% Mizar problem: t8_pralg_1,pralg_1,529,36 
fof(t8_pralg_1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ! [D] : 
                  ( ( ~ v3_struct_0(D)
                    & v6_unialg_1(D)
                    & v7_unialg_1(D)
                    & v8_unialg_1(D)
                    & l1_unialg_1(D) )
                 => ( ( m3_unialg_2(A,B)
                      & m3_unialg_2(C,D)
                      & r1_unialg_2(B,D) )
                   => m3_unialg_2(k5_pralg_1(A,C),k5_pralg_1(B,D)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_unialg_1,antisymmetry_r2_hidden,cc1_arytm_3,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_arytm_3,cc2_funct_1,cc3_arytm_3,commutativity_k2_tarski,commutativity_k3_xboole_0,d11_finseq_1,d11_unialg_1,d1_pralg_1,d2_pralg_1,d2_unialg_2,d3_finseq_1,d3_pralg_1,d3_unialg_2,d4_finseq_1,d4_finseq_2,d4_pralg_1,d4_unialg_2,d5_pralg_1,d5_tarski,d5_unialg_2,d6_unialg_2,d7_unialg_2,d8_unialg_2,dt_g1_unialg_1,dt_k13_finseq_1,dt_k15_mcart_1,dt_k16_mcart_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_pralg_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_unialg_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_mcart_1,dt_k2_partfun1,dt_k2_pralg_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_unialg_1,dt_k2_unialg_2,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_pralg_1,dt_k3_unialg_1,dt_k3_unialg_2,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_partfun1,dt_k4_pralg_1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k5_pralg_1,dt_k7_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m1_unialg_2,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m2_unialg_2,dt_m3_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m1_unialg_2,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m2_unialg_2,existence_m3_unialg_2,fc12_relat_1,fc13_relat_1,fc1_finseq_2,fc1_ordinal2,fc1_partfun1,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc1_unialg_1,fc2_subset_1,fc2_unialg_1,fc3_subset_1,fc3_unialg_1,fc4_funct_1,fc4_relat_1,fc4_subset_1,fc4_unialg_1,fc5_relat_1,fc6_funct_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fraenkel_a_2_0_finseq_2,fraenkel_a_3_1_pralg_1,fraenkel_a_3_2_pralg_1,fraenkel_a_4_0_pralg_1,free_g1_unialg_1,idempotence_k3_xboole_0,rc1_arytm_3,rc1_finseq_2,rc1_funct_1,rc1_partfun1,rc1_pboole,rc1_relat_1,rc1_subset_1,rc1_unialg_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_unialg_1,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc3_unialg_1,rc4_funct_1,rc4_unialg_1,rc5_funct_1,rc5_struct_0,rc5_unialg_1,redefinition_k1_pralg_1,redefinition_k2_finseq_1,redefinition_k2_partfun1,redefinition_k2_pralg_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m2_unialg_2,reflexivity_r1_tarski,reflexivity_r1_unialg_2,symmetry_r1_unialg_2,t106_zfmisc_1,t10_finseq_2,t119_zfmisc_1,t11_finseq_2,t16_unialg_2,t1_subset,t1_unialg_2,t1_xboole_1,t2_boole,t2_subset,t2_tarski,t2_unialg_2,t31_finseq_3,t3_subset,t3_unialg_2,t4_subset,t4_unialg_2,t5_subset,t68_funct_1,t6_boole,t6_pralg_1,t6_unialg_2,t76_funct_1,t7_boole,t8_boole,t8_unialg_2,t9_funct_1]),
    [file(pralg_1,t8_pralg_1)]).

fof(abstractness_v3_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v3_unialg_1(A)
       => A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) ) ) ),
    file(unialg_1,v3_unialg_1),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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_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_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(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

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

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d11_finseq_1,axiom,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    []).

fof(d11_unialg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( B = k3_unialg_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A))
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => ! [D] : 
                        ( ( ~ v1_xboole_0(D)
                          & v1_funct_1(D)
                          & v1_unialg_1(D,u1_struct_0(A))
                          & m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) )
                       => ( D = k1_funct_1(u1_unialg_1(A),C)
                         => k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D) ) ) ) ) ) ) ) ) ),
    file(unialg_1,d11_unialg_1),
    []).

fof(d1_pralg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m2_finseq_1(D,A)
                 => ( D = k1_pralg_1(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(C)
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E)) ) ) ) ) ) ) ) ) ),
    file(pralg_1,d1_pralg_1),
    []).

fof(d2_pralg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m2_finseq_1(D,B)
                 => ( D = k2_pralg_1(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(C)
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => k1_funct_1(D,E) = k2_mcart_1(k1_funct_1(C,E)) ) ) ) ) ) ) ) ) ),
    file(pralg_1,d2_pralg_1),
    []).

fof(d2_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
          <=> k3_unialg_1(A) = k3_unialg_1(B) ) ) ) ),
    file(unialg_2,d2_unialg_2),
    []).

fof(d3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    []).

fof(d3_pralg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_funct_1(C)
                & v1_unialg_1(C,A)
                & v2_unialg_1(C,A)
                & m2_relset_1(C,k3_finseq_2(A),A) )
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & v1_funct_1(D)
                    & v1_unialg_1(D,B)
                    & v2_unialg_1(D,B)
                    & m2_relset_1(D,k3_finseq_2(B),B) )
                 => ( k2_unialg_1(A,C) = k2_unialg_1(B,D)
                   => ! [E] : 
                        ( ( ~ v1_xboole_0(E)
                          & v1_funct_1(E)
                          & v1_unialg_1(E,k2_zfmisc_1(A,B))
                          & v2_unialg_1(E,k2_zfmisc_1(A,B))
                          & m2_relset_1(E,k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) )
                       => ( E = k3_pralg_1(A,B,C,D)
                        <=> ( k1_relat_1(E) = k4_finseq_2(k2_unialg_1(A,C),k2_zfmisc_1(A,B))
                            & ! [F] : 
                                ( m2_finseq_1(F,k2_zfmisc_1(A,B))
                               => ( r2_hidden(F,k1_relat_1(E))
                                 => k1_funct_1(E,F) = k4_tarski(k1_funct_1(C,k1_pralg_1(A,B,F)),k1_funct_1(D,k2_pralg_1(A,B,F))) ) ) ) ) ) ) ) ) ) ) ),
    file(pralg_1,d3_pralg_1),
    []).

fof(d3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k1_unialg_2(A) = k2_relat_1(u1_unialg_1(A)) ) ),
    file(unialg_2,d3_unialg_2),
    []).

fof(d4_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    []).

fof(d4_finseq_2,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_2(A,B) = a_2_0_finseq_2(A,B) ) ),
    file(finseq_2,d4_finseq_2),
    []).

fof(d4_pralg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ! [C] : 
                ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))))
               => ( C = k4_pralg_1(A,B)
                <=> ( k3_finseq_1(C) = k3_finseq_1(u1_unialg_1(A))
                    & ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r2_hidden(D,k4_finseq_1(C))
                         => ! [E] : 
                              ( ( ~ v1_xboole_0(E)
                                & v1_funct_1(E)
                                & v1_unialg_1(E,u1_struct_0(A))
                                & v2_unialg_1(E,u1_struct_0(A))
                                & m2_relset_1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) )
                             => ! [F] : 
                                  ( ( ~ v1_xboole_0(F)
                                    & v1_funct_1(F)
                                    & v1_unialg_1(F,u1_struct_0(B))
                                    & v2_unialg_1(F,u1_struct_0(B))
                                    & m2_relset_1(F,k3_finseq_2(u1_struct_0(B)),u1_struct_0(B)) )
                                 => ( ( E = k1_funct_1(u1_unialg_1(A),D)
                                      & F = k1_funct_1(u1_unialg_1(B),D) )
                                   => k1_funct_1(C,D) = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),E,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pralg_1,d4_pralg_1),
    []).

fof(d4_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
              <=> ! [D] : 
                    ( m2_finseq_1(D,B)
                   => ( k3_finseq_1(D) = k2_unialg_1(u1_struct_0(A),C)
                     => r2_hidden(k1_funct_1(C,D),B) ) ) ) ) ) ) ),
    file(unialg_2,d4_unialg_2),
    []).

fof(d5_pralg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k5_pralg_1(A,B) = g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)) ) ) ) ),
    file(pralg_1,d5_pralg_1),
    []).

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

fof(d5_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_unialg_2(B,A)
          <=> ! [C] : 
                ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
               => r2_unialg_2(A,B,C) ) ) ) ) ),
    file(unialg_2,d5_unialg_2),
    []).

fof(d6_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_2(A,B,C) = k2_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),C,k4_finseq_2(k2_unialg_1(u1_struct_0(A),C),B)) ) ) ) ) ),
    file(unialg_2,d6_unialg_2),
    []).

fof(d7_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(B),B))
             => ( C = k3_unialg_2(A,B)
              <=> ( k4_finseq_1(C) = k4_finseq_1(u1_unialg_1(A))
                  & ! [D,E] : 
                      ( m2_unialg_2(E,u1_struct_0(A),k1_unialg_2(A))
                     => ( ( r2_hidden(D,k4_finseq_1(C))
                          & E = k1_funct_1(u1_unialg_1(A),D) )
                       => k1_funct_1(C,D) = k2_unialg_2(A,B,E) ) ) ) ) ) ) ) ),
    file(unialg_2,d7_unialg_2),
    []).

fof(d8_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(B,A)
          <=> ( m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A)))
              & ! [C] : 
                  ( ( ~ v1_xboole_0(C)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( C = u1_struct_0(B)
                   => ( u1_unialg_1(B) = k3_unialg_2(A,C)
                      & v1_unialg_2(C,A) ) ) ) ) ) ) ) ),
    file(unialg_2,d8_unialg_2),
    []).

fof(dt_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ( v3_unialg_1(g1_unialg_1(A,B))
        & l1_unialg_1(g1_unialg_1(A,B)) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

fof(dt_k15_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k15_mcart_1(A))
        & v1_funct_1(k15_mcart_1(A)) ) ) ),
    file(mcart_1,k15_mcart_1),
    []).

fof(dt_k16_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k16_mcart_1(A))
        & v1_funct_1(k16_mcart_1(A)) ) ) ),
    file(mcart_1,k16_mcart_1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    []).

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

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

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => m2_finseq_1(k1_pralg_1(A,B,C),A) ) ),
    file(pralg_1,k1_pralg_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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

fof(dt_k1_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_unialg_2(k1_unialg_2(A),u1_struct_0(A)) ) ),
    file(unialg_2,k1_unialg_2),
    []).

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_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    []).

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

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(dt_k2_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => m2_finseq_1(k2_pralg_1(A,B,C),B) ) ),
    file(pralg_1,k2_pralg_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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

fof(dt_k2_unialg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(B)
        & v1_unialg_1(B,A)
        & m1_relset_1(B,k13_finseq_1(A),A) )
     => m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers) ) ),
    file(unialg_1,k2_unialg_1),
    []).

fof(dt_k2_unialg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_unialg_2(A)) )
     => ( ~ v1_xboole_0(k2_unialg_2(A,B,C))
        & v1_funct_1(k2_unialg_2(A,B,C))
        & v1_unialg_1(k2_unialg_2(A,B,C),B)
        & v2_unialg_1(k2_unialg_2(A,B,C),B)
        & m2_relset_1(k2_unialg_2(A,B,C),k3_finseq_2(B),B) ) ) ),
    file(unialg_2,k2_unialg_2),
    []).

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    []).

fof(dt_k3_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(dt_k3_pralg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(C)
        & v1_unialg_1(C,A)
        & v2_unialg_1(C,A)
        & m1_relset_1(C,k3_finseq_2(A),A)
        & ~ v1_xboole_0(D)
        & v1_funct_1(D)
        & v1_unialg_1(D,B)
        & v2_unialg_1(D,B)
        & m1_relset_1(D,k3_finseq_2(B),B) )
     => ( ~ v1_xboole_0(k3_pralg_1(A,B,C,D))
        & v1_funct_1(k3_pralg_1(A,B,C,D))
        & v1_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B))
        & v2_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B))
        & m2_relset_1(k3_pralg_1(A,B,C,D),k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) ) ) ),
    file(pralg_1,k3_pralg_1),
    []).

fof(dt_k3_unialg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m2_finseq_1(k3_unialg_1(A),k5_numbers) ) ),
    file(unialg_1,k3_unialg_1),
    []).

fof(dt_k3_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m2_finseq_1(k3_unialg_2(A,B),k4_partfun1(k13_finseq_1(B),B)) ) ),
    file(unialg_2,k3_unialg_2),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k4_pralg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => m2_finseq_1(k4_pralg_1(A,B),k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ),
    file(pralg_1,k4_pralg_1),
    []).

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

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_pralg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( ~ v3_struct_0(k5_pralg_1(A,B))
        & v3_unialg_1(k5_pralg_1(A,B))
        & v6_unialg_1(k5_pralg_1(A,B))
        & v7_unialg_1(k5_pralg_1(A,B))
        & v8_unialg_1(k5_pralg_1(A,B))
        & l1_unialg_1(k5_pralg_1(A,B)) ) ) ),
    file(pralg_1,k5_pralg_1),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => l1_struct_0(A) ) ),
    file(unialg_1,l1_unialg_1),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

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_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_unialg_2(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(unialg_2,m1_unialg_2),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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(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(dt_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v1_funct_1(C)
            & v1_unialg_1(C,A)
            & v2_unialg_1(C,A)
            & m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ),
    file(unialg_2,m2_unialg_2),
    []).

fof(dt_m3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) ) ) ) ),
    file(unialg_2,m3_unialg_2),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))) ) ),
    file(unialg_1,u1_unialg_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l1_unialg_1,axiom,(
    ? [A] : l1_unialg_1(A) ),
    file(unialg_1,l1_unialg_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

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_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_unialg_2(B,A) ) ),
    file(unialg_2,m1_unialg_2),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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(existence_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ? [C] : m2_unialg_2(C,A,B) ) ),
    file(unialg_2,m2_unialg_2),
    []).

fof(existence_m3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m3_unialg_2(B,A) ) ),
    file(unialg_2,m3_unialg_2),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    []).

fof(fc1_finseq_2,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ),
    file(finseq_2,fc1_finseq_2),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    []).

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_unialg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => ( ~ v3_struct_0(g1_unialg_1(A,B))
        & v3_unialg_1(g1_unialg_1(A,B)) ) ) ),
    file(unialg_1,fc1_unialg_1),
    []).

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

fof(fc2_unialg_1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc2_unialg_1),
    []).

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

fof(fc3_unialg_1,axiom,(
    ! [A] : 
      ( ( v7_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc3_unialg_1),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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(fc4_unialg_1,axiom,(
    ! [A] : 
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( ~ v1_xboole_0(u1_unialg_1(A))
        & v1_relat_1(u1_unialg_1(A))
        & v2_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A)) ) ) ),
    file(unialg_1,fc4_unialg_1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

fof(fraenkel_a_2_0_finseq_2,axiom,(
    ! [A,B,C] : 
      ( v4_ordinal2(B)
     => ( r2_hidden(A,a_2_0_finseq_2(B,C))
      <=> ? [D] : 
            ( m2_finseq_2(D,C,k3_finseq_2(C))
            & A = D
            & k3_finseq_1(D) = B ) ) ) ),
    file(finseq_2,a_2_0_finseq_2),
    []).

fof(fraenkel_a_3_1_pralg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & ~ v3_struct_0(C)
        & v6_unialg_1(C)
        & v7_unialg_1(C)
        & v8_unialg_1(C)
        & l1_unialg_1(C)
        & m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B)) )
     => ( r2_hidden(A,a_3_1_pralg_1(B,C,D))
      <=> ? [E] : 
            ( m2_finseq_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),k3_finseq_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))))
            & A = E
            & k3_finseq_1(E) = k2_unialg_1(u1_struct_0(B),D) ) ) ) ),
    file(pralg_1,a_3_1_pralg_1),
    []).

fof(fraenkel_a_3_2_pralg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B)) )
     => ( r2_hidden(A,a_3_2_pralg_1(B,C,D))
      <=> ? [E] : 
            ( m2_finseq_2(E,C,k3_finseq_2(C))
            & A = E
            & k3_finseq_1(E) = k2_unialg_1(u1_struct_0(B),D) ) ) ) ),
    file(pralg_1,a_3_2_pralg_1),
    []).

fof(fraenkel_a_4_0_pralg_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & ~ v3_struct_0(C)
        & v6_unialg_1(C)
        & v7_unialg_1(C)
        & v8_unialg_1(C)
        & l1_unialg_1(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pralg_1(B,C))))
        & m2_unialg_2(E,u1_struct_0(B),k1_unialg_2(B)) )
     => ( r2_hidden(A,a_4_0_pralg_1(B,C,D,E))
      <=> ? [F] : 
            ( m2_finseq_2(F,D,k3_finseq_2(D))
            & A = F
            & k3_finseq_1(F) = k2_unialg_1(u1_struct_0(B),E) ) ) ) ),
    file(pralg_1,a_4_0_pralg_1),
    []).

fof(free_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ! [C,D] : 
          ( g1_unialg_1(A,B) = g1_unialg_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

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_finseq_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) ),
    file(finseq_2,rc1_finseq_2),
    []).

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

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_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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_unialg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_relset_1(B,k13_finseq_1(A),A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_unialg_1(B,A)
          & v2_unialg_1(B,A) ) ) ),
    file(unialg_1,rc1_unialg_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_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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & v3_unialg_1(A) ) ),
    file(unialg_1,rc2_unialg_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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A) ) ),
    file(unialg_1,rc3_unialg_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(rc4_unialg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v4_unialg_1(B,A)
          & v5_unialg_1(B,A) ) ) ),
    file(unialg_1,rc4_unialg_1),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc5_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A)
      & v6_unialg_1(A)
      & v7_unialg_1(A)
      & v8_unialg_1(A) ) ),
    file(unialg_1,rc5_unialg_1),
    []).

fof(redefinition_k1_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => k1_pralg_1(A,B,C) = k15_mcart_1(C) ) ),
    file(pralg_1,k1_pralg_1),
    []).

fof(redefinition_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    []).

fof(redefinition_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(redefinition_k2_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => k2_pralg_1(A,B,C) = k16_mcart_1(C) ) ),
    file(pralg_1,k2_pralg_1),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

fof(redefinition_k3_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(redefinition_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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(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(redefinition_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(unialg_2,m2_unialg_2),
    []).

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

fof(reflexivity_r1_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => r1_unialg_2(A,A) ) ),
    file(unialg_2,r1_unialg_2),
    []).

fof(symmetry_r1_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( r1_unialg_2(A,B)
       => r1_unialg_2(B,A) ) ) ),
    file(unialg_2,r1_unialg_2),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

fof(t10_finseq_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k3_finseq_1(B) = A
                  & k3_finseq_1(C) = A
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k2_finseq_1(A))
                       => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) )
               => B = C ) ) ) ) ),
    file(finseq_2,t10_finseq_2),
    []).

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    []).

fof(t11_finseq_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(B))
                  & k1_funct_1(B,C) = A ) ) ) ) ),
    file(finseq_2,t11_finseq_2),
    []).

fof(t16_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => r1_unialg_2(A,B) ) ) ) ),
    file(unialg_2,t16_unialg_2),
    []).

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

fof(t1_unialg_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => k3_xboole_0(k4_finseq_2(A,B),k4_finseq_2(A,C)) = k4_finseq_2(A,C) ) ) ) ),
    file(unialg_2,t1_unialg_2),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t2_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_funct_1(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k4_finseq_2(k2_unialg_1(A,B),A) ) ) ),
    file(unialg_2,t2_unialg_2),
    []).

fof(t31_finseq_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k3_finseq_1(A) = k3_finseq_1(B)
          <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ),
    file(finseq_3,t31_finseq_3),
    []).

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

fof(t3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(u1_unialg_1(B)) ) ) ) ),
    file(unialg_2,t3_unialg_2),
    []).

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(t4_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( r1_unialg_2(A,B)
                  & r1_unialg_2(B,C) )
               => r1_unialg_2(A,C) ) ) ) ) ),
    file(unialg_2,t4_unialg_2),
    []).

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(t68_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( B = k7_relat_1(C,A)
          <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)
              & ! [D] : 
                  ( r2_hidden(D,k1_relat_1(B))
                 => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ),
    file(funct_1,t68_funct_1),
    []).

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

fof(t6_pralg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ! [C] : 
                ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
               => ! [D] : 
                    ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                   => ! [E] : 
                        ( m2_unialg_2(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B)))
                       => ! [F] : 
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( C = k1_funct_1(u1_unialg_1(A),F)
                                & D = k1_funct_1(u1_unialg_1(B),F)
                                & E = k1_funct_1(u1_unialg_1(k5_pralg_1(A,B)),F)
                                & r2_hidden(F,k4_finseq_1(u1_unialg_1(A))) )
                             => ( k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(A),C)
                                & k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(B),D)
                                & E = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),C,D) ) ) ) ) ) ) ) ) ) ),
    file(pralg_1,t6_pralg_1),
    []).

fof(t6_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
         => m2_unialg_2(k1_funct_1(u1_unialg_1(A),B),u1_struct_0(A),k1_unialg_2(A)) ) ) ),
    file(unialg_2,t6_unialg_2),
    []).

fof(t76_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B))
        & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ),
    file(funct_1,t76_funct_1),
    []).

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_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_1(B,k2_unialg_2(A,B,C)) = k2_unialg_1(u1_struct_0(A),C) ) ) ) ) ),
    file(unialg_2,t8_unialg_2),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).