% Mizar problem: t2_gate_4,gate_4,195,23 
fof(t2_gate_4,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1] : ~ ( ~ v1_xboole_0(A)
      & ~ v1_xboole_0(Q)
      & ~ ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1)))
          & v1_xboole_0(H1) )
      & ~ ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1)))
          & v1_xboole_0(I1) )
      & ~ ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1)))
          & v1_xboole_0(J1) )
      & ~ ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1)))
          & v1_xboole_0(K1) )
      & ~ ( ~ v1_xboole_0(L1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1)))
          & v1_xboole_0(L1) )
      & ~ ( ~ v1_xboole_0(M1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1)))
          & v1_xboole_0(M1) )
      & ~ ( ~ v1_xboole_0(N1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1)))
          & v1_xboole_0(N1) )
      & ~ ( ~ v1_xboole_0(O1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1)))
          & v1_xboole_0(O1) )
      & ~ ( ~ v1_xboole_0(P1)
          & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1)))
          & v1_xboole_0(P1) )
      & ~ ( ~ v1_xboole_0(Q1)
          & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1)))
          & v1_xboole_0(Q1) )
      & ~ ( ~ v1_xboole_0(R1)
          & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1)))
          & v1_xboole_0(R1) )
      & ~ ( ~ v1_xboole_0(S1)
          & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1)))
          & v1_xboole_0(S1) )
      & ~ ( ~ v1_xboole_0(T1)
          & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1)))
          & v1_xboole_0(T1) )
      & ~ ( ~ v1_xboole_0(U1)
          & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1)))
          & v1_xboole_0(U1) )
      & ~ ( ~ v1_xboole_0(V1)
          & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1)))
          & v1_xboole_0(V1) )
      & ~ ( ~ v1_xboole_0(W1)
          & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1)))
          & v1_xboole_0(W1) )
      & ~ ( ~ ( ~ v1_xboole_0(G1)
              & v1_xboole_0(k2_gate_1(Q,G1)) )
          & ~ ( ~ v1_xboole_0(k2_gate_1(Q,G1))
              & v1_xboole_0(G1) )
          & ~ ( ~ v1_xboole_0(F1)
              & v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1)))
              & v1_xboole_0(F1) )
          & ~ ( ~ v1_xboole_0(E1)
              & v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1)))
              & v1_xboole_0(E1) )
          & ~ ( ~ v1_xboole_0(D1)
              & v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1)))
              & v1_xboole_0(D1) )
          & ~ ( ~ v1_xboole_0(C1)
              & v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1)))
              & v1_xboole_0(C1) )
          & ~ ( ~ v1_xboole_0(B1)
              & v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1)))
              & v1_xboole_0(B1) )
          & ~ ( ~ v1_xboole_0(A1)
              & v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1)))
              & v1_xboole_0(A1) )
          & ~ ( ~ v1_xboole_0(Z)
              & v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1)))
              & v1_xboole_0(Z) )
          & ~ ( ~ v1_xboole_0(Y)
              & v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1)))
              & v1_xboole_0(Y) )
          & ~ ( ~ v1_xboole_0(X)
              & v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1)))
              & v1_xboole_0(X) )
          & ~ ( ~ v1_xboole_0(W)
              & v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1)))
              & v1_xboole_0(W) )
          & ~ ( ~ v1_xboole_0(V)
              & v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1)))
              & v1_xboole_0(V) )
          & ~ ( ~ v1_xboole_0(U)
              & v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1)))
              & v1_xboole_0(U) )
          & ~ ( ~ v1_xboole_0(T)
              & v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1)))
              & v1_xboole_0(T) )
          & ~ ( ~ v1_xboole_0(S)
              & v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1)))
              & v1_xboole_0(S) )
          & ~ ( ~ v1_xboole_0(R)
              & v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1)))
              & v1_xboole_0(R) )
          & ~ ( ~ v1_xboole_0(X1)
              & v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1)))
              & v1_xboole_0(X1) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_gate_1,dt_k4_gate_1,t6_gate_1,t8_gate_1]),
    [file(gate_4,t2_gate_4)]).

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

fof(dt_k4_gate_1,axiom,(
    $true ),
    file(gate_1,k4_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(t8_gate_1,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
      & ~ ( ( ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
            | ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
          & v1_xboole_0(k4_gate_1(A,B)) ) ) ),
    file(gate_1,t8_gate_1),
    []).