% Mizar problem: t27_trees_1,trees_1,275,27 
fof(t27_trees_1,conjecture,(
    ! [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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ~ ( ~ ( r2_xboole_0(A,B)
                        & r2_xboole_0(B,C) )
                    & ~ ( r2_xboole_0(A,B)
                        & r1_tarski(B,C) )
                    & ~ ( r1_tarski(A,B)
                        & r2_xboole_0(B,C) ) )
               => r2_xboole_0(A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc2_finset_1,reflexivity_r1_tarski,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,rc1_finseq_1,cc1_finseq_1,t3_subset,t56_xboole_1,t58_xboole_1,t59_xboole_1]),
    [file(trees_1,t27_trees_1)]).

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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

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

fof(irreflexivity_r2_xboole_0,axiom,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(antisymmetry_r2_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    []).

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

fof(t56_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r2_xboole_0(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,t56_xboole_1),
    []).

fof(t58_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r2_xboole_0(A,B)
        & r1_tarski(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,t58_xboole_1),
    []).

fof(t59_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,t59_xboole_1),
    []).