% Mizar problem: t43_coh_sp,coh_sp,1328,22 
fof(t43_coh_sp,conjecture,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => B = k4_tarski(k4_tarski(k22_coh_sp(A,B),k23_coh_sp(A,B)),k2_mcart_1(B)) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_partfun1,cc1_relset_1,cc2_funct_1,cc2_funct_2,cc3_funct_2,cc4_funct_2,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,d1_mcart_1,d20_coh_sp,d21_coh_sp,d22_coh_sp,d23_coh_sp,d25_coh_sp,d26_coh_sp,d5_tarski,dt_k15_coh_sp,dt_k16_coh_sp,dt_k17_coh_sp,dt_k18_coh_sp,dt_k19_coh_sp,dt_k1_funct_1,dt_k1_funct_2,dt_k1_mcart_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_coh_sp,dt_k21_coh_sp,dt_k22_coh_sp,dt_k23_coh_sp,dt_k2_mcart_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_tarski,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_coh_sp,fc1_fraenkel,fc1_funct_2,fc1_subset_1,fc1_toler_1,fc2_funct_2,fc2_subset_1,fc3_subset_1,fc4_subset_1,fc5_coh_sp,fc6_coh_sp,fc7_coh_sp,fc8_coh_sp,fc9_coh_sp,fraenkel_a_1_3_coh_sp,fraenkel_a_1_4_coh_sp,fraenkel_a_1_5_coh_sp,fraenkel_a_1_6_coh_sp,rc1_fraenkel,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc1_subset_1,rc2_funct_1,rc2_funct_2,rc2_partfun1,rc2_subset_1,rc3_funct_1,rc3_partfun1,rc4_funct_1,redefinition_k18_coh_sp,redefinition_k19_coh_sp,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t2_tarski,t3_subset,t41_coh_sp,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_mcart_1]),
    [file(coh_sp,t43_coh_sp)]).

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

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_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(cc2_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

fof(cc4_funct_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( ( v1_funct_1(B)
          & v1_partfun1(B,A,A)
          & v1_relat_2(B)
          & v1_funct_2(B,A,A) )
       => ( v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,A,A)
          & v2_funct_2(B,A,A)
          & v3_funct_2(B,A,A) ) ) ) ),
    file(funct_2,cc4_funct_2),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d1_mcart_1,axiom,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => ! [B] : 
          ( B = k1_mcart_1(A)
        <=> ! [C,D] : 
              ( A = k4_tarski(C,D)
             => B = C ) ) ) ),
    file(mcart_1,d1_mcart_1),
    []).

fof(d20_coh_sp,axiom,(
    ! [A] : k16_coh_sp(A) = k3_tarski(a_1_3_coh_sp(A)) ),
    file(coh_sp,d20_coh_sp),
    []).

fof(d21_coh_sp,axiom,(
    ! [A] : k17_coh_sp(A) = a_1_4_coh_sp(A) ),
    file(coh_sp,d21_coh_sp),
    []).

fof(d22_coh_sp,axiom,(
    ! [A] : k20_coh_sp(A) = k3_tarski(a_1_5_coh_sp(A)) ),
    file(coh_sp,d22_coh_sp),
    []).

fof(d23_coh_sp,axiom,(
    ! [A] : k21_coh_sp(A) = a_1_6_coh_sp(A) ),
    file(coh_sp,d23_coh_sp),
    []).

fof(d25_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => k22_coh_sp(A,B) = k1_mcart_1(k1_mcart_1(B)) ) ),
    file(coh_sp,d25_coh_sp),
    []).

fof(d26_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => k23_coh_sp(A,B) = k2_mcart_1(k1_mcart_1(B)) ) ),
    file(coh_sp,d26_coh_sp),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_k15_coh_sp,axiom,(
    $true ),
    file(coh_sp,k15_coh_sp),
    []).

fof(dt_k16_coh_sp,axiom,(
    $true ),
    file(coh_sp,k16_coh_sp),
    []).

fof(dt_k17_coh_sp,axiom,(
    $true ),
    file(coh_sp,k17_coh_sp),
    []).

fof(dt_k18_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k17_coh_sp(A))
     => m1_subset_1(k18_coh_sp(A,B),k1_zfmisc_1(A)) ) ),
    file(coh_sp,k18_coh_sp),
    []).

fof(dt_k19_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k17_coh_sp(A))
     => ( v1_relat_2(k19_coh_sp(A,B))
        & v3_relat_2(k19_coh_sp(A,B))
        & v1_partfun1(k19_coh_sp(A,B),k2_mcart_1(B),k2_mcart_1(B))
        & m2_relset_1(k19_coh_sp(A,B),k2_mcart_1(B),k2_mcart_1(B)) ) ) ),
    file(coh_sp,k19_coh_sp),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k20_coh_sp,axiom,(
    $true ),
    file(coh_sp,k20_coh_sp),
    []).

fof(dt_k21_coh_sp,axiom,(
    $true ),
    file(coh_sp,k21_coh_sp),
    []).

fof(dt_k22_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => m1_subset_1(k22_coh_sp(A,B),k17_coh_sp(A)) ) ),
    file(coh_sp,k22_coh_sp),
    []).

fof(dt_k23_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => m1_subset_1(k23_coh_sp(A,B),k17_coh_sp(A)) ) ),
    file(coh_sp,k23_coh_sp),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B)) ) ) ),
    file(coh_sp,fc10_coh_sp),
    []).

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_toler_1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_relat_2(k1_xboole_0)
    & v2_relat_2(k1_xboole_0)
    & v3_relat_2(k1_xboole_0)
    & v4_relat_2(k1_xboole_0)
    & v5_relat_2(k1_xboole_0)
    & v6_relat_2(k1_xboole_0)
    & v7_relat_2(k1_xboole_0)
    & v8_relat_2(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0) ),
    file(toler_1,fc1_toler_1),
    []).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_coh_sp,axiom,(
    ! [A] : ~ v1_xboole_0(k15_coh_sp(A)) ),
    file(coh_sp,fc5_coh_sp),
    []).

fof(fc6_coh_sp,axiom,(
    ! [A] : ~ v1_xboole_0(k16_coh_sp(A)) ),
    file(coh_sp,fc6_coh_sp),
    []).

fof(fc7_coh_sp,axiom,(
    ! [A] : ~ v1_xboole_0(k17_coh_sp(A)) ),
    file(coh_sp,fc7_coh_sp),
    []).

fof(fc8_coh_sp,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k20_coh_sp(A))
      & v1_fraenkel(k20_coh_sp(A)) ) ),
    file(coh_sp,fc8_coh_sp),
    []).

fof(fc9_coh_sp,axiom,(
    ! [A] : ~ v1_xboole_0(k21_coh_sp(A)) ),
    file(coh_sp,fc9_coh_sp),
    []).

fof(fraenkel_a_1_3_coh_sp,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_3_coh_sp(B))
    <=> ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(B))
          & A = k15_coh_sp(C) ) ) ),
    file(coh_sp,a_1_3_coh_sp),
    []).

fof(fraenkel_a_1_4_coh_sp,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_4_coh_sp(B))
    <=> ? [C,D] : 
          ( m1_subset_1(C,k16_coh_sp(B))
          & m1_subset_1(D,k1_zfmisc_1(B))
          & A = k4_tarski(C,D)
          & v1_relat_2(C)
          & v3_relat_2(C)
          & v1_partfun1(C,D,D)
          & m2_relset_1(C,D,D) ) ) ),
    file(coh_sp,a_1_4_coh_sp),
    []).

fof(fraenkel_a_1_5_coh_sp,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_5_coh_sp(B))
    <=> ? [C,D] : 
          ( m1_subset_1(C,k17_coh_sp(B))
          & m1_subset_1(D,k17_coh_sp(B))
          & A = k1_funct_2(k18_coh_sp(B,C),k18_coh_sp(B,D)) ) ) ),
    file(coh_sp,a_1_5_coh_sp),
    []).

fof(fraenkel_a_1_6_coh_sp,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_6_coh_sp(B))
    <=> ? [C,D,E] : 
          ( m1_subset_1(C,k17_coh_sp(B))
          & m1_subset_1(D,k17_coh_sp(B))
          & m1_subset_1(E,k20_coh_sp(B))
          & A = k4_tarski(k4_tarski(C,D),E)
          & ( k18_coh_sp(B,D) = k1_xboole_0
           => k18_coh_sp(B,C) = k1_xboole_0 )
          & v1_funct_1(E)
          & v1_funct_2(E,k18_coh_sp(B,C),k18_coh_sp(B,D))
          & m2_relset_1(E,k18_coh_sp(B,C),k18_coh_sp(B,D))
          & ! [F,G] : 
              ( r2_hidden(k4_tarski(F,G),k19_coh_sp(B,C))
             => r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,G)),k19_coh_sp(B,D)) ) ) ) ),
    file(coh_sp,a_1_6_coh_sp),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_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(rc2_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_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(rc3_partfun1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    []).

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(redefinition_k18_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k17_coh_sp(A))
     => k18_coh_sp(A,B) = k2_mcart_1(B) ) ),
    file(coh_sp,k18_coh_sp),
    []).

fof(redefinition_k19_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k17_coh_sp(A))
     => k19_coh_sp(A,B) = k1_mcart_1(B) ) ),
    file(coh_sp,k19_coh_sp),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t41_coh_sp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k21_coh_sp(A))
     => ? [C] : 
          ( m1_subset_1(C,k20_coh_sp(A))
          & ? [D] : 
              ( m1_subset_1(D,k17_coh_sp(A))
              & ? [E] : 
                  ( m1_subset_1(E,k17_coh_sp(A))
                  & B = k4_tarski(k4_tarski(D,E),C)
                  & ( k18_coh_sp(A,E) = k1_xboole_0
                   => k18_coh_sp(A,D) = k1_xboole_0 )
                  & v1_funct_1(C)
                  & v1_funct_2(C,k18_coh_sp(A,D),k18_coh_sp(A,E))
                  & m2_relset_1(C,k18_coh_sp(A,D),k18_coh_sp(A,E))
                  & ! [F,G] : 
                      ( r2_hidden(k4_tarski(F,G),k19_coh_sp(A,D))
                     => r2_hidden(k4_tarski(k1_funct_1(C,F),k1_funct_1(C,G)),k19_coh_sp(A,E)) ) ) ) ) ) ),
    file(coh_sp,t41_coh_sp),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

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

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(t8_mcart_1,axiom,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A ) ),
    file(mcart_1,t8_mcart_1),
    []).