% Mizar problem: t29_pnproc_1,pnproc_1,719,51 
fof(t29_pnproc_1,conjecture,(
    ! [A,B] : 
      ( m1_pnproc_1(B,A)
     => ! [C] : 
          ( m1_pnproc_1(C,A)
         => ! [D] : 
              ( m1_pnproc_1(D,A)
             => ( r2_pnproc_1(A,k4_pnproc_1(A,B,C),D)
               => r1_pnproc_1(A,k5_pnproc_1(A,k5_pnproc_1(A,D,B),C),k5_pnproc_1(A,D,k4_pnproc_1(A,B,C))) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k4_pnproc_1,dt_k4_pnproc_1,dt_k5_pnproc_1,dt_m1_pnproc_1,existence_m1_pnproc_1,rc1_funct_1,redefinition_r1_pnproc_1,reflexivity_r1_pnproc_1,reflexivity_r2_pnproc_1,symmetry_r1_pnproc_1,t23_pnproc_1,t27_pnproc_1,t28_pnproc_1]),
    [file(pnproc_1,t29_pnproc_1)]).

fof(commutativity_k4_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => k4_pnproc_1(A,B,C) = k4_pnproc_1(A,C,B) ) ),
    file(pnproc_1,k4_pnproc_1),
    []).

fof(dt_k4_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => m1_pnproc_1(k4_pnproc_1(A,B,C),A) ) ),
    file(pnproc_1,k4_pnproc_1),
    []).

fof(dt_k5_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => m1_pnproc_1(k5_pnproc_1(A,B,C),A) ) ),
    file(pnproc_1,k5_pnproc_1),
    []).

fof(dt_m1_pnproc_1,axiom,(
    ! [A,B] : 
      ( m1_pnproc_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pnproc_1,m1_pnproc_1),
    []).

fof(existence_m1_pnproc_1,axiom,(
    ! [A] : 
    ? [B] : m1_pnproc_1(B,A) ),
    file(pnproc_1,m1_pnproc_1),
    []).

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

fof(redefinition_r1_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => ( r1_pnproc_1(A,B,C)
      <=> B = C ) ) ),
    file(pnproc_1,r1_pnproc_1),
    []).

fof(reflexivity_r1_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => r1_pnproc_1(A,B,B) ) ),
    file(pnproc_1,r1_pnproc_1),
    []).

fof(reflexivity_r2_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => r2_pnproc_1(A,B,B) ) ),
    file(pnproc_1,r2_pnproc_1),
    []).

fof(symmetry_r1_pnproc_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => ( r1_pnproc_1(A,B,C)
       => r1_pnproc_1(A,C,B) ) ) ),
    file(pnproc_1,r1_pnproc_1),
    []).

fof(t23_pnproc_1,axiom,(
    ! [A,B] : 
      ( m1_pnproc_1(B,A)
     => ! [C] : 
          ( m1_pnproc_1(C,A)
         => ! [D] : 
              ( m1_pnproc_1(D,A)
             => r1_pnproc_1(A,k4_pnproc_1(A,k4_pnproc_1(A,B,C),D),k4_pnproc_1(A,B,k4_pnproc_1(A,C,D))) ) ) ) ),
    file(pnproc_1,t23_pnproc_1),
    []).

fof(t27_pnproc_1,axiom,(
    ! [A,B] : 
      ( m1_pnproc_1(B,A)
     => ! [C] : 
          ( m1_pnproc_1(C,A)
         => ( r2_pnproc_1(A,B,C)
           => r1_pnproc_1(A,C,k4_pnproc_1(A,k5_pnproc_1(A,C,B),B)) ) ) ) ),
    file(pnproc_1,t27_pnproc_1),
    []).

fof(t28_pnproc_1,axiom,(
    ! [A,B] : 
      ( m1_pnproc_1(B,A)
     => ! [C] : 
          ( m1_pnproc_1(C,A)
         => r1_pnproc_1(A,k5_pnproc_1(A,k4_pnproc_1(A,B,C),B),C) ) ) ),
    file(pnproc_1,t28_pnproc_1),
    []).