% Mizar problem: t14_arytm_2,arytm_2,2035,35 
fof(t14_arytm_2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => k8_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k8_arytm_2(A,B),k8_arytm_2(A,C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,cc4_arytm_3,commutativity_k10_arytm_3,commutativity_k11_arytm_3,commutativity_k2_xboole_0,commutativity_k5_arytm_2,commutativity_k6_arytm_2,commutativity_k7_arytm_2,commutativity_k8_arytm_2,connectedness_r3_arytm_3,d1_arytm_2,d2_arytm_2,d6_arytm_2,d7_arytm_2,d8_arytm_2,d9_arytm_2,dt_k10_arytm_3,dt_k11_arytm_3,dt_k12_arytm_3,dt_k1_arytm_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_xboole_0,dt_k3_arytm_2,dt_k4_arytm_2,dt_k4_xboole_0,dt_k5_arytm_2,dt_k6_arytm_2,dt_k6_arytm_3,dt_k7_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_m2_subset_1,existence_m1_subset_1,existence_m2_subset_1,fc1_arytm_2,fc1_subset_1,fc1_xboole_0,fc2_arytm_2,fc2_ordinal1,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc8_arytm_3,fraenkel_a_0_0_arytm_2,fraenkel_a_0_2_arytm_2,fraenkel_a_1_0_arytm_2,fraenkel_a_2_0_arytm_2,fraenkel_a_2_2_arytm_2,idempotence_k2_xboole_0,l23_arytm_2,l66_arytm_2,l67_arytm_2,rc1_arytm_3,rc1_ordinal1,rc1_subset_1,rc1_xboole_0,rc2_arytm_3,rc2_ordinal1,rc2_subset_1,rc2_xboole_0,rc3_arytm_3,rc3_ordinal1,redefinition_k12_arytm_3,redefinition_m2_subset_1,reflexivity_r1_tarski,t1_boole,t1_subset,t2_subset,t2_tarski,t3_boole,t3_subset,t4_arytm_2,t4_boole,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(arytm_2,t14_arytm_2)]).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc4_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ( v3_ordinal1(A)
       => ( v1_ordinal1(A)
          & v2_ordinal1(A)
          & v3_ordinal1(A)
          & v4_ordinal2(A) ) ) ) ),
    file(arytm_3,cc4_arytm_3),
    []).

fof(commutativity_k10_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => k10_arytm_3(A,B) = k10_arytm_3(B,A) ) ),
    file(arytm_3,k10_arytm_3),
    []).

fof(commutativity_k11_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => k11_arytm_3(A,B) = k11_arytm_3(B,A) ) ),
    file(arytm_3,k11_arytm_3),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k5_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_arytm_2)
        & m1_subset_1(B,k1_arytm_2) )
     => k5_arytm_2(A,B) = k5_arytm_2(B,A) ) ),
    file(arytm_2,k5_arytm_2),
    []).

fof(commutativity_k6_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_arytm_2)
        & m1_subset_1(B,k1_arytm_2) )
     => k6_arytm_2(A,B) = k6_arytm_2(B,A) ) ),
    file(arytm_2,k6_arytm_2),
    []).

fof(commutativity_k7_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => k7_arytm_2(A,B) = k7_arytm_2(B,A) ) ),
    file(arytm_2,k7_arytm_2),
    []).

fof(commutativity_k8_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => k8_arytm_2(A,B) = k8_arytm_2(B,A) ) ),
    file(arytm_2,k8_arytm_2),
    []).

fof(connectedness_r3_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => ( r3_arytm_3(A,B)
        | r3_arytm_3(B,A) ) ) ),
    file(arytm_3,r3_arytm_3),
    []).

fof(d1_arytm_2,axiom,(
    k1_arytm_2 = k4_xboole_0(a_0_0_arytm_2,k1_tarski(k6_arytm_3)) ),
    file(arytm_2,d1_arytm_2),
    []).

fof(d2_arytm_2,axiom,(
    k2_arytm_2 = k4_xboole_0(k2_xboole_0(k6_arytm_3,k1_arytm_2),a_0_2_arytm_2) ),
    file(arytm_2,d2_arytm_2),
    []).

fof(d6_arytm_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
     => ! [B] : 
          ( m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
         => k5_arytm_2(A,B) = a_2_0_arytm_2(A,B) ) ) ),
    file(arytm_2,d6_arytm_2),
    []).

fof(d7_arytm_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
     => ! [B] : 
          ( m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
         => k6_arytm_2(A,B) = a_2_2_arytm_2(A,B) ) ) ),
    file(arytm_2,d7_arytm_2),
    []).

fof(d8_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( B = k12_arytm_3
             => k7_arytm_2(A,B) = A )
            & ( A = k12_arytm_3
             => k7_arytm_2(A,B) = B )
            & ~ ( B != k12_arytm_3
                & A != k12_arytm_3
                & k7_arytm_2(A,B) != k4_arytm_2(k5_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) ) ) ) ) ),
    file(arytm_2,d8_arytm_2),
    []).

fof(d9_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => k8_arytm_2(A,B) = k4_arytm_2(k6_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) ) ) ),
    file(arytm_2,d9_arytm_2),
    []).

fof(dt_k10_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => m1_subset_1(k10_arytm_3(A,B),k6_arytm_3) ) ),
    file(arytm_3,k10_arytm_3),
    []).

fof(dt_k11_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => m1_subset_1(k11_arytm_3(A,B),k6_arytm_3) ) ),
    file(arytm_3,k11_arytm_3),
    []).

fof(dt_k12_arytm_3,axiom,
    ( v1_xboole_0(k12_arytm_3)
    & m1_subset_1(k12_arytm_3,k6_arytm_3) ),
    file(arytm_3,k12_arytm_3),
    []).

fof(dt_k1_arytm_2,axiom,(
    m1_subset_1(k1_arytm_2,k1_zfmisc_1(k1_zfmisc_1(k6_arytm_3))) ),
    file(arytm_2,k1_arytm_2),
    []).

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_k2_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => m2_subset_1(k3_arytm_2(A),k1_zfmisc_1(k6_arytm_3),k1_arytm_2) ) ),
    file(arytm_2,k3_arytm_2),
    []).

fof(dt_k4_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_arytm_2)
     => m1_subset_1(k4_arytm_2(A),k2_arytm_2) ) ),
    file(arytm_2,k4_arytm_2),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_arytm_2)
        & m1_subset_1(B,k1_arytm_2) )
     => m2_subset_1(k5_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2) ) ),
    file(arytm_2,k5_arytm_2),
    []).

fof(dt_k6_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_arytm_2)
        & m1_subset_1(B,k1_arytm_2) )
     => m2_subset_1(k6_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2) ) ),
    file(arytm_2,k6_arytm_2),
    []).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    []).

fof(dt_k7_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => m1_subset_1(k7_arytm_2(A,B),k2_arytm_2) ) ),
    file(arytm_2,k7_arytm_2),
    []).

fof(dt_k8_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => m1_subset_1(k8_arytm_2(A,B),k2_arytm_2) ) ),
    file(arytm_2,k8_arytm_2),
    []).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc1_arytm_2,axiom,(
    ~ v1_xboole_0(k1_arytm_2) ),
    file(arytm_2,fc1_arytm_2),
    []).

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

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

fof(fc2_arytm_2,axiom,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    []).

fof(fc2_ordinal1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

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

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc8_arytm_3,axiom,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    []).

fof(fraenkel_a_0_0_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k6_arytm_3))
          & A = B
          & ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r2_hidden(C,B)
               => ( ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ( r3_arytm_3(D,C)
                       => r2_hidden(D,B) ) )
                  & ? [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                      & r2_hidden(D,B)
                      & ~ r3_arytm_3(D,C) ) ) ) ) ) ) ),
    file(arytm_2,a_0_0_arytm_2),
    []).

fof(fraenkel_a_0_2_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k6_arytm_3)
          & A = a_1_0_arytm_2(B)
          & B != k12_arytm_3 ) ) ),
    file(arytm_2,a_0_2_arytm_2),
    []).

fof(fraenkel_a_1_0_arytm_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k6_arytm_3)
     => ( r2_hidden(A,a_1_0_arytm_2(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k6_arytm_3)
            & A = C
            & ~ r3_arytm_3(B,C) ) ) ) ),
    file(arytm_2,a_1_0_arytm_2),
    []).

fof(fraenkel_a_2_0_arytm_2,axiom,(
    ! [A,B,C] : 
      ( ( m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
        & m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) )
     => ( r2_hidden(A,a_2_0_arytm_2(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,k6_arytm_3)
            & m1_subset_1(E,k6_arytm_3)
            & A = k10_arytm_3(D,E)
            & r2_hidden(D,B)
            & r2_hidden(E,C) ) ) ) ),
    file(arytm_2,a_2_0_arytm_2),
    []).

fof(fraenkel_a_2_2_arytm_2,axiom,(
    ! [A,B,C] : 
      ( ( m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
        & m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) )
     => ( r2_hidden(A,a_2_2_arytm_2(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,k6_arytm_3)
            & m1_subset_1(E,k6_arytm_3)
            & A = k11_arytm_3(D,E)
            & r2_hidden(D,B)
            & r2_hidden(E,C) ) ) ) ),
    file(arytm_2,a_2_2_arytm_2),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(l23_arytm_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
     => k3_arytm_2(k4_arytm_2(A)) = A ) ),
    file(arytm_2,l23_arytm_2),
    []).

fof(l66_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ~ ( k8_arytm_2(A,B) = k12_arytm_3
              & A != k12_arytm_3
              & B != k12_arytm_3 ) ) ) ),
    file(arytm_2,l66_arytm_2),
    []).

fof(l67_arytm_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
     => ! [B] : 
          ( m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
         => ! [C] : 
              ( m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2)
             => k6_arytm_2(A,k5_arytm_2(B,C)) = k5_arytm_2(k6_arytm_2(A,B),k6_arytm_2(A,C)) ) ) ) ),
    file(arytm_2,l67_arytm_2),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

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

fof(rc2_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(arytm_3,rc2_arytm_3),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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

fof(rc3_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc3_arytm_3),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_k12_arytm_3,axiom,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t4_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( A = k12_arytm_3
           => k8_arytm_2(A,B) = k12_arytm_3 ) ) ) ),
    file(arytm_2,t4_arytm_2),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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),
    []).