% Mizar problem: t32_pua2mss1,pua2mss1,2023,40 
fof(t32_pua2mss1,conjecture,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => r7_pua2mss1(A,k12_pua2mss1(A,B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_msualg_1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_eqrel_1,cc1_finseq_1,cc1_fraenkel,cc1_funct_1,cc1_nat_1,cc1_partfun1,cc1_pua2mss1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_eqrel_1,cc2_funct_1,cc2_nat_1,cc2_pua2mss1,cc3_nat_1,cc3_pua2mss1,cc4_pua2mss1,commutativity_k2_tarski,commutativity_k3_xboole_0,commutativity_k5_subset_1,d10_pua2mss1,d10_xboole_0,d11_finseq_1,d11_pua2mss1,d12_pua2mss1,d15_funct_1,d15_pua2mss1,d16_pua2mss1,d17_pua2mss1,d18_pboole,d19_pboole,d1_funct_2,d1_pua2mss1,d2_finseq_1,d3_finseq_1,d3_pboole,d3_tarski,d3_xboole_0,d4_finseq_1,d5_funct_1,d5_tarski,d6_eqrel_1,d8_funct_1,dt_g1_msualg_1,dt_g3_msualg_1,dt_k12_pua2mss1,dt_k13_finseq_1,dt_k13_pua2mss1,dt_k14_pua2mss1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_pua2mss1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_mcart_1,dt_k2_partfun1,dt_k2_pua2mss1,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_tarski,dt_k3_xboole_0,dt_k4_card_3,dt_k4_finseq_1,dt_k4_partfun1,dt_k4_pua2mss1,dt_k4_relset_1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k5_pua2mss1,dt_k5_relat_1,dt_k5_setfam_1,dt_k5_subset_1,dt_k6_pboole,dt_k6_relat_1,dt_k7_pboole,dt_k7_relat_1,dt_k9_relat_1,dt_l1_msualg_1,dt_l1_struct_0,dt_l1_unialg_1,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_eqrel_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_pua2mss1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_pua2mss1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_m3_pua2mss1,dt_m4_pua2mss1,dt_u1_msualg_1,dt_u1_struct_0,dt_u1_unialg_1,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l1_unialg_1,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_eqrel_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_pua2mss1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_pua2mss1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,existence_m3_pua2mss1,existence_m4_pua2mss1,fc10_relat_1,fc11_finseq_1,fc12_relat_1,fc13_relat_1,fc16_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_funct_1,fc1_partfun1,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_funct_1,fc2_msafree,fc2_partfun1,fc2_setfam_1,fc2_subset_1,fc2_unialg_1,fc3_card_3,fc3_msafree,fc3_pua2mss1,fc3_setfam_1,fc3_subset_1,fc4_card_3,fc4_funct_1,fc4_relat_1,fc4_subset_1,fc4_unialg_1,fc5_card_3,fc5_relat_1,fc6_funct_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_finseq_1,fc9_relat_1,fraenkel_a_2_0_pua2mss1,fraenkel_a_2_1_pua2mss1,fraenkel_a_2_2_pua2mss1,fraenkel_a_2_3_pua2mss1,fraenkel_a_3_1_pua2mss1,fraenkel_a_3_2_pua2mss1,fraenkel_a_3_3_pua2mss1,fraenkel_a_3_4_pua2mss1,fraenkel_a_3_5_pua2mss1,free_g1_msualg_1,free_g3_msualg_1,idempotence_k3_xboole_0,idempotence_k5_subset_1,irreflexivity_r2_subset_1,rc1_finseq_1,rc1_finseq_2,rc1_fraenkel,rc1_funct_1,rc1_msualg_1,rc1_nat_1,rc1_partfun1,rc1_pua2mss1,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc2_finseq_1,rc2_funct_1,rc2_msualg_1,rc2_nat_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_funct_1,rc3_msualg_1,rc3_nat_1,rc3_relat_1,rc3_struct_0,rc4_finseq_1,rc4_funct_1,rc5_funct_1,rc5_msualg_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k13_pua2mss1,redefinition_k14_pua2mss1,redefinition_k1_pua2mss1,redefinition_k2_finseq_1,redefinition_k2_partfun1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k4_pua2mss1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_pua2mss1,redefinition_k5_setfam_1,redefinition_k5_subset_1,redefinition_k7_pboole,redefinition_m1_pua2mss1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r2_subset_1,reflexivity_r1_tarski,s5_pboole__e3_72__pua2mss1,s5_pboole__e5_72__pua2mss1,symmetry_r1_xboole_0,symmetry_r2_subset_1,t10_card_5,t11_pua2mss1,t12_pua2mss1,t12_relset_1,t148_relat_1,t15_pua2mss1,t16_pua2mss1,t1_subset,t23_funct_1,t28_xboole_1,t2_boole,t2_pua2mss1,t2_subset,t2_tarski,t3_subset,t3_xboole_0,t4_funct_2,t4_subset,t5_subset,t6_boole,t6_pua2mss1,t70_funct_1,t71_relat_1,t73_funct_1,t79_relat_1,t7_boole,t7_mcart_1,t8_boole,t90_relat_1,t91_relat_1,t9_pua2mss1]),
    [file(pua2mss1,t32_pua2mss1)]).

fof(abstractness_v1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_msualg_1(A)
       => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ),
    file(msualg_1,v1_msualg_1),
    []).

fof(abstractness_v4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(B,A)
       => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ),
    file(msualg_1,v4_msualg_1),
    []).

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

fof(cc1_eqrel_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

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_pua2mss1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( m1_finseq_1(B,A)
         => v2_relat_1(B) ) ) ),
    file(pua2mss1,cc1_pua2mss1),
    []).

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(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

fof(cc2_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc2_pua2mss1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v8_unialg_1(A)
       => ~ v3_struct_0(A) ) ) ),
    file(pua2mss1,cc2_pua2mss1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc3_pua2mss1,axiom,(
    ! [A,B] : 
      ( m2_pua2mss1(B,A)
     => ( v2_relat_1(B)
        & v2_funct_1(B) ) ) ),
    file(pua2mss1,cc3_pua2mss1),
    []).

fof(cc4_pua2mss1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_pua2mss1(B,A)
         => ( ~ v1_xboole_0(B)
            & v2_relat_1(B)
            & v2_funct_1(B) ) ) ) ),
    file(pua2mss1,cc4_pua2mss1),
    []).

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(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d10_pua2mss1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_pua2mss1(A,B,C)
              <=> ( r1_pua2mss1(A,B,C)
                  & ! [D] : 
                      ( m2_finseq_1(D,C)
                     => ( ~ r1_xboole_0(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B))
                       => r1_tarski(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B)) ) ) ) ) ) ) ) ),
    file(pua2mss1,d10_pua2mss1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_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_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_eqrel_1(B,u1_struct_0(A))
         => ( m3_pua2mss1(B,A)
          <=> ! [C] : 
                ( m1_pua2mss1(C,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
               => r2_pua2mss1(u1_struct_0(A),C,B) ) ) ) ) ),
    file(pua2mss1,d11_pua2mss1),
    []).

fof(d12_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_pua2mss1(B,u1_struct_0(A))
         => ( m4_pua2mss1(B,A)
          <=> m3_pua2mss1(k4_pua2mss1(u1_struct_0(A),B),A) ) ) ) ),
    file(pua2mss1,d12_pua2mss1),
    []).

fof(d15_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_relat_1(A)
      <=> ! [B] : ~ ( r2_hidden(B,k1_relat_1(A))
            & v1_xboole_0(k1_funct_1(A,B)) ) ) ) ),
    file(funct_1,d15_funct_1),
    []).

fof(d15_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => ! [C] : 
              ( ( v1_msualg_1(C)
                & l1_msualg_1(C) )
             => ( C = k12_pua2mss1(A,B)
              <=> ( u1_struct_0(C) = B
                  & u1_msualg_1(C) = a_2_2_pua2mss1(A,B)
                  & ! [D] : 
                      ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(A)))
                     => ! [E] : 
                          ( m2_finseq_2(E,B,k3_finseq_2(B))
                         => ( ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,D)))
                           => ( k1_funct_1(u2_msualg_1(C),k4_tarski(D,E)) = E
                              & r1_tarski(k9_relat_1(k2_pua2mss1(A,D),k4_card_3(E)),k1_funct_1(u3_msualg_1(C),k4_tarski(D,E))) ) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d15_pua2mss1),
    []).

fof(d16_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,B)
             => ! [D] : 
                  ( m2_pua2mss1(D,u1_msualg_1(B))
                 => ( r6_pua2mss1(A,B,C,D)
                  <=> ( m4_pua2mss1(u4_msualg_1(B,C),A)
                      & k1_relat_1(D) = k4_finseq_1(u1_unialg_1(A))
                      & ! [E] : 
                          ( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
                         => m2_pua2mss1(k7_relat_1(u5_msualg_1(B,C),k1_funct_1(D,E)),k2_pua2mss1(A,E)) ) ) ) ) ) ) ) ),
    file(pua2mss1,d16_pua2mss1),
    []).

fof(d17_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ( r7_pua2mss1(A,B)
          <=> ? [C] : 
                ( l3_msualg_1(C,B)
                & ? [D] : 
                    ( m2_pua2mss1(D,u1_msualg_1(B))
                    & r6_pua2mss1(A,B,C,D) ) ) ) ) ) ),
    file(pua2mss1,d17_pua2mss1),
    []).

fof(d18_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    []).

fof(d19_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,k3_finseq_2(A))
         => ( C = k6_pboole(A,B)
          <=> ! [D] : 
                ( m2_finseq_2(D,A,k3_finseq_2(A))
               => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ),
    file(pboole,d19_pboole),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_pua2mss1,axiom,(
    ! [A] : 
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k4_finseq_1(u1_unialg_1(A)))
         => k2_pua2mss1(A,B) = k1_funct_1(u1_unialg_1(A),B) ) ) ),
    file(pua2mss1,d1_pua2mss1),
    []).

fof(d2_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    []).

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_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

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(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_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(d6_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    []).

fof(d8_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    []).

fof(dt_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(dt_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ( v4_msualg_1(g3_msualg_1(A,B,C),A)
        & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ),
    file(msualg_1,g3_msualg_1),
    []).

fof(dt_k12_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ( v1_msualg_1(k12_pua2mss1(A,B))
        & l1_msualg_1(k12_pua2mss1(A,B)) ) ) ),
    file(pua2mss1,k12_pua2mss1),
    []).

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

fof(dt_k13_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => m1_subset_1(k13_pua2mss1(A,B,C),k4_finseq_1(u1_unialg_1(A))) ) ),
    file(pua2mss1,k13_pua2mss1),
    []).

fof(dt_k14_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => m2_finseq_2(k14_pua2mss1(A,B,C),B,k3_finseq_2(B)) ) ),
    file(pua2mss1,k14_pua2mss1),
    []).

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_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => m1_subset_1(k1_pua2mss1(A,B),k1_zfmisc_1(k4_partfun1(k3_finseq_2(A),A))) ) ),
    file(pua2mss1,k1_pua2mss1),
    []).

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_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_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_subset_1(B,k4_finseq_1(u1_unialg_1(A))) )
     => m1_pua2mss1(k2_pua2mss1(A,B),k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A))) ) ),
    file(pua2mss1,k2_pua2mss1),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

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

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

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

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_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k4_pua2mss1,axiom,(
    ! [A,B] : 
      ( m2_pua2mss1(B,A)
     => m1_eqrel_1(k4_pua2mss1(A,B),A) ) ),
    file(pua2mss1,k4_pua2mss1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_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_pua2mss1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m2_pua2mss1(k5_pua2mss1(A,B),A) ) ),
    file(pua2mss1,k5_pua2mss1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k6_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ),
    file(pboole,k6_pboole),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => m1_pboole(k7_pboole(A,B,C,D),A) ) ),
    file(pboole,k7_pboole),
    []).

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_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_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_l2_msualg_1,axiom,(
    $true ),
    file(msualg_1,l2_msualg_1),
    []).

fof(dt_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(dt_m1_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ! [D] : 
          ( m1_pua2mss1(D,A,B,C)
         => ( v1_funct_1(D)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(pua2mss1,m1_pua2mss1),
    []).

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_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_pua2mss1,axiom,(
    ! [A,B] : 
      ( m2_pua2mss1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pua2mss1,m2_pua2mss1),
    []).

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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

fof(dt_m3_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => m1_eqrel_1(B,u1_struct_0(A)) ) ) ),
    file(pua2mss1,m3_pua2mss1),
    []).

fof(dt_m4_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m4_pua2mss1(B,A)
         => m2_pua2mss1(B,u1_struct_0(A)) ) ) ),
    file(pua2mss1,m4_pua2mss1),
    []).

fof(dt_u1_msualg_1,axiom,(
    $true ),
    file(msualg_1,u1_msualg_1),
    []).

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(dt_u2_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u2_msualg_1(A))
        & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)))
        & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ),
    file(msualg_1,u2_msualg_1),
    []).

fof(dt_u3_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u3_msualg_1(A))
        & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A))
        & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ),
    file(msualg_1,u3_msualg_1),
    []).

fof(dt_u4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ),
    file(msualg_1,u4_msualg_1),
    []).

fof(dt_u5_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ),
    file(msualg_1,u5_msualg_1),
    []).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_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_l2_msualg_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) ),
    file(msualg_1,l2_msualg_1),
    []).

fof(existence_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : l3_msualg_1(B,A) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_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_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ? [D] : m1_pua2mss1(D,A,B,C) ) ),
    file(pua2mss1,m1_pua2mss1),
    []).

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_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_pua2mss1,axiom,(
    ! [A] : 
    ? [B] : m2_pua2mss1(B,A) ),
    file(pua2mss1,m2_pua2mss1),
    []).

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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

fof(existence_m3_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m3_pua2mss1(B,A) ) ),
    file(pua2mss1,m3_pua2mss1),
    []).

fof(existence_m4_pua2mss1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m4_pua2mss1(B,A) ) ),
    file(pua2mss1,m4_pua2mss1),
    []).

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    []).

fof(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

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(fc16_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & v1_fraenkel(k13_finseq_1(A)) ) ),
    file(finseq_1,fc16_finseq_1),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

fof(fc1_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

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(fc2_finseq_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) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_funct_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    []).

fof(fc2_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ~ v1_xboole_0(k3_card_3(B)) ) ),
    file(msafree,fc2_msafree),
    []).

fof(fc2_partfun1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    []).

fof(fc2_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) ),
    file(card_3,fc3_card_3),
    []).

fof(fc3_msafree,axiom,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ~ v1_xboole_0(u1_msualg_1(A)) ) ),
    file(msafree,fc3_msafree),
    []).

fof(fc3_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ( ~ v3_struct_0(k12_pua2mss1(A,B))
        & v1_msualg_1(k12_pua2mss1(A,B))
        & ~ v2_msualg_1(k12_pua2mss1(A,B)) ) ) ),
    file(pua2mss1,fc3_pua2mss1),
    []).

fof(fc3_setfam_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    []).

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

fof(fc4_card_3,axiom,(
    ! [A,B,C] : 
      ( ( v1_setfam_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k4_card_3(C))
        & v1_fraenkel(k4_card_3(C)) ) ) ),
    file(card_3,fc4_card_3),
    []).

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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k4_card_3(A))
        & v1_fraenkel(k4_card_3(A)) ) ) ),
    file(card_3,fc5_card_3),
    []).

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(fc9_finseq_1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ),
    file(finseq_1,fc9_finseq_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

fof(fraenkel_a_2_0_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_eqrel_1(C,B) )
     => ( r2_hidden(A,a_2_0_pua2mss1(B,C))
      <=> ? [D] : 
            ( m2_finseq_2(D,C,k3_finseq_2(C))
            & A = k4_card_3(D) ) ) ) ),
    file(pua2mss1,a_2_0_pua2mss1),
    []).

fof(fraenkel_a_2_1_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & m1_eqrel_1(C,k1_relat_1(B)) )
     => ( r2_hidden(A,a_2_1_pua2mss1(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_zfmisc_1(k1_relat_1(B)),C)
            & A = k7_relat_1(B,D) ) ) ) ),
    file(pua2mss1,a_2_1_pua2mss1),
    []).

fof(fraenkel_a_2_2_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m3_pua2mss1(C,B) )
     => ( r2_hidden(A,a_2_2_pua2mss1(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(B)))
            & m2_finseq_2(E,C,k3_finseq_2(C))
            & A = k4_tarski(D,E)
            & ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,D))) ) ) ) ),
    file(pua2mss1,a_2_2_pua2mss1),
    []).

fof(fraenkel_a_2_3_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m3_pua2mss1(C,B) )
     => ( r2_hidden(A,a_2_3_pua2mss1(B,C))
      <=> ? [D] : 
            ( m2_finseq_2(D,C,k3_finseq_2(C))
            & A = k4_card_3(D) ) ) ) ),
    file(pua2mss1,a_2_3_pua2mss1),
    []).

fof(fraenkel_a_3_1_pua2mss1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m1_eqrel_1(D,B) )
     => ( r2_hidden(A,a_3_1_pua2mss1(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_zfmisc_1(B),D)
            & A = k3_xboole_0(E,C)
            & ~ r1_xboole_0(E,C) ) ) ) ),
    file(pua2mss1,a_3_1_pua2mss1),
    []).

fof(fraenkel_a_3_2_pua2mss1,axiom,(
    ! [A,B,C,D] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m3_pua2mss1(C,B)
        & m1_subset_1(D,k4_finseq_1(u1_unialg_1(B))) )
     => ( r2_hidden(A,a_3_2_pua2mss1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_msualg_1(k12_pua2mss1(B,C)))
            & A = E
            & k13_pua2mss1(B,C,E) = D ) ) ) ),
    file(pua2mss1,a_3_2_pua2mss1),
    []).

fof(fraenkel_a_3_3_pua2mss1,axiom,(
    ! [A,B,C,D] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m3_pua2mss1(C,B)
        & m1_subset_1(D,u1_msualg_1(k12_pua2mss1(B,C))) )
     => ( r2_hidden(A,a_3_3_pua2mss1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_msualg_1(k12_pua2mss1(B,C)))
            & A = E
            & k13_pua2mss1(B,C,E) = k13_pua2mss1(B,C,D) ) ) ) ),
    file(pua2mss1,a_3_3_pua2mss1),
    []).

fof(fraenkel_a_3_4_pua2mss1,axiom,(
    ! [A,B,C,D] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m1_subset_1(C,k4_finseq_1(u1_unialg_1(B)))
        & m1_eqrel_1(D,k3_finseq_2(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_4_pua2mss1(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_zfmisc_1(k3_finseq_2(u1_struct_0(B))),D)
            & A = k5_subset_1(k3_finseq_2(u1_struct_0(B)),E,k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,C)))
            & ~ r2_subset_1(E,k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,C))) ) ) ) ),
    file(pua2mss1,a_3_4_pua2mss1),
    []).

fof(fraenkel_a_3_5_pua2mss1,axiom,(
    ! [A,B,C,D] : 
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m1_subset_1(C,k4_finseq_1(u1_unialg_1(B)))
        & m1_eqrel_1(D,k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,C))) )
     => ( r2_hidden(A,a_3_5_pua2mss1(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_zfmisc_1(k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,C))),D)
            & A = k2_partfun1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,C),E) ) ) ) ),
    file(pua2mss1,a_3_5_pua2mss1),
    []).

fof(free_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ! [E,F,G,H] : 
          ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(free_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ! [D,E,F] : 
          ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(msualg_1,g3_msualg_1),
    []).

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

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(irreflexivity_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r2_subset_1(A,A) ) ),
    file(subset_1,r2_subset_1),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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

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_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & v1_msualg_1(A) ) ),
    file(msualg_1,rc1_msualg_1),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_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_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pua2mss1,rc1_pua2mss1),
    []).

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

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_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(rc2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_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_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & v2_msualg_1(A) ) ),
    file(msualg_1,rc2_msualg_1),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_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(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_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_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A) ) ),
    file(msualg_1,rc3_msualg_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_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(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_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(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_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : 
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A) ) ) ),
    file(msualg_1,rc5_msualg_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(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k13_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => k13_pua2mss1(A,B,C) = k1_mcart_1(C) ) ),
    file(pua2mss1,k13_pua2mss1),
    []).

fof(redefinition_k14_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => k14_pua2mss1(A,B,C) = k2_mcart_1(C) ) ),
    file(pua2mss1,k14_pua2mss1),
    []).

fof(redefinition_k1_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => k1_pua2mss1(A,B) = k2_relat_1(B) ) ),
    file(pua2mss1,k1_pua2mss1),
    []).

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_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_k4_pua2mss1,axiom,(
    ! [A,B] : 
      ( m2_pua2mss1(B,A)
     => k4_pua2mss1(A,B) = k2_relat_1(B) ) ),
    file(pua2mss1,k4_pua2mss1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

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

fof(redefinition_k5_pua2mss1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => k5_pua2mss1(A,B) = k6_relat_1(B) ) ),
    file(pua2mss1,k5_pua2mss1),
    []).

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(redefinition_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(pboole,k7_pboole),
    []).

fof(redefinition_m1_pua2mss1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ! [D] : 
          ( m1_pua2mss1(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(pua2mss1,m1_pua2mss1),
    []).

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_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r2_subset_1),
    []).

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

fof(s5_pboole__e3_72__pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ? [C] : 
          ( m1_pboole(C,u1_msualg_1(k12_pua2mss1(A,B)))
          & ! [D] : 
              ( m1_subset_1(D,u1_msualg_1(k12_pua2mss1(A,B)))
             => k1_funct_1(C,D) = k2_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,k13_pua2mss1(A,B,D)),k4_card_3(k14_pua2mss1(A,B,D))) ) ) ) ),
    file(pua2mss1,s5_pboole__e3_72__pua2mss1),
    []).

fof(s5_pboole__e5_72__pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ? [C] : 
          ( m1_pboole(C,k4_finseq_1(u1_unialg_1(A)))
          & ! [D] : 
              ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(A)))
             => k1_funct_1(C,D) = a_3_2_pua2mss1(A,B,D) ) ) ) ),
    file(pua2mss1,s5_pboole__e5_72__pua2mss1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(symmetry_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
       => r2_subset_1(B,A) ) ) ),
    file(subset_1,r2_subset_1),
    []).

fof(t10_card_5,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(B))
      <=> ? [C] : 
            ( r2_hidden(C,k1_relat_1(B))
            & r2_hidden(A,k1_funct_1(B,C)) ) ) ) ),
    file(card_5,t10_card_5),
    []).

fof(t11_pua2mss1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => m1_eqrel_1(a_3_1_pua2mss1(A,B,C),B) ) ) ) ),
    file(pua2mss1,t11_pua2mss1),
    []).

fof(t12_pua2mss1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m1_eqrel_1(B,k1_relat_1(A))
         => m1_eqrel_1(a_2_1_pua2mss1(A,B),A) ) ) ),
    file(pua2mss1,t12_pua2mss1),
    []).

fof(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t148_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ),
    file(relat_1,t148_relat_1),
    []).

fof(t15_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v2_relat_1(B)
        & v1_funct_1(B) )
     => ( ( k3_card_3(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,k1_relat_1(B))
                & r2_hidden(D,k1_relat_1(B)) )
             => ( C = D
                | r1_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) )
       => m2_pua2mss1(B,A) ) ) ),
    file(pua2mss1,t15_pua2mss1),
    []).

fof(t16_pua2mss1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_eqrel_1(C,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,C)
                    & m2_relset_1(D,A,C) )
                 => ( ( r1_tarski(C,k2_relat_1(D))
                      & v2_funct_1(D) )
                   => m2_pua2mss1(D,B) ) ) ) ) ) ),
    file(pua2mss1,t16_pua2mss1),
    []).

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

fof(t23_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    []).

fof(t28_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    []).

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

fof(t2_pua2mss1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( k4_card_3(A) = k4_card_3(B)
           => A = B ) ) ) ),
    file(pua2mss1,t2_pua2mss1),
    []).

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(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t4_funct_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_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(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(t6_pua2mss1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r1_tarski(k2_relat_1(B),k3_tarski(A))
          & ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ~ ( k1_relat_1(C) = k1_relat_1(B)
                  & r1_tarski(k2_relat_1(C),A)
                  & r2_hidden(B,k4_card_3(C)) ) ) ) ) ),
    file(pua2mss1,t6_pua2mss1),
    []).

fof(t70_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    []).

fof(t71_relat_1,axiom,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    []).

fof(t73_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(B,k1_relat_1(C))
          & r2_hidden(B,A) )
       => r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A))) ) ) ),
    file(funct_1,t73_funct_1),
    []).

fof(t79_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    []).

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

fof(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

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

fof(t90_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    []).

fof(t91_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    []).

fof(t9_pua2mss1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => m1_eqrel_1(a_2_0_pua2mss1(A,B),k3_finseq_2(A)) ) ) ),
    file(pua2mss1,t9_pua2mss1),
    []).