% Mizar problem: t12_group_7,group_7,1766,24 
fof(t12_group_7,conjecture,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( ( v1_group_7(B)
            & v2_group_7(B,A)
            & v3_group_7(B,A)
            & m1_pboole(B,A) )
         => k2_group_7(A,B) = k3_group_7(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,antisymmetry_r2_hidden,cc10_membered,cc10_monoid_0,cc11_membered,cc11_monoid_0,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_group_1,cc1_group_2,cc1_group_7,cc1_membered,cc1_monoid_0,cc1_realset1,cc1_relat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_monoid_0,cc6_monoid_0,cc7_monoid_0,cc8_monoid_0,cc9_monoid_0,commutativity_k2_tarski,commutativity_k2_xboole_0,d10_xboole_0,d1_binop_1,d1_funct_4,d2_group_7,d3_group_7,d3_pboole,d3_realset1,d3_tarski,d5_group_2,d5_tarski,d9_group_7,dt_g1_group_1,dt_k12_pralg_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_group_7,dt_k1_pralg_2,dt_k1_realset1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_group_1,dt_k2_group_7,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_group_7,dt_k4_card_3,dt_k4_tarski,dt_k7_relat_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_group_2,dt_m1_pboole,dt_m1_pralg_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_group_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_struct_0,existence_m1_group_2,existence_m1_pboole,existence_m1_pralg_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_membered,fc11_membered,fc12_membered,fc12_relat_1,fc13_membered,fc13_relat_1,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_finset_1,fc1_group_1,fc1_group_7,fc1_pralg_2,fc1_realset1,fc1_struct_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_finset_1,fc2_group_7,fc2_realset1,fc2_relat_1,fc3_group_7,fc3_realset1,fc4_group_7,fc4_relat_1,fc5_relat_1,fc6_group_7,fc6_membered,fc7_membered,fc7_relat_1,fc8_membered,fc9_finset_1,fc9_membered,free_g1_group_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,l5_group_7,rc1_finseq_1,rc1_finset_1,rc1_group_1,rc1_group_2,rc1_group_7,rc1_membered,rc1_monoid_0,rc1_pralg_2,rc1_realset1,rc1_relat_1,rc2_group_1,rc2_group_7,rc2_realset1,rc2_relat_1,rc3_finseq_1,rc3_finset_1,rc3_group_1,rc3_relat_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_group_7,redefinition_m1_pralg_2,redefinition_m2_relset_1,reflexivity_r1_tarski,s1_xboole_0__e1_30_1_2__group_7,s4_pboole__e5_30_1_2__group_7,t12_funct_4,t12_xboole_1,t14_funct_4,t18_card_3,t1_boole,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t63_group_2,t68_group_2,t6_boole,t7_boole,t8_boole,t9_funct_1,t9_group_7]),
    [file(group_7,t12_group_7)]).

fof(abstractness_v1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_group_1(A)
       => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ),
    file(group_1,v1_group_1),
    []).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc10_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_monoid_0(A)
          & v15_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v16_monoid_0(A) ) ) ) ),
    file(monoid_0,cc10_monoid_0),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc11_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_group_1(A)
          & v13_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v16_monoid_0(A) ) ) ) ),
    file(monoid_0,cc11_monoid_0),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(group_1,cc1_group_1),
    []).

fof(cc1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => v4_group_1(B) ) ) ),
    file(group_2,cc1_group_2),
    []).

fof(cc1_group_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_group_7(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) ),
    file(group_7,cc1_group_7),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_monoid_0,axiom,(
    ! [A] : 
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(monoid_0,cc1_monoid_0),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc5_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v13_monoid_0(A) ) ) ) ),
    file(monoid_0,cc5_monoid_0),
    []).

fof(cc6_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_group_1(A)
          & v13_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v3_group_1(A) ) ) ) ),
    file(monoid_0,cc6_monoid_0),
    []).

fof(cc7_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v13_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v11_monoid_0(A)
          & v12_monoid_0(A) ) ) ) ),
    file(monoid_0,cc7_monoid_0),
    []).

fof(cc8_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v11_monoid_0(A)
          & v12_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v13_monoid_0(A) ) ) ) ),
    file(monoid_0,cc8_monoid_0),
    []).

fof(cc9_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v16_monoid_0(A) )
       => ( ~ v3_struct_0(A)
          & v14_monoid_0(A)
          & v15_monoid_0(A) ) ) ) ),
    file(monoid_0,cc9_monoid_0),
    []).

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

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

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    []).

fof(d2_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_group_1(C)
            & l1_group_1(C) )
         => ( C = k2_group_7(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & ! [D] : 
                  ( m1_pralg_2(D,k4_card_3(k12_pralg_1(A,B)))
                 => ! [E] : 
                      ( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
                     => ! [F] : ~ ( r2_hidden(F,A)
                          & ! [G] : 
                              ( ( ~ v3_struct_0(G)
                                & l1_group_1(G) )
                             => ! [H] : 
                                  ( ( v1_relat_1(H)
                                    & v1_funct_1(H) )
                                 => ~ ( G = k1_funct_1(B,F)
                                      & H = k1_binop_1(u1_group_1(C),D,E)
                                      & k1_funct_1(H,F) = k1_binop_1(u1_group_1(G),k1_funct_1(D,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) ) ) ),
    file(group_7,d2_group_7),
    []).

fof(d3_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v2_group_7(B,A)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & ! [D] : 
                ( ( ~ v3_struct_0(D)
                  & v3_group_1(D)
                  & l1_group_1(D) )
               => D != k1_funct_1(B,C) ) ) ) ) ),
    file(group_7,d3_group_7),
    []).

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_realset1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B)) ) ),
    file(realset1,d3_realset1),
    []).

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

fof(d5_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ( m1_group_2(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)) ) ) ) ) ),
    file(group_2,d5_group_2),
    []).

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

fof(d9_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_group_1(C)
            & m1_group_2(C,k2_group_7(A,B)) )
         => ( C = k3_group_7(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,u1_struct_0(C))
              <=> ? [E] : 
                    ( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
                    & ? [F] : 
                        ( v1_finset_1(F)
                        & m1_subset_1(F,k1_zfmisc_1(A))
                        & ? [G] : 
                            ( m1_pboole(G,F)
                            & E = k2_group_1(k2_group_7(A,B))
                            & D = k1_funct_4(E,G)
                            & ! [H] : ~ ( r2_hidden(H,F)
                                & ! [I] : 
                                    ( ( ~ v3_struct_0(I)
                                      & v3_group_1(I)
                                      & l1_group_1(I) )
                                   => ~ ( I = k1_funct_1(B,H)
                                        & r2_hidden(k1_funct_1(G,H),u1_struct_0(I))
                                        & k1_funct_1(G,H) != k2_group_1(I) ) ) ) ) ) ) ) ) ) ) ),
    file(group_7,d9_group_7),
    []).

fof(dt_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_group_1(g1_group_1(A,B))
        & l1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,g1_group_1),
    []).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) ),
    file(pralg_1,k12_pralg_1),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

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

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

fof(dt_k1_group_7,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_group_7(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k1_group_7(A,B,C))
        & l1_group_1(k1_group_7(A,B,C)) ) ) ),
    file(group_7,k1_group_7),
    []).

fof(dt_k1_pralg_2,axiom,(
    $true ),
    file(pralg_2,k1_pralg_2),
    []).

fof(dt_k1_realset1,axiom,(
    $true ),
    file(realset1,k1_realset1),
    []).

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_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ),
    file(group_1,k2_group_1),
    []).

fof(dt_k2_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v1_group_1(k2_group_7(A,B))
        & l1_group_1(k2_group_7(A,B)) ) ) ),
    file(group_7,k2_group_7),
    []).

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

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

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

fof(dt_k3_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ( v1_group_1(k3_group_7(A,B))
        & m1_group_2(k3_group_7(A,B),k2_group_7(A,B)) ) ) ),
    file(group_7,k3_group_7),
    []).

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

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

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_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

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

fof(dt_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) ) ) ) ),
    file(group_2,m1_group_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_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ! [B] : 
          ( m1_pralg_2(B,A)
         => m1_pboole(B,k1_pralg_2(A)) ) ) ),
    file(pralg_2,m1_pralg_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_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_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    []).

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

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

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

fof(existence_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ? [B] : m1_group_2(B,A) ) ),
    file(group_2,m1_group_2),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ? [B] : m1_pralg_2(B,A) ) ),
    file(pralg_2,m1_pralg_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_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc12_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    []).

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_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    []).

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(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc14_membered,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    []).

fof(fc15_membered,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    []).

fof(fc16_membered,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_group_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g1_group_1(A,B))
        & v1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,fc1_group_1),
    []).

fof(fc1_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k12_pralg_1(A,B))
        & v2_relat_1(k12_pralg_1(A,B))
        & v1_funct_1(k12_pralg_1(A,B)) ) ) ),
    file(group_7,fc1_group_7),
    []).

fof(fc1_pralg_2,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B))
        & v1_pralg_2(k4_card_3(B)) ) ) ),
    file(pralg_2,fc1_pralg_2),
    []).

fof(fc1_realset1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k1_realset1(A,B)) ) ),
    file(realset1,fc1_realset1),
    []).

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(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

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_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc2_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) ),
    file(group_7,fc2_group_7),
    []).

fof(fc2_realset1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_realset1(A,B))
        & v1_funct_1(k1_realset1(A,B)) ) ) ),
    file(realset1,fc2_realset1),
    []).

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(fc3_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v2_group_1(k2_group_7(A,B))
        & v3_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) ),
    file(group_7,fc3_group_7),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc4_group_7,axiom,(
    ! [A,B] : 
      ( ( v1_group_7(B)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v4_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) ),
    file(group_7,fc4_group_7),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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_group_7,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_group_7(A,B)))
        & m1_subset_1(D,u1_struct_0(k3_group_7(A,B))) )
     => ( v1_relat_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D))
        & v1_funct_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D)) ) ) ),
    file(group_7,fc6_group_7),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

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_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(free_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] : 
          ( g1_group_1(A,B) = g1_group_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(group_1,g1_group_1),
    []).

fof(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

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

fof(l5_group_7,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( v1_group_7(C)
                & m1_pboole(C,A) )
             => ! [D] : 
                  ( m1_pralg_2(D,k4_card_3(k12_pralg_1(A,C)))
                 => r2_hidden(k1_funct_1(D,B),u1_struct_0(k1_group_7(A,C,B))) ) ) ) ) ),
    file(group_7,l5_group_7),
    []).

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_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_group_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & v1_group_1(A) ) ),
    file(group_1,rc1_group_1),
    []).

fof(rc1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ? [B] : 
          ( m1_group_2(B,A)
          & ~ v3_struct_0(B)
          & v1_group_1(B)
          & v2_group_1(B)
          & v3_group_1(B)
          & v4_group_1(B) ) ) ),
    file(group_2,rc1_group_2),
    []).

fof(rc1_group_7,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_group_7(B) ) ),
    file(group_7,rc1_group_7),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_monoid_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v1_monoid_0(A) ) ),
    file(monoid_0,rc1_monoid_0),
    []).

fof(rc1_pralg_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A) ) ),
    file(pralg_2,rc1_pralg_2),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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

fof(rc2_group_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A) ) ),
    file(group_1,rc2_group_1),
    []).

fof(rc2_group_7,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_pralg_1(A)
      & v1_group_7(A) ) ),
    file(group_7,rc2_group_7),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_group_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A)
      & v2_group_1(A)
      & v3_group_1(A)
      & v4_group_1(A) ) ),
    file(group_1,rc3_group_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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_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_k1_group_7,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_group_7(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k1_group_7(A,B,C) = k1_funct_1(B,C) ) ),
    file(group_7,k1_group_7),
    []).

fof(redefinition_m1_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ! [B] : 
          ( m1_pralg_2(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(pralg_2,m1_pralg_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(s1_xboole_0__e1_30_1_2__group_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(A)
        & v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : 
        ! [E] : 
          ( r2_hidden(E,D)
        <=> ( r2_hidden(E,A)
            & ? [F] : 
                ( ~ v3_struct_0(F)
                & v3_group_1(F)
                & l1_group_1(F)
                & ? [G] : 
                    ( m1_subset_1(G,u1_struct_0(F))
                    & F = k1_funct_1(B,E)
                    & G = k1_funct_1(C,E)
                    & G != k2_group_1(F) ) ) ) ) ) ),
    file(group_7,s1_xboole_0__e1_30_1_2__group_7),
    []).

fof(s4_pboole__e5_30_1_2__group_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(A)
        & m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => ? [D] : 
          ( m1_pboole(D,C)
          & ! [E] : 
              ( r2_hidden(E,C)
             => k1_funct_1(D,E) = k1_funct_1(B,E) ) ) ) ),
    file(group_7,s4_pboole__e5_30_1_2__group_7),
    []).

fof(t12_funct_4,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(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    []).

fof(t12_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    []).

fof(t14_funct_4,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(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    []).

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

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

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

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

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

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(t63_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_group_2(A,A) ) ),
    file(group_2,t63_group_2),
    []).

fof(t68_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_group_2(C,A)
             => ( u1_struct_0(B) = u1_struct_0(C)
               => g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(C),u1_group_1(C)) ) ) ) ) ),
    file(group_2,t68_group_2),
    []).

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

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

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

fof(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),
    []).

fof(t9_group_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_group_7(D)
            & v2_group_7(D,A)
            & m1_pboole(D,A) )
         => ! [E] : 
              ( ( ~ v3_struct_0(E)
                & v3_group_1(E)
                & l1_group_1(E) )
             => ( ( r2_hidden(B,A)
                  & E = k1_funct_1(D,B)
                  & C = k2_group_1(k2_group_7(A,D)) )
               => k1_funct_1(C,B) = k2_group_1(E) ) ) ) ) ),
    file(group_7,t9_group_7),
    []).