% Mizar problem: t63_rfunct_1,rfunct_1,1240,72 
fof(t63_rfunct_1,conjecture,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(k7_relat_1(B,A),C)
            & k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(B,k7_relat_1(C,A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_seq_1,dt_k15_seq_1,dt_k20_seq_1,dt_k3_rfunct_1,dt_k3_seq_1,dt_k4_seq_1,dt_k7_relat_1,fc2_rfunct_1,fc2_seq_1,fc3_seq_1,fc4_funct_1,fc4_seq_1,fc7_seq_1,fc8_seq_1,rc1_funct_1,rc1_seq_1,t40_rfunct_1,t60_rfunct_1,t62_rfunct_1]),
    [file(rfunct_1,t63_rfunct_1)]).

fof(commutativity_k3_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => k3_seq_1(A,B) = k3_seq_1(B,A) ) ),
    file(seq_1,k3_seq_1),
    []).

fof(dt_k15_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k15_seq_1(A))
        & v1_funct_1(k15_seq_1(A)) ) ) ),
    file(seq_1,k15_seq_1),
    []).

fof(dt_k20_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k20_seq_1(A))
        & v1_funct_1(k20_seq_1(A)) ) ) ),
    file(seq_1,k20_seq_1),
    []).

fof(dt_k3_rfunct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k3_rfunct_1(A))
        & v1_funct_1(k3_rfunct_1(A)) ) ) ),
    file(rfunct_1,k3_rfunct_1),
    []).

fof(dt_k3_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k3_seq_1(A,B))
        & v1_funct_1(k3_seq_1(A,B)) ) ) ),
    file(seq_1,k3_seq_1),
    []).

fof(dt_k4_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k4_seq_1(A,B))
        & v1_funct_1(k4_seq_1(A,B)) ) ) ),
    file(seq_1,k4_seq_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(fc2_rfunct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k3_rfunct_1(A))
        & v1_funct_1(k3_rfunct_1(A))
        & v1_seq_1(k3_rfunct_1(A)) ) ) ),
    file(rfunct_1,fc2_rfunct_1),
    []).

fof(fc2_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_seq_1(k7_relat_1(A,B)) ) ) ),
    file(seq_1,fc2_seq_1),
    []).

fof(fc3_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k3_seq_1(A,B))
        & v1_funct_1(k3_seq_1(A,B))
        & v1_seq_1(k3_seq_1(A,B)) ) ) ),
    file(seq_1,fc3_seq_1),
    []).

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_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k4_seq_1(A,B))
        & v1_funct_1(k4_seq_1(A,B))
        & v1_seq_1(k4_seq_1(A,B)) ) ) ),
    file(seq_1,fc4_seq_1),
    []).

fof(fc7_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k15_seq_1(A))
        & v1_funct_1(k15_seq_1(A))
        & v1_seq_1(k15_seq_1(A)) ) ) ),
    file(seq_1,fc7_seq_1),
    []).

fof(fc8_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k20_seq_1(A))
        & v1_funct_1(k20_seq_1(A))
        & v1_seq_1(k20_seq_1(A)) ) ) ),
    file(seq_1,fc8_seq_1),
    []).

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(t40_rfunct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k4_seq_1(A,B) = k3_seq_1(A,k15_seq_1(B)) ) ) ),
    file(rfunct_1,t40_rfunct_1),
    []).

fof(t60_rfunct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(k7_relat_1(B,A),C)
            & k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(B,k7_relat_1(C,A)) ) ) ) ),
    file(rfunct_1,t60_rfunct_1),
    []).

fof(t62_rfunct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( k7_relat_1(k15_seq_1(B),A) = k15_seq_1(k7_relat_1(B,A))
        & k7_relat_1(k3_rfunct_1(B),A) = k3_rfunct_1(k7_relat_1(B,A))
        & k7_relat_1(k20_seq_1(B),A) = k20_seq_1(k7_relat_1(B,A)) ) ) ),
    file(rfunct_1,t62_rfunct_1),
    []).