_numbers,axiom,(
    ~ v1_xboole_0(k4_numbers) ),
    file(numbers,fc4_numbers),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

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) ) ) ),
    file(turing_1,d5_turing_1),
    []).

fof(t68_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => ~ ( A != k1_xboole_0
          & B != k1_xboole_0
          & C != k1_xboole_0
          & ? [E,F,G] : 
              ( D = k3_mcart_1(E,F,G)
              & ~ ( k5_mcart_1(A,B,C,D) = E
                  & k6_mcart_1(A,B,C,D) = F
                  & k7_mcart_1(A,B,C,D) = G ) ) ) ) ),
    file(mcart_1,t68_mcart_1),
    []).