% Mizar problem: t2_gate_3,gate_3,98,33 
fof(t2_gate_3,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M] : ~ ( ~ ( ~ v1_xboole_0(A)
          & v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I))) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I)))
          & v1_xboole_0(A) )
      & ~ ( ~ v1_xboole_0(B)
          & v1_xboole_0(k2_gate_1(k1_gate_1(J),I)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),I))
          & v1_xboole_0(B) )
      & ~ ( ~ v1_xboole_0(C)
          & v1_xboole_0(k2_gate_1(J,k1_gate_1(I))) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(J,k1_gate_1(I)))
          & v1_xboole_0(C) )
      & ~ ( ~ v1_xboole_0(D)
          & v1_xboole_0(k2_gate_1(J,I)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(J,I))
          & v1_xboole_0(D) )
      & ~ ( ~ v1_xboole_0(E)
          & v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K))) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K)))
          & v1_xboole_0(E) )
      & ~ ( ~ v1_xboole_0(F)
          & v1_xboole_0(k2_gate_1(k1_gate_1(L),K)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),K))
          & v1_xboole_0(F) )
      & ~ ( ~ v1_xboole_0(G)
          & v1_xboole_0(k2_gate_1(L,k1_gate_1(K))) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(L,k1_gate_1(K)))
          & v1_xboole_0(G) )
      & ~ ( ~ v1_xboole_0(H)
          & v1_xboole_0(k2_gate_1(L,K)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(L,K))
          & v1_xboole_0(H) )
      & ~ ( ~ v1_xboole_0(K)
          & v1_xboole_0(k2_gate_1(k1_gate_1(J),M)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),M))
          & v1_xboole_0(K) )
      & ~ ( ~ v1_xboole_0(L)
          & v1_xboole_0(k2_gate_1(I,M)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(I,M))
          & v1_xboole_0(L) )
      & ~ ( ~ ( ~ v1_xboole_0(F)
              & v1_xboole_0(k2_gate_1(A,M)) )
          & ~ ( ~ v1_xboole_0(k2_gate_1(A,M))
              & v1_xboole_0(F) )
          & ~ ( ~ v1_xboole_0(H)
              & v1_xboole_0(k2_gate_1(B,M)) )
          & ~ ( ~ v1_xboole_0(k2_gate_1(B,M))
              & v1_xboole_0(H) )
          & ~ ( ~ v1_xboole_0(G)
              & v1_xboole_0(k2_gate_1(D,M)) )
          & ~ ( ~ v1_xboole_0(k2_gate_1(D,M))
              & v1_xboole_0(G) )
          & ~ ( ~ v1_xboole_0(E)
              & v1_xboole_0(k3_gate_1(k2_gate_1(C,M),k1_gate_1(M))) )
          & ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(C,M),k1_gate_1(M)))
              & v1_xboole_0(E) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k1_gate_1,dt_k2_gate_1,dt_k3_gate_1,t4_gate_1,t6_gate_1,t7_gate_1]),
    [file(gate_3,t2_gate_3)]).

fof(dt_k1_gate_1,axiom,(
    $true ),
    file(gate_1,k1_gate_1),
    []).

fof(dt_k2_gate_1,axiom,(
    $true ),
    file(gate_1,k2_gate_1),
    []).

fof(dt_k3_gate_1,axiom,(
    $true ),
    file(gate_1,k3_gate_1),
    []).

fof(t4_gate_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_gate_1(A))
    <=> v1_xboole_0(A) ) ),
    file(gate_1,t4_gate_1),
    []).

fof(t6_gate_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_gate_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) ) ) ),
    file(gate_1,t6_gate_1),
    []).

fof(t7_gate_1,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & v1_xboole_0(A)
          & v1_xboole_0(B) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B) )
          & v1_xboole_0(k3_gate_1(A,B)) ) ) ),
    file(gate_1,t7_gate_1),
    []).