% Mizar problem: t8_dtconstr,dtconstr,269,37 
fof(t8_dtconstr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => r1_xboole_0(k5_lang1(A),k6_lang1(A)) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,d2_lang1,d3_lang1,dt_k1_xboole_0,dt_k5_lang1,dt_k6_lang1,dt_l1_lang1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_lang1,existence_l1_struct_0,existence_m1_subset_1,fc1_struct_0,fc2_finseq_1,fraenkel_a_1_0_dtconstr,fraenkel_a_1_0_lang1,fraenkel_a_1_1_dtconstr,fraenkel_a_1_1_lang1,rc1_finseq_1,rc3_finseq_1,rc3_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,symmetry_r1_xboole_0,t1_subset,t2_subset,t2_tarski,t3_xboole_0,t6_boole,t7_boole,t8_boole]),
    [file(dtconstr,t8_dtconstr)]).

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(d2_lang1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => k5_lang1(A) = a_1_0_lang1(A) ) ),
    file(lang1,d2_lang1),
    []).

fof(d3_lang1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => k6_lang1(A) = a_1_1_lang1(A) ) ),
    file(lang1,d3_lang1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k5_lang1,axiom,(
    $true ),
    file(lang1,k5_lang1),
    []).

fof(dt_k6_lang1,axiom,(
    $true ),
    file(lang1,k6_lang1),
    []).

fof(dt_l1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => l1_struct_0(A) ) ),
    file(lang1,l1_lang1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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

fof(existence_l1_lang1,axiom,(
    ? [A] : l1_lang1(A) ),
    file(lang1,l1_lang1),
    []).

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

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

fof(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(fraenkel_a_1_0_dtconstr,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_lang1(B) )
     => ( r2_hidden(A,a_1_0_dtconstr(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ! [D] : 
                ( ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & v1_finseq_1(D) )
               => ~ r1_lang1(B,C,D) ) ) ) ) ),
    file(dtconstr,a_1_0_dtconstr),
    []).

fof(fraenkel_a_1_0_lang1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_lang1(B) )
     => ( r2_hidden(A,a_1_0_lang1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ! [D] : 
                ( ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & v1_finseq_1(D) )
               => ~ r1_lang1(B,C,D) ) ) ) ) ),
    file(lang1,a_1_0_lang1),
    []).

fof(fraenkel_a_1_1_dtconstr,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_lang1(B) )
     => ( r2_hidden(A,a_1_1_dtconstr(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ? [D] : 
                ( v1_relat_1(D)
                & v1_funct_1(D)
                & v1_finseq_1(D)
                & r1_lang1(B,C,D) ) ) ) ) ),
    file(dtconstr,a_1_1_dtconstr),
    []).

fof(fraenkel_a_1_1_lang1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_lang1(B) )
     => ( r2_hidden(A,a_1_1_lang1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ? [D] : 
                ( v1_relat_1(D)
                & v1_funct_1(D)
                & v1_finseq_1(D)
                & r1_lang1(B,C,D) ) ) ) ) ),
    file(lang1,a_1_1_lang1),
    []).

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(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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_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(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_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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

fof(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),
    []).