% Mizar problem: t54_rewrite1,rewrite1,1549,11 
fof(t54_rewrite1,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v4_rewrite1(A) )
     => ! [B,C,D] : 
          ( ( r4_rewrite1(A,B,C)
            & r4_rewrite1(A,B,D) )
         => C = D ) ) ),
    inference(mizar_bg_added,[status(thm)],[d19_rewrite1,d6_rewrite1,d8_rewrite1,t38_rewrite1]),
    [file(rewrite1,t54_rewrite1)]).

fof(d19_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_rewrite1(A)
      <=> ! [B,C] : 
            ( ( r3_rewrite1(A,B)
              & r3_rewrite1(A,C)
              & r2_rewrite1(A,B,C) )
           => B = C ) ) ) ),
    file(rewrite1,d19_rewrite1),
    []).

fof(d6_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r4_rewrite1(A,B,C)
        <=> ( r3_rewrite1(A,C)
            & r1_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d6_rewrite1),
    []).

fof(d8_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r6_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,D,B)
              & r1_rewrite1(A,D,C) ) ) ) ),
    file(rewrite1,d8_rewrite1),
    []).

fof(t38_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( ( r5_rewrite1(A,B,C)
            | r6_rewrite1(A,B,C) )
         => r2_rewrite1(A,B,C) ) ) ),
    file(rewrite1,t38_rewrite1),
    []).