% Mizar problem: t1_gate_5,gate_5,81,19 
fof(t1_gate_5,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M] : ~ ( ~ ( ~ v1_xboole_0(I)
          & v1_xboole_0(k2_gate_1(A,C)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(A,C))
          & v1_xboole_0(I) )
      & ~ ( ~ v1_xboole_0(J)
          & v1_xboole_0(k10_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0))
          & v1_xboole_0(J) )
      & ~ ( ~ v1_xboole_0(K)
          & v1_xboole_0(k11_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0))
          & v1_xboole_0(K) )
      & ~ ( ~ v1_xboole_0(L)
          & v1_xboole_0(k10_gate_1(k2_gate_1(B,D),k1_xboole_0,K)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(B,D),k1_xboole_0,K))
          & v1_xboole_0(L) )
      & ~ ( ~ v1_xboole_0(M)
          & v1_xboole_0(k11_gate_1(k2_gate_1(B,D),k1_xboole_0,K)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(B,D),k1_xboole_0,K))
          & v1_xboole_0(M) )
      & ~ ( ~ v1_xboole_0(E)
          & v1_xboole_0(I) )
      & ~ ( ~ v1_xboole_0(I)
          & v1_xboole_0(E) )
      & ~ ( ~ v1_xboole_0(F)
          & v1_xboole_0(J) )
      & ~ ( ~ v1_xboole_0(J)
          & v1_xboole_0(F) )
      & ~ ( ~ v1_xboole_0(G)
          & v1_xboole_0(L) )
      & ~ ( ~ v1_xboole_0(L)
          & v1_xboole_0(G) )
      & ~ ( ~ v1_xboole_0(H)
          & v1_xboole_0(M) )
      & ~ ( ~ v1_xboole_0(M)
          & v1_xboole_0(H) )
      & ~ ( ~ ( ~ v1_xboole_0(E)
              & v1_xboole_0(k1_gate_5(A,B,C,D)) )
          & ~ ( ~ v1_xboole_0(k1_gate_5(A,B,C,D))
              & v1_xboole_0(E) )
          & ~ ( ~ v1_xboole_0(F)
              & v1_xboole_0(k2_gate_5(A,B,C,D)) )
          & ~ ( ~ v1_xboole_0(k2_gate_5(A,B,C,D))
              & v1_xboole_0(F) )
          & ~ ( ~ v1_xboole_0(G)
              & v1_xboole_0(k3_gate_5(A,B,C,D)) )
          & ~ ( ~ v1_xboole_0(k3_gate_5(A,B,C,D))
              & v1_xboole_0(G) )
          & ~ ( ~ v1_xboole_0(H)
              & v1_xboole_0(k4_gate_5(A,B,C,D)) )
          & ~ ( ~ v1_xboole_0(k4_gate_5(A,B,C,D))
              & v1_xboole_0(H) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d1_gate_5,d2_gate_5,d37_gate_1,d38_gate_1,d3_gate_5,d4_gate_5,dt_k10_gate_1,dt_k11_gate_1,dt_k1_gate_5,dt_k1_xboole_0,dt_k2_gate_1,dt_k2_gate_5,dt_k35_gate_1,dt_k36_gate_1,dt_k3_gate_5,dt_k4_gate_1,dt_k4_gate_5,fc1_xboole_0,l1_gate_5,l2_gate_5,rc1_xboole_0,rc2_xboole_0,t6_gate_1,t8_gate_1]),
    [file(gate_5,t1_gate_5)]).

fof(d1_gate_5,axiom,(
    ! [A,B,C,D] : k1_gate_5(A,B,C,D) = k2_gate_1(A,C) ),
    file(gate_5,d1_gate_5),
    []).

fof(d2_gate_5,axiom,(
    ! [A,B,C,D] : k2_gate_5(A,B,C,D) = k10_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0) ),
    file(gate_5,d2_gate_5),
    []).

fof(d37_gate_1,axiom,(
    ! [A,B,C,D,E] : k35_gate_1(A,B,C,D,E) = k10_gate_1(C,D,k11_gate_1(A,B,E)) ),
    file(gate_1,d37_gate_1),
    []).

fof(d38_gate_1,axiom,(
    ! [A,B,C,D,E] : k36_gate_1(A,B,C,D,E) = k11_gate_1(C,D,k11_gate_1(A,B,E)) ),
    file(gate_1,d38_gate_1),
    []).

fof(d3_gate_5,axiom,(
    ! [A,B,C,D] : k3_gate_5(A,B,C,D) = k35_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0,k2_gate_1(B,D),k1_xboole_0) ),
    file(gate_5,d3_gate_5),
    []).

fof(d4_gate_5,axiom,(
    ! [A,B,C,D] : k4_gate_5(A,B,C,D) = k36_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0,k2_gate_1(B,D),k1_xboole_0) ),
    file(gate_5,d4_gate_5),
    []).

fof(dt_k10_gate_1,axiom,(
    $true ),
    file(gate_1,k10_gate_1),
    []).

fof(dt_k11_gate_1,axiom,(
    $true ),
    file(gate_1,k11_gate_1),
    []).

fof(dt_k1_gate_5,axiom,(
    $true ),
    file(gate_5,k1_gate_5),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

fof(dt_k2_gate_5,axiom,(
    $true ),
    file(gate_5,k2_gate_5),
    []).

fof(dt_k35_gate_1,axiom,(
    $true ),
    file(gate_1,k35_gate_1),
    []).

fof(dt_k36_gate_1,axiom,(
    $true ),
    file(gate_1,k36_gate_1),
    []).

fof(dt_k3_gate_5,axiom,(
    $true ),
    file(gate_5,k3_gate_5),
    []).

fof(dt_k4_gate_1,axiom,(
    $true ),
    file(gate_1,k4_gate_1),
    []).

fof(dt_k4_gate_5,axiom,(
    $true ),
    file(gate_5,k4_gate_5),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(l1_gate_5,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k10_gate_1(A,B,k1_xboole_0))
          & v1_xboole_0(k4_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & v1_xboole_0(k10_gate_1(A,B,k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(A,k1_xboole_0,B))
          & v1_xboole_0(k4_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & v1_xboole_0(k10_gate_1(A,k1_xboole_0,B)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k1_xboole_0,A,B))
          & v1_xboole_0(k4_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & v1_xboole_0(k10_gate_1(k1_xboole_0,A,B)) ) ) ),
    file(gate_5,l1_gate_5),
    []).

fof(l2_gate_5,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k11_gate_1(A,B,k1_xboole_0))
          & v1_xboole_0(k2_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(A,B))
          & v1_xboole_0(k11_gate_1(A,B,k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(A,k1_xboole_0,B))
          & v1_xboole_0(k2_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(A,B))
          & v1_xboole_0(k11_gate_1(A,k1_xboole_0,B)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k1_xboole_0,A,B))
          & v1_xboole_0(k2_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(A,B))
          & v1_xboole_0(k11_gate_1(k1_xboole_0,A,B)) ) ) ),
    file(gate_5,l2_gate_5),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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),
    []).