% Mizar problem: t55_group_4,group_4,1341,23 
fof(t55_group_4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => u1_struct_0(k6_group_4(A)) = a_1_1_group_4(A) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,antisymmetry_r2_hidden,cc1_finseq_1,cc1_group_1,cc1_group_2,cc1_int_1,cc1_nat_1,cc1_relset_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc4_int_1,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_subset_1,commutativity_k5_subset_1,d10_xboole_0,d1_group_3,d1_rlvect_1,d1_tarski,d2_group_4,d2_xboole_0,d3_group_4,d3_tarski,d3_xboole_0,d4_finseq_4,d4_group_4,d4_tarski,d4_xboole_0,d5_funct_1,d5_group_2,d5_group_4,d6_group_4,d7_group_4,d7_xboole_0,d8_group_4,d9_group_2,dt_g1_group_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_group_1,dt_k1_group_3,dt_k1_numbers,dt_k1_realset1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finsop_1,dt_k2_group_4,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_group_1,dt_k3_group_4,dt_k3_tarski,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_group_4,dt_k4_numbers,dt_k4_subset_1,dt_k4_xboole_0,dt_k5_group_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_subset_1,dt_k6_domain_1,dt_k6_group_1,dt_k6_group_4,dt_k6_subset_1,dt_k7_group_2,dt_l1_group_1,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_group_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_group_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_group_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc11_finseq_1,fc17_finseq_1,fc1_group_1,fc1_group_3,fc1_numbers,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_subset_1,fc4_numbers,fc4_subset_1,fraenkel_a_1_0_group_4,fraenkel_a_1_1_group_4,fraenkel_a_2_3_group_4,free_g1_group_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,rc1_finseq_1,rc1_group_1,rc1_group_2,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_finseq_1,rc2_group_1,rc2_int_1,rc2_nat_1,rc2_subset_1,rc3_finseq_1,rc3_group_1,rc3_nat_1,rc3_struct_0,rc4_finseq_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_subset_1,redefinition_k6_domain_1,redefinition_k6_subset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_group_2,reflexivity_r1_group_2,reflexivity_r1_tarski,s1_orders_1__e22_53_1__group_4,s2_group_4__e10_53_1__group_4,symmetry_r1_group_2,symmetry_r1_xboole_0,t1_boole,t1_subset,t1_xboole_1,t21_group_4,t2_boole,t2_subset,t2_tarski,t2_xboole_1,t31_finseq_3,t37_group_4,t37_zfmisc_1,t38_group_4,t3_boole,t3_subset,t40_group_4,t40_xboole_1,t41_group_4,t48_group_4,t49_group_2,t4_boole,t4_subset,t52_group_4,t54_group_4,t5_subset,t61_group_2,t63_group_2,t64_group_2,t65_group_2,t66_group_2,t6_boole,t6_group_4,t71_group_2,t7_boole,t83_xboole_1,t87_group_2,t88_group_2,t89_group_2,t8_boole,t8_xboole_1,t90_group_2,t91_orders_1,t92_zfmisc_1,t94_zfmisc_1]),
    [file(group_4,t55_group_4)]).

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(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_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_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k4_numbers)
     => v1_int_1(A) ) ),
    file(int_1,cc1_int_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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_int_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)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_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(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

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(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

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

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

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

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_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_group_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( B = k1_group_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v1_group_1(C)
                & m1_group_2(C,A) ) ) ) ) ),
    file(group_3,d1_group_3),
    []).

fof(d1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( r1_rlvect_1(A,B)
        <=> r2_hidden(B,u1_struct_0(A)) ) ) ),
    file(rlvect_1,d1_rlvect_1),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_group_4,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => k2_group_4(A) = A ) ),
    file(group_4,d2_group_4),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d3_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,u1_struct_0(A))
         => k3_group_4(A,B) = k2_finsop_1(u1_struct_0(A),B,u1_group_1(A)) ) ) ),
    file(group_4,d3_group_4),
    []).

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_4,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    []).

fof(d4_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] : 
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( D = k4_group_4(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(C)
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(C))
                           => k1_funct_1(D,E) = k6_group_1(A,k2_group_4(k4_finseq_4(k5_numbers,k4_numbers,B,E)),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) ) ) ) ) ) ) ) ) ),
    file(group_4,d4_group_4),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

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_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_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v1_group_1(C)
                & m1_group_2(C,A) )
             => ( C = k5_group_4(A,B)
              <=> ( r1_tarski(B,u1_struct_0(C))
                  & ! [D] : 
                      ( ( v1_group_1(D)
                        & m1_group_2(D,A) )
                     => ( r1_tarski(B,u1_struct_0(D))
                       => m1_group_2(C,D) ) ) ) ) ) ) ) ),
    file(group_4,d5_group_4),
    []).

fof(d6_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_group_4(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & k5_group_4(A,C) = g1_group_1(u1_struct_0(A),u1_group_1(A))
                & k5_group_4(A,k6_subset_1(u1_struct_0(A),C,k6_domain_1(u1_struct_0(A),B))) != g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ),
    file(group_4,d6_group_4),
    []).

fof(d7_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( v2_group_4(B,A)
          <=> ( g1_group_1(u1_struct_0(B),u1_group_1(B)) != g1_group_1(u1_struct_0(A),u1_group_1(A))
              & ! [C] : 
                  ( ( v1_group_1(C)
                    & m1_group_2(C,A) )
                 => ( m1_group_2(B,C)
                   => ( g1_group_1(u1_struct_0(B),u1_group_1(B)) = C
                      | C = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ) ) ) ),
    file(group_4,d7_group_4),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(d8_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( ? [C] : 
                  ( v1_group_1(C)
                  & m1_group_2(C,A)
                  & v2_group_4(C,A) )
             => ( B = k6_group_4(A)
              <=> u1_struct_0(B) = k1_setfam_1(a_1_0_group_4(A)) ) )
            & ( ! [C] : 
                  ( ( v1_group_1(C)
                    & m1_group_2(C,A) )
                 => ~ v2_group_4(C,A) )
             => ( B = k6_group_4(A)
              <=> B = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ) ),
    file(group_4,d8_group_4),
    []).

fof(d9_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)
         => k7_group_2(A,B) = u1_struct_0(B) ) ) ),
    file(group_2,d9_group_2),
    []).

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_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

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

fof(dt_k1_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_1),
    []).

fof(dt_k1_group_3,axiom,(
    $true ),
    file(group_3,k1_group_3),
    []).

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

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_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_finsop_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => m1_subset_1(k2_finsop_1(A,B,C),A) ) ),
    file(finsop_1,k2_finsop_1),
    []).

fof(dt_k2_group_4,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => m1_subset_1(k2_group_4(A),k4_numbers) ) ),
    file(group_4,k2_group_4),
    []).

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

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_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_group_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_group_1(A,B),u1_struct_0(A)) ) ),
    file(group_1,k3_group_1),
    []).

fof(dt_k3_group_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_finseq_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_group_4(A,B),u1_struct_0(A)) ) ),
    file(group_4,k3_group_4),
    []).

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_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_group_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_finseq_1(B,k4_numbers)
        & m1_finseq_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k4_group_4(A,B,C),u1_struct_0(A)) ) ),
    file(group_4,k4_group_4),
    []).

fof(dt_k4_numbers,axiom,(
    $true ),
    file(numbers,k4_numbers),
    []).

fof(dt_k4_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(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(dt_k5_group_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_group_1(k5_group_4(A,B))
        & m1_group_2(k5_group_4(A,B),A) ) ) ),
    file(group_4,k5_group_4),
    []).

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_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_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(dt_k6_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_int_1(B)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k6_group_1),
    []).

fof(dt_k6_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k6_group_4(A))
        & m1_group_2(k6_group_4(A),A) ) ) ),
    file(group_4,k6_group_4),
    []).

fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k7_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m1_subset_1(k7_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k7_group_2),
    []).

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_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_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_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_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_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

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_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_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(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(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_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_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ~ v1_xboole_0(k1_group_3(A)) ) ),
    file(group_3,fc1_group_3),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc4_numbers,axiom,(
    ~ v1_xboole_0(k4_numbers) ),
    file(numbers,fc4_numbers),
    []).

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(fraenkel_a_1_0_group_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,a_1_0_group_4(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & ? [D] : 
                ( v1_group_1(D)
                & m1_group_2(D,B)
                & C = u1_struct_0(D)
                & v2_group_4(D,B) ) ) ) ) ),
    file(group_4,a_1_0_group_4),
    []).

fof(fraenkel_a_1_1_group_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v1_group_1(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,a_1_1_group_4(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ~ v1_group_4(C,B) ) ) ) ),
    file(group_4,a_1_1_group_4),
    []).

fof(fraenkel_a_2_3_group_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v1_group_1(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,a_2_3_group_4(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & ? [E] : 
                ( v1_group_1(E)
                & m1_group_2(E,B)
                & r2_hidden(E,C)
                & D = k7_group_2(B,E) ) ) ) ) ),
    file(group_4,a_2_3_group_4),
    []).

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_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

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(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_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_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_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_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_group_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A) ) ),
    file(group_1,rc2_group_1),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_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_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_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_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_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(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_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_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_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

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

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_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

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_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_r1_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
      <=> B = C ) ) ),
    file(group_2,r1_group_2),
    []).

fof(reflexivity_r1_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => r1_group_2(A,B,B) ) ),
    file(group_2,r1_group_2),
    []).

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

fof(s1_orders_1__e22_53_1__group_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v1_xboole_0(B) )
     => ( ( ! [C] : 
              ( m1_subset_1(C,B)
             => ? [D] : 
                  ( v1_group_1(D)
                  & m1_group_2(D,A)
                  & ? [E] : 
                      ( v1_group_1(E)
                      & m1_group_2(E,A)
                      & C = D
                      & C = E
                      & m1_group_2(D,E) ) ) )
          & ! [C] : 
              ( m1_subset_1(C,B)
             => ! [F] : 
                  ( m1_subset_1(F,B)
                 => ( ( ? [G] : 
                          ( v1_group_1(G)
                          & m1_group_2(G,A)
                          & ? [H] : 
                              ( v1_group_1(H)
                              & m1_group_2(H,A)
                              & C = G
                              & F = H
                              & m1_group_2(G,H) ) )
                      & ? [I] : 
                          ( v1_group_1(I)
                          & m1_group_2(I,A)
                          & ? [J] : 
                              ( v1_group_1(J)
                              & m1_group_2(J,A)
                              & F = I
                              & C = J
                              & m1_group_2(I,J) ) ) )
                   => C = F ) ) )
          & ! [C] : 
              ( m1_subset_1(C,B)
             => ! [F] : 
                  ( m1_subset_1(F,B)
                 => ! [K] : 
                      ( m1_subset_1(K,B)
                     => ( ( ? [L] : 
                              ( v1_group_1(L)
                              & m1_group_2(L,A)
                              & ? [M] : 
                                  ( v1_group_1(M)
                                  & m1_group_2(M,A)
                                  & C = L
                                  & F = M
                                  & m1_group_2(L,M) ) )
                          & ? [N] : 
                              ( v1_group_1(N)
                              & m1_group_2(N,A)
                              & ? [O] : 
                                  ( v1_group_1(O)
                                  & m1_group_2(O,A)
                                  & F = N
                                  & K = O
                                  & m1_group_2(N,O) ) ) )
                       => ? [P] : 
                            ( v1_group_1(P)
                            & m1_group_2(P,A)
                            & ? [Q] : 
                                ( v1_group_1(Q)
                                & m1_group_2(Q,A)
                                & C = P
                                & K = Q
                                & m1_group_2(P,Q) ) ) ) ) ) )
          & ! [C] : ~ ( r1_tarski(C,B)
              & ! [F] : 
                  ( m1_subset_1(F,B)
                 => ! [K] : 
                      ( m1_subset_1(K,B)
                     => ~ ( r2_hidden(F,C)
                          & r2_hidden(K,C)
                          & ~ ? [R] : 
                                ( v1_group_1(R)
                                & m1_group_2(R,A)
                                & ? [S] : 
                                    ( v1_group_1(S)
                                    & m1_group_2(S,A)
                                    & F = R
                                    & K = S
                                    & m1_group_2(R,S) ) )
                          & ~ ? [T] : 
                                ( v1_group_1(T)
                                & m1_group_2(T,A)
                                & ? [U] : 
                                    ( v1_group_1(U)
                                    & m1_group_2(U,A)
                                    & K = T
                                    & F = U
                                    & m1_group_2(T,U) ) ) ) ) )
              & ! [F] : 
                  ( m1_subset_1(F,B)
                 => ? [K] : 
                      ( m1_subset_1(K,B)
                      & r2_hidden(K,C)
                      & ~ ? [V] : 
                            ( v1_group_1(V)
                            & m1_group_2(V,A)
                            & ? [W] : 
                                ( v1_group_1(W)
                                & m1_group_2(W,A)
                                & K = V
                                & F = W
                                & m1_group_2(V,W) ) ) ) ) ) )
       => ? [C] : 
            ( m1_subset_1(C,B)
            & ! [F] : 
                ( m1_subset_1(F,B)
               => ~ ( C != F
                    & ? [X] : 
                        ( v1_group_1(X)
                        & m1_group_2(X,A)
                        & ? [Y] : 
                            ( v1_group_1(Y)
                            & m1_group_2(Y,A)
                            & C = X
                            & F = Y
                            & m1_group_2(X,Y) ) ) ) ) ) ) ) ),
    file(group_4,s1_orders_1__e22_53_1__group_4),
    []).

fof(s2_group_4__e10_53_1__group_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [D] : 
          ( r1_tarski(D,k1_group_3(A))
          & ! [E] : 
              ( ( v1_group_1(E)
                & m1_group_2(E,A) )
             => ( r2_hidden(E,D)
              <=> ( r1_tarski(k6_subset_1(u1_struct_0(A),C,k6_domain_1(u1_struct_0(A),B)),k7_group_2(A,E))
                  & ~ r1_rlvect_1(E,B) ) ) ) ) ) ),
    file(group_4,s2_group_4__e10_53_1__group_4),
    []).

fof(symmetry_r1_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
       => r1_group_2(A,C,B) ) ) ),
    file(group_2,r1_group_2),
    []).

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

fof(t21_group_4,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] : 
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( r1_tarski(k2_relat_1(C),k7_group_2(A,B))
               => r1_rlvect_1(B,k3_group_4(A,C)) ) ) ) ) ),
    file(group_4,t21_group_4),
    []).

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

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

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

fof(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).

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

fof(t37_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_rlvect_1(k5_group_4(A,C),B)
              <=> ? [D] : 
                    ( m2_finseq_1(D,u1_struct_0(A))
                    & ? [E] : 
                        ( m2_finseq_1(E,k4_numbers)
                        & k3_finseq_1(D) = k3_finseq_1(E)
                        & r1_tarski(k2_relat_1(D),C)
                        & k3_group_4(A,k4_group_4(A,E,D)) = B ) ) ) ) ) ) ),
    file(group_4,t37_group_4),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t38_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,C)
               => r1_rlvect_1(k5_group_4(A,C),B) ) ) ) ) ),
    file(group_4,t38_group_4),
    []).

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

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

fof(t40_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => r1_group_2(A,k5_group_4(A,k7_group_2(A,B)),B) ) ) ),
    file(group_4,t40_group_4),
    []).

fof(t40_xboole_1,axiom,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_1),
    []).

fof(t41_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => m1_group_2(k5_group_4(A,B),k5_group_4(A,C)) ) ) ) ) ),
    file(group_4,t41_group_4),
    []).

fof(t48_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( v2_group_4(B,A)
               => ( r1_rlvect_1(B,C)
                  | k5_group_4(A,k4_subset_1(u1_struct_0(A),k7_group_2(A,B),k6_domain_1(u1_struct_0(A),C))) = A ) ) ) ) ) ),
    file(group_4,t48_group_4),
    []).

fof(t49_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_group_2(C,B)
         => ( r1_rlvect_1(C,A)
           => r1_rlvect_1(B,A) ) ) ) ),
    file(group_2,t49_group_2),
    []).

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

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

fof(t52_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( ? [D] : 
                    ( v1_group_1(D)
                    & m1_group_2(D,C)
                    & v2_group_4(D,C) )
               => ( r1_rlvect_1(k6_group_4(C),B)
                <=> ! [D] : 
                      ( ( v1_group_1(D)
                        & m1_group_2(D,C) )
                     => ( v2_group_4(D,C)
                       => r1_rlvect_1(D,B) ) ) ) ) ) ) ) ),
    file(group_4,t52_group_4),
    []).

fof(t54_group_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( v2_group_4(B,A)
           => m1_group_2(k6_group_4(A),B) ) ) ) ),
    file(group_4,t54_group_4),
    []).

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(t61_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( B != k1_xboole_0
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k1_group_1(A,C,D),B) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_hidden(C,B)
                   => r2_hidden(k3_group_1(A,C),B) ) )
              & ! [C] : 
                  ( ( v1_group_1(C)
                    & m1_group_2(C,A) )
                 => u1_struct_0(C) != B ) ) ) ) ),
    file(group_2,t61_group_2),
    []).

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(t64_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( m1_group_2(A,B)
              & m1_group_2(B,A) )
           => g1_group_1(u1_struct_0(A),u1_group_1(A)) = g1_group_1(u1_struct_0(B),u1_group_1(B)) ) ) ) ),
    file(group_2,t64_group_2),
    []).

fof(t65_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( ( m1_group_2(A,B)
                  & m1_group_2(B,C) )
               => m1_group_2(A,C) ) ) ) ) ),
    file(group_2,t65_group_2),
    []).

fof(t66_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)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_group_2(B,C) ) ) ) ) ),
    file(group_2,t66_group_2),
    []).

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

fof(t6_group_4,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_group_2(D,B)
                 => ( r1_rlvect_1(D,C)
                   => r1_rlvect_1(D,k6_group_1(B,A,C)) ) ) ) ) ) ),
    file(group_4,t6_group_4),
    []).

fof(t71_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_subset_1(C,u1_struct_0(A))
               => r1_rlvect_1(B,C) )
           => g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ),
    file(group_2,t71_group_2),
    []).

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

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).

fof(t87_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)
         => k7_group_2(A,B) != k1_xboole_0 ) ) ),
    file(group_2,t87_group_2),
    []).

fof(t88_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_group_2(C,B)
         => ( r2_hidden(A,k7_group_2(B,C))
          <=> r1_rlvect_1(C,A) ) ) ) ),
    file(group_2,t88_group_2),
    []).

fof(t89_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => ( ( r2_hidden(B,k7_group_2(A,D))
                      & r2_hidden(C,k7_group_2(A,D)) )
                   => r2_hidden(k1_group_1(A,B,C),k7_group_2(A,D)) ) ) ) ) ) ),
    file(group_2,t89_group_2),
    []).

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

fof(t8_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    []).

fof(t90_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_group_2(C,A)
             => ( r2_hidden(B,k7_group_2(A,C))
               => r2_hidden(k3_group_1(A,B),k7_group_2(A,C)) ) ) ) ) ),
    file(group_2,t90_group_2),
    []).

fof(t91_orders_1,axiom,(
    ! [A] : 
      ( ~ ( ? [B] : 
              ( B != k1_xboole_0
              & r2_hidden(B,A) )
          & k3_tarski(A) = k1_xboole_0 )
      & ~ ( k3_tarski(A) != k1_xboole_0
          & ! [B] : ~ ( B != k1_xboole_0
              & r2_hidden(B,A) ) ) ) ),
    file(orders_1,t91_orders_1),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).

fof(t94_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) ),
    file(zfmisc_1,t94_zfmisc_1),
    []).