% Mizar problem: t27_monoid_1,monoid_1,755,37 
fof(t27_monoid_1,conjecture,(
    ! [A] : 
      ( u1_struct_0(k13_monoid_1(A)) = k1_fraenkel(A,k5_numbers)
      & u1_group_1(k13_monoid_1(A)) = k8_monoid_1(k5_numbers,k5_numbers,k5_numbers,k47_binop_2,A)
      & u1_vectsp_1(k13_monoid_1(A)) = k5_monoid_1(k5_numbers,A,0) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,abstractness_v1_vectsp_1,antisymmetry_r2_hidden,cc10_membered,cc10_monoid_0,cc11_membered,cc11_monoid_0,cc12_membered,cc12_monoid_0,cc13_membered,cc13_monoid_0,cc14_membered,cc14_monoid_0,cc15_membered,cc16_membered,cc16_monoid_0,cc17_membered,cc17_monoid_0,cc18_membered,cc18_monoid_0,cc19_membered,cc19_monoid_0,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_monoid_0,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc20_membered,cc20_monoid_0,cc21_monoid_0,cc22_monoid_0,cc27_monoid_0,cc29_monoid_0,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_nat_1,cc33_monoid_0,cc36_monoid_0,cc3_membered,cc3_nat_1,cc4_membered,cc5_monoid_0,cc6_membered,cc6_monoid_0,cc7_monoid_0,cc8_monoid_0,cc9_membered,cc9_monoid_0,d22_monoid_0,d26_monoid_0,d29_monoid_0,d4_monoid_1,dt_g1_group_1,dt_g1_vectsp_1,dt_k11_monoid_1,dt_k12_monoid_1,dt_k13_monoid_1,dt_k1_fraenkel,dt_k1_funct_2,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k33_binop_2,dt_k3_binop_1,dt_k3_gr_cy_1,dt_k47_binop_2,dt_k5_monoid_0,dt_k5_monoid_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_monoid_0,dt_k7_monoid_0,dt_k8_monoid_0,dt_k8_monoid_1,dt_k9_monoid_1,dt_l1_group_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_m1_fraenkel,dt_m1_monoid_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_monoid_0,dt_m2_relset_1,dt_m5_monoid_0,dt_u1_group_1,dt_u1_struct_0,dt_u1_vectsp_1,existence_l1_group_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_m1_fraenkel,existence_m1_monoid_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_monoid_0,existence_m2_relset_1,existence_m5_monoid_0,fc12_relat_1,fc14_finset_1,fc1_funcop_1,fc1_monoid_0,fc1_monoid_1,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_funcop_1,fc2_membered,fc2_monoid_1,fc3_funcop_1,fc4_ordinal2,fc4_relat_1,fc4_subset_1,fc5_membered,fc6_membered,fc9_funcop_1,free_g1_group_1,free_g1_vectsp_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_monoid_0,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc3_struct_0,rc4_finset_1,rc4_funct_1,rc5_funct_1,rc5_monoid_0,rc5_struct_0,rc6_finseq_1,rc6_monoid_0,rc7_finseq_1,rc7_monoid_0,rc8_finseq_1,rc8_monoid_0,redefinition_k11_monoid_1,redefinition_k12_monoid_1,redefinition_k1_fraenkel,redefinition_k5_monoid_1,redefinition_k5_numbers,redefinition_k6_monoid_0,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m5_monoid_0,reflexivity_r1_tarski,spc0_boole,t18_monoid_1,t1_numerals,t1_subset,t23_monoid_1,t2_subset,t3_subset,t44_monoid_0,t4_subset,t52_monoid_0,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(monoid_1,t27_monoid_1)]).

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(abstractness_v1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( v1_vectsp_1(A)
       => A = g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) ) ) ),
    file(vectsp_1,v1_vectsp_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(cc12_monoid_0,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_vectsp_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(monoid_0,cc12_monoid_0),
    []).

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(cc13_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ~ v3_struct_0(B) ) ) ),
    file(monoid_0,cc13_monoid_0),
    []).

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(cc14_monoid_0,axiom,(
    ! [A] : 
      ( ( v1_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => v1_monoid_0(B) ) ) ),
    file(monoid_0,cc14_monoid_0),
    []).

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(cc16_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v2_group_1(B)
            & v6_vectsp_1(B)
            & v8_vectsp_1(B) ) ) ) ),
    file(monoid_0,cc16_monoid_0),
    []).

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(cc17_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v4_group_1(B) ) ) ) ),
    file(monoid_0,cc17_monoid_0),
    []).

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(cc18_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v7_group_1(B) ) ) ) ),
    file(monoid_0,cc18_monoid_0),
    []).

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(cc19_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v13_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v11_monoid_0(B)
            & v12_monoid_0(B)
            & v13_monoid_0(B) ) ) ) ),
    file(monoid_0,cc19_monoid_0),
    []).

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

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_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_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(cc20_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v16_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v14_monoid_0(B)
            & v15_monoid_0(B)
            & v16_monoid_0(B) ) ) ) ),
    file(monoid_0,cc20_monoid_0),
    []).

fof(cc21_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v17_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
            & v17_monoid_0(B) ) ) ) ),
    file(monoid_0,cc21_monoid_0),
    []).

fof(cc22_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v1_monoid_0(B) ) ) ) ) ),
    file(monoid_0,cc22_monoid_0),
    []).

fof(cc27_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v7_group_1(B) ) ) ) ) ),
    file(monoid_0,cc27_monoid_0),
    []).

fof(cc29_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v4_group_1(B) ) ) ) ) ),
    file(monoid_0,cc29_monoid_0),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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

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(cc33_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v16_monoid_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v14_monoid_0(B)
              & v15_monoid_0(B)
              & v16_monoid_0(B) ) ) ) ) ),
    file(monoid_0,cc33_monoid_0),
    []).

fof(cc36_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => ( ( ~ v3_struct_0(B)
              & v4_group_1(B)
              & v13_monoid_0(B) )
           => ( ~ v3_struct_0(B)
              & v2_group_1(B)
              & v3_group_1(B)
              & v14_monoid_0(B)
              & v15_monoid_0(B)
              & v16_monoid_0(B) ) ) ) ) ),
    file(monoid_0,cc36_monoid_0),
    []).

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

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_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_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

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_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

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(d22_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ! [B] : 
          ( l1_vectsp_1(B)
         => ( m1_monoid_0(B,A)
          <=> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ),
    file(monoid_0,d22_monoid_0),
    []).

fof(d26_monoid_0,axiom,(
    k5_monoid_0 = g1_group_1(k1_numbers,k33_binop_2) ),
    file(monoid_0,d26_monoid_0),
    []).

fof(d29_monoid_0,axiom,(
    k47_binop_2 = u1_group_1(k7_monoid_0) ),
    file(monoid_0,d29_monoid_0),
    []).

fof(d4_monoid_1,axiom,(
    ! [A] : k13_monoid_1(A) = k12_monoid_1(k8_monoid_0,A) ),
    file(monoid_1,d4_monoid_1),
    []).

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_g1_vectsp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( v1_vectsp_1(g1_vectsp_1(A,B,C))
        & l1_vectsp_1(g1_vectsp_1(A,B,C)) ) ) ),
    file(vectsp_1,g1_vectsp_1),
    []).

fof(dt_k11_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k11_monoid_1(A,B))
        & v1_vectsp_1(k11_monoid_1(A,B))
        & v1_vectsp_2(k11_monoid_1(A,B))
        & v1_monoid_0(k11_monoid_1(A,B))
        & l1_vectsp_1(k11_monoid_1(A,B)) ) ) ),
    file(monoid_1,k11_monoid_1),
    []).

fof(dt_k12_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v16_monoid_0(A)
        & v17_monoid_0(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k12_monoid_1(A,B))
        & v4_group_1(k12_monoid_1(A,B))
        & v7_group_1(k12_monoid_1(A,B))
        & v1_vectsp_1(k12_monoid_1(A,B))
        & v1_vectsp_2(k12_monoid_1(A,B))
        & v1_monoid_0(k12_monoid_1(A,B))
        & v16_monoid_0(k12_monoid_1(A,B))
        & v17_monoid_0(k12_monoid_1(A,B))
        & l1_vectsp_1(k12_monoid_1(A,B)) ) ) ),
    file(monoid_1,k12_monoid_1),
    []).

fof(dt_k13_monoid_1,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k13_monoid_1(A))
      & v4_group_1(k13_monoid_1(A))
      & v7_group_1(k13_monoid_1(A))
      & v1_vectsp_1(k13_monoid_1(A))
      & v1_vectsp_2(k13_monoid_1(A))
      & v1_monoid_0(k13_monoid_1(A))
      & v16_monoid_0(k13_monoid_1(A))
      & v17_monoid_0(k13_monoid_1(A))
      & l1_vectsp_1(k13_monoid_1(A)) ) ),
    file(monoid_1,k13_monoid_1),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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

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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

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

fof(dt_k33_binop_2,axiom,
    ( v1_funct_1(k33_binop_2)
    & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ),
    file(binop_2,k33_binop_2),
    []).

fof(dt_k3_binop_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) )
     => m1_subset_1(k3_binop_1(A,B),A) ) ),
    file(binop_1,k3_binop_1),
    []).

fof(dt_k3_gr_cy_1,axiom,
    ( ~ v3_struct_0(k3_gr_cy_1)
    & v1_group_1(k3_gr_cy_1)
    & v3_group_1(k3_gr_cy_1)
    & v4_group_1(k3_gr_cy_1)
    & l1_group_1(k3_gr_cy_1) ),
    file(gr_cy_1,k3_gr_cy_1),
    []).

fof(dt_k47_binop_2,axiom,
    ( v1_funct_1(k47_binop_2)
    & v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & m2_relset_1(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) ),
    file(binop_2,k47_binop_2),
    []).

fof(dt_k5_monoid_0,axiom,
    ( ~ v3_struct_0(k5_monoid_0)
    & v1_group_1(k5_monoid_0)
    & v2_group_1(k5_monoid_0)
    & v4_group_1(k5_monoid_0)
    & v7_group_1(k5_monoid_0)
    & v13_monoid_0(k5_monoid_0)
    & v16_monoid_0(k5_monoid_0)
    & l1_group_1(k5_monoid_0) ),
    file(monoid_0,k5_monoid_0),
    []).

fof(dt_k5_monoid_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => m2_fraenkel(k5_monoid_1(A,B,C),B,A,k1_fraenkel(B,A)) ) ),
    file(monoid_1,k5_monoid_1),
    []).

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_k6_monoid_0,axiom,
    ( ~ v3_struct_0(k6_monoid_0)
    & v1_group_1(k6_monoid_0)
    & v2_group_1(k6_monoid_0)
    & v13_monoid_0(k6_monoid_0)
    & m2_monoid_0(k6_monoid_0,k5_monoid_0) ),
    file(monoid_0,k6_monoid_0),
    []).

fof(dt_k7_monoid_0,axiom,
    ( ~ v3_struct_0(k7_monoid_0)
    & v1_group_1(k7_monoid_0)
    & v2_group_1(k7_monoid_0)
    & v17_monoid_0(k7_monoid_0)
    & m5_monoid_0(k7_monoid_0,k5_monoid_0,k6_monoid_0) ),
    file(monoid_0,k7_monoid_0),
    []).

fof(dt_k8_monoid_0,axiom,
    ( ~ v3_struct_0(k8_monoid_0)
    & v1_vectsp_1(k8_monoid_0)
    & v1_vectsp_2(k8_monoid_0)
    & m1_monoid_0(k8_monoid_0,k7_monoid_0) ),
    file(monoid_0,k8_monoid_0),
    []).

fof(dt_k8_monoid_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k8_monoid_1(A,B,C,D,E))
        & v1_funct_2(k8_monoid_1(A,B,C,D,E),k2_zfmisc_1(k1_fraenkel(E,A),k1_fraenkel(E,B)),k1_fraenkel(E,C))
        & m2_relset_1(k8_monoid_1(A,B,C,D,E),k2_zfmisc_1(k1_fraenkel(E,A),k1_fraenkel(E,B)),k1_fraenkel(E,C)) ) ) ),
    file(monoid_1,k8_monoid_1),
    []).

fof(dt_k9_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => l1_group_1(k9_monoid_1(A,B)) ) ),
    file(monoid_1,k9_monoid_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_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ! [B] : 
          ( m1_monoid_0(B,A)
         => l1_vectsp_1(B) ) ) ),
    file(monoid_0,m1_monoid_0),
    []).

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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

fof(dt_m2_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ! [B] : 
          ( m2_monoid_0(B,A)
         => l1_group_1(B) ) ) ),
    file(monoid_0,m2_monoid_0),
    []).

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_m5_monoid_0,axiom,(
    ! [A,B] : 
      ( ( l1_group_1(A)
        & m2_monoid_0(B,A) )
     => ! [C] : 
          ( m5_monoid_0(C,A,B)
         => m2_monoid_0(C,A) ) ) ),
    file(monoid_0,m5_monoid_0),
    []).

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(dt_u1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ),
    file(vectsp_1,u1_vectsp_1),
    []).

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_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(existence_m1_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ? [B] : m1_monoid_0(B,A) ) ),
    file(monoid_0,m1_monoid_0),
    []).

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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

fof(existence_m2_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ? [B] : m2_monoid_0(B,A) ) ),
    file(monoid_0,m2_monoid_0),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m5_monoid_0,axiom,(
    ! [A,B] : 
      ( ( l1_group_1(A)
        & m2_monoid_0(B,A) )
     => ? [C] : m5_monoid_0(C,A,B) ) ),
    file(monoid_0,m5_monoid_0),
    []).

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(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(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    []).

fof(fc1_monoid_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(g1_vectsp_1(A,B,C))
        & v1_vectsp_1(g1_vectsp_1(A,B,C)) ) ) ),
    file(monoid_0,fc1_monoid_0),
    []).

fof(fc1_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ~ v3_struct_0(k9_monoid_1(A,B)) ) ),
    file(monoid_1,fc1_monoid_1),
    []).

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

fof(fc1_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_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc2_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k9_monoid_1(A,B))
        & v1_monoid_0(k9_monoid_1(A,B)) ) ) ),
    file(monoid_1,fc2_monoid_1),
    []).

fof(fc3_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

fof(fc4_ordinal2,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B)) ) ) ),
    file(ordinal2,fc4_ordinal2),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

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(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    []).

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(free_g1_vectsp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ! [D,E,F] : 
          ( g1_vectsp_1(A,B,C) = g1_vectsp_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(vectsp_1,g1_vectsp_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_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

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_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_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(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_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

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

fof(rc4_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(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

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

fof(rc5_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ? [B] : 
          ( m1_monoid_0(B,A)
          & v1_vectsp_1(B) ) ) ),
    file(monoid_0,rc5_monoid_0),
    []).

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(rc6_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_group_1(A) )
     => ? [B] : 
          ( m1_monoid_0(B,A)
          & ~ v3_struct_0(B)
          & v2_group_1(B)
          & v1_vectsp_1(B)
          & v6_vectsp_1(B)
          & v8_vectsp_1(B)
          & v1_vectsp_2(B) ) ) ),
    file(monoid_0,rc6_monoid_0),
    []).

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(rc7_monoid_0,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ? [B] : 
          ( m2_monoid_0(B,A)
          & v1_group_1(B) ) ) ),
    file(monoid_0,rc7_monoid_0),
    []).

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(rc8_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ? [B] : 
          ( m2_monoid_0(B,A)
          & ~ v3_struct_0(B)
          & v1_group_1(B) ) ) ),
    file(monoid_0,rc8_monoid_0),
    []).

fof(redefinition_k11_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_group_1(A) )
     => k11_monoid_1(A,B) = k9_monoid_1(A,B) ) ),
    file(monoid_1,k11_monoid_1),
    []).

fof(redefinition_k12_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v16_monoid_0(A)
        & v17_monoid_0(A)
        & l1_group_1(A) )
     => k12_monoid_1(A,B) = k9_monoid_1(A,B) ) ),
    file(monoid_1,k12_monoid_1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k5_monoid_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k5_monoid_1(A,B,C) = k2_funcop_1(B,C) ) ),
    file(monoid_1,k5_monoid_1),
    []).

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

fof(redefinition_k6_monoid_0,axiom,(
    k6_monoid_0 = k3_gr_cy_1 ),
    file(monoid_0,k6_monoid_0),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_m5_monoid_0,axiom,(
    ! [A,B] : 
      ( ( l1_group_1(A)
        & m2_monoid_0(B,A) )
     => ! [C] : 
          ( m5_monoid_0(C,A,B)
        <=> m2_monoid_0(C,B) ) ) ),
    file(monoid_0,m5_monoid_0),
    []).

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

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(t18_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ( u1_struct_0(k9_monoid_1(B,A)) = k1_fraenkel(A,u1_struct_0(B))
        & u1_group_1(k9_monoid_1(B,A)) = k8_monoid_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_group_1(B),A) ) ) ),
    file(monoid_1,t18_monoid_1),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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

fof(t23_monoid_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v2_group_1(B)
        & l1_group_1(B) )
     => u1_vectsp_1(k11_monoid_1(B,A)) = k5_monoid_1(u1_struct_0(B),A,k3_binop_1(u1_struct_0(B),u1_group_1(B))) ) ),
    file(monoid_1,t23_monoid_1),
    []).

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(t44_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & m2_monoid_0(A,k5_monoid_0) )
     => k3_binop_1(u1_struct_0(A),u1_group_1(A)) = 0 ) ),
    file(monoid_0,t44_monoid_0),
    []).

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_monoid_0,axiom,(
    k8_monoid_0 = g1_vectsp_1(k5_numbers,k47_binop_2,0) ),
    file(monoid_0,t52_monoid_0),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

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

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

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