% Mizar problem: t104_rfunct_1,rfunct_1,1962,21 
fof(t104_rfunct_1,conjecture,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r3_rfunct_1(C,A)
          & r3_rfunct_1(C,B) )
       => r3_rfunct_1(C,k2_xboole_0(A,B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,d11_rfunct_1,dt_k2_xboole_0,idempotence_k2_xboole_0,rc1_funct_1,rc1_seq_1,t102_rfunct_1,t103_rfunct_1]),
    [file(rfunct_1,t104_rfunct_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(d11_rfunct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] : 
          ( r3_rfunct_1(A,B)
        <=> ( r1_rfunct_1(A,B)
            & r2_rfunct_1(A,B) ) ) ) ),
    file(rfunct_1,d11_rfunct_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(rc1_seq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A) ) ),
    file(seq_1,rc1_seq_1),
    []).

fof(t102_rfunct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r1_rfunct_1(C,A)
          & r1_rfunct_1(C,B) )
       => r1_rfunct_1(C,k2_xboole_0(A,B)) ) ) ),
    file(rfunct_1,t102_rfunct_1),
    []).

fof(t103_rfunct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r2_rfunct_1(C,A)
          & r2_rfunct_1(C,B) )
       => r2_rfunct_1(C,k2_xboole_0(A,B)) ) ) ),
    file(rfunct_1,t103_rfunct_1),
    []).