% Mizar problem: t85_monoid_0,monoid_0,2453,27 
fof(t85_monoid_0,conjecture,(
    ! [A] : 
      ( u1_struct_0(k19_monoid_0(A)) = k1_funct_2(A,A)
      & u1_group_1(k19_monoid_0(A)) = k1_realset1(k17_monoid_0(A),k1_funct_2(A,A))
      & u1_vectsp_1(k19_monoid_0(A)) = k6_partfun1(A) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,abstractness_v1_vectsp_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,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,cc19_membered,cc1_finseq_1,cc1_funct_1,cc1_funct_2,cc1_membered,cc1_monoid_0,cc1_partfun1,cc1_relset_1,cc20_membered,cc22_monoid_0,cc29_monoid_0,cc2_funct_1,cc2_funct_2,cc2_membered,cc3_funct_2,cc3_int_1,cc3_membered,cc3_vectsp_1,cc4_funct_2,cc4_int_1,cc4_membered,cc4_vectsp_1,cc5_funct_2,cc6_funct_2,d22_monoid_0,d39_monoid_0,d3_realset1,d40_monoid_0,dt_g1_group_1,dt_g1_vectsp_1,dt_k15_monoid_0,dt_k17_monoid_0,dt_k18_monoid_0,dt_k19_monoid_0,dt_k1_funct_2,dt_k1_realset1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_binop_1,dt_k4_partfun1,dt_k6_partfun1,dt_k6_relat_1,dt_k7_relat_1,dt_l1_group_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_m1_monoid_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_monoid_0,dt_m2_relset_1,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_monoid_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_monoid_0,existence_m2_relset_1,fc1_funct_2,fc1_group_1,fc1_monoid_0,fc1_partfun1,fc1_realset1,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_funct_1,fc2_funct_2,fc2_partfun1,fc2_realset1,fc4_funct_1,fc4_subset_1,fc6_membered,free_g1_group_1,free_g1_vectsp_1,rc1_finseq_1,rc1_funct_1,rc1_funct_2,rc1_group_1,rc1_membered,rc1_monoid_0,rc1_partfun1,rc1_subset_1,rc2_funct_1,rc2_funct_2,rc2_group_1,rc2_int_1,rc2_partfun1,rc2_subset_1,rc2_vectsp_1,rc3_finseq_1,rc3_funct_1,rc3_partfun1,rc3_struct_0,rc3_vectsp_1,rc4_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_k6_partfun1,redefinition_m2_relset_1,reflexivity_r1_tarski,t19_monoid_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t83_monoid_0,t84_monoid_0,t8_boole]),
    [file(monoid_0,t85_monoid_0)]).

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

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

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

fof(cc1_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(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(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_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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

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

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

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

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

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_funct_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( ( v1_funct_1(B)
          & v1_partfun1(B,A,A)
          & v1_relat_2(B)
          & v1_funct_2(B,A,A) )
       => ( v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,A,A)
          & v2_funct_2(B,A,A)
          & v3_funct_2(B,A,A) ) ) ) ),
    file(funct_2,cc4_funct_2),
    []).

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

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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(d39_monoid_0,axiom,(
    ! [A] : k17_monoid_0(A) = u1_group_1(k15_monoid_0(A)) ),
    file(monoid_0,d39_monoid_0),
    []).

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

fof(d40_monoid_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v1_group_1(B)
        & v2_group_1(B)
        & m2_monoid_0(B,k15_monoid_0(A)) )
     => ( B = k18_monoid_0(A)
      <=> u1_struct_0(B) = k1_funct_2(A,A) ) ) ),
    file(monoid_0,d40_monoid_0),
    []).

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_k15_monoid_0,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k15_monoid_0(A))
      & v1_group_1(k15_monoid_0(A))
      & v2_group_1(k15_monoid_0(A))
      & v4_group_1(k15_monoid_0(A))
      & v1_monoid_0(k15_monoid_0(A))
      & l1_group_1(k15_monoid_0(A)) ) ),
    file(monoid_0,k15_monoid_0),
    []).

fof(dt_k17_monoid_0,axiom,(
    ! [A] : 
      ( v1_funct_1(k17_monoid_0(A))
      & v1_funct_2(k17_monoid_0(A),k2_zfmisc_1(k4_partfun1(A,A),k4_partfun1(A,A)),k4_partfun1(A,A))
      & m2_relset_1(k17_monoid_0(A),k2_zfmisc_1(k4_partfun1(A,A),k4_partfun1(A,A)),k4_partfun1(A,A)) ) ),
    file(monoid_0,k17_monoid_0),
    []).

fof(dt_k18_monoid_0,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k18_monoid_0(A))
      & v1_group_1(k18_monoid_0(A))
      & v2_group_1(k18_monoid_0(A))
      & m2_monoid_0(k18_monoid_0(A),k15_monoid_0(A)) ) ),
    file(monoid_0,k18_monoid_0),
    []).

fof(dt_k19_monoid_0,axiom,(
    ! [A] : 
      ( v1_vectsp_1(k19_monoid_0(A))
      & v1_vectsp_2(k19_monoid_0(A))
      & m1_monoid_0(k19_monoid_0(A),k18_monoid_0(A)) ) ),
    file(monoid_0,k19_monoid_0),
    []).

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

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

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

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_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

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

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

fof(dt_l1_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_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_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_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_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_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(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

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_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_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    []).

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

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

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

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

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

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

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

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

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

fof(fc4_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(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(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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_group_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & v1_group_1(A) ) ),
    file(group_1,rc1_group_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_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

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_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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

fof(rc2_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & v1_vectsp_1(A) ) ),
    file(vectsp_1,rc2_vectsp_1),
    []).

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

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

fof(rc3_partfun1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    []).

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

fof(rc3_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v1_vectsp_1(A) ) ),
    file(vectsp_1,rc3_vectsp_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_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_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(t19_monoid_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v1_vectsp_2(A)
       => u1_vectsp_1(A) = k3_binop_1(u1_struct_0(A),u1_group_1(A)) ) ) ),
    file(monoid_0,t19_monoid_0),
    []).

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

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

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

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

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

fof(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(t83_monoid_0,axiom,(
    ! [A] : u1_group_1(k18_monoid_0(A)) = k1_realset1(k17_monoid_0(A),k1_funct_2(A,A)) ),
    file(monoid_0,t83_monoid_0),
    []).

fof(t84_monoid_0,axiom,(
    ! [A] : k3_binop_1(u1_struct_0(k18_monoid_0(A)),u1_group_1(k18_monoid_0(A))) = k6_partfun1(A) ),
    file(monoid_0,t84_monoid_0),
    []).

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