% Mizar problem: t2_gate_5,gate_5,224,19 
fof(t2_gate_5,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] : ~ ( ~ ( ~ v1_xboole_0(M)
          & v1_xboole_0(k2_gate_1(A,D)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(A,D))
          & v1_xboole_0(M) )
      & ~ ( ~ v1_xboole_0(N)
          & v1_xboole_0(k10_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0))
          & v1_xboole_0(N) )
      & ~ ( ~ v1_xboole_0(P)
          & v1_xboole_0(k11_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0))
          & v1_xboole_0(P) )
      & ~ ( ~ v1_xboole_0(O)
          & v1_xboole_0(k10_gate_1(k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0))
          & v1_xboole_0(O) )
      & ~ ( ~ v1_xboole_0(Q)
          & v1_xboole_0(k11_gate_1(k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0))
          & v1_xboole_0(Q) )
      & ~ ( ~ v1_xboole_0(R)
          & v1_xboole_0(k10_gate_1(O,k2_gate_1(A,F),P)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(O,k2_gate_1(A,F),P))
          & v1_xboole_0(R) )
      & ~ ( ~ v1_xboole_0(T)
          & v1_xboole_0(k11_gate_1(O,k2_gate_1(A,F),P)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(O,k2_gate_1(A,F),P))
          & v1_xboole_0(T) )
      & ~ ( ~ v1_xboole_0(S)
          & v1_xboole_0(k10_gate_1(k2_gate_1(C,E),k2_gate_1(B,F),Q)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(C,E),k2_gate_1(B,F),Q))
          & v1_xboole_0(S) )
      & ~ ( ~ v1_xboole_0(U)
          & v1_xboole_0(k11_gate_1(k2_gate_1(C,E),k2_gate_1(B,F),Q)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(C,E),k2_gate_1(B,F),Q))
          & v1_xboole_0(U) )
      & ~ ( ~ v1_xboole_0(V)
          & v1_xboole_0(k10_gate_1(S,k1_xboole_0,T)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(S,k1_xboole_0,T))
          & v1_xboole_0(V) )
      & ~ ( ~ v1_xboole_0(X)
          & v1_xboole_0(k11_gate_1(S,k1_xboole_0,T)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(S,k1_xboole_0,T))
          & v1_xboole_0(X) )
      & ~ ( ~ v1_xboole_0(W)
          & v1_xboole_0(k10_gate_1(k2_gate_1(C,F),X,U)) )
      & ~ ( ~ v1_xboole_0(k10_gate_1(k2_gate_1(C,F),X,U))
          & v1_xboole_0(W) )
      & ~ ( ~ v1_xboole_0(Y)
          & v1_xboole_0(k11_gate_1(k2_gate_1(C,F),X,U)) )
      & ~ ( ~ v1_xboole_0(k11_gate_1(k2_gate_1(C,F),X,U))
          & v1_xboole_0(Y) )
      & ~ ( ~ v1_xboole_0(G)
          & v1_xboole_0(M) )
      & ~ ( ~ v1_xboole_0(M)
          & v1_xboole_0(G) )
      & ~ ( ~ v1_xboole_0(H)
          & v1_xboole_0(N) )
      & ~ ( ~ v1_xboole_0(N)
          & v1_xboole_0(H) )
      & ~ ( ~ v1_xboole_0(I)
          & v1_xboole_0(R) )
      & ~ ( ~ v1_xboole_0(R)
          & v1_xboole_0(I) )
      & ~ ( ~ v1_xboole_0(J)
          & v1_xboole_0(V) )
      & ~ ( ~ v1_xboole_0(V)
          & v1_xboole_0(J) )
      & ~ ( ~ v1_xboole_0(K)
          & v1_xboole_0(W) )
      & ~ ( ~ v1_xboole_0(W)
          & v1_xboole_0(K) )
      & ~ ( ~ v1_xboole_0(L)
          & v1_xboole_0(Y) )
      & ~ ( ~ v1_xboole_0(Y)
          & v1_xboole_0(L) )
      & ~ ( ~ ( ~ v1_xboole_0(G)
              & v1_xboole_0(k5_gate_5(A,B,C,D,E)) )
          & ~ ( ~ v1_xboole_0(k5_gate_5(A,B,C,D,E))
              & v1_xboole_0(G) )
          & ~ ( ~ v1_xboole_0(H)
              & v1_xboole_0(k6_gate_5(A,B,C,D,E)) )
          & ~ ( ~ v1_xboole_0(k6_gate_5(A,B,C,D,E))
              & v1_xboole_0(H) )
          & ~ ( ~ v1_xboole_0(I)
              & v1_xboole_0(k10_gate_5(A,B,C,D,E,F)) )
          & ~ ( ~ v1_xboole_0(k10_gate_5(A,B,C,D,E,F))
              & v1_xboole_0(I) )
          & ~ ( ~ v1_xboole_0(J)
              & v1_xboole_0(k11_gate_5(A,B,C,D,E,F)) )
          & ~ ( ~ v1_xboole_0(k11_gate_5(A,B,C,D,E,F))
              & v1_xboole_0(J) )
          & ~ ( ~ v1_xboole_0(K)
              & v1_xboole_0(k12_gate_5(A,B,C,D,E,F)) )
          & ~ ( ~ v1_xboole_0(k12_gate_5(A,B,C,D,E,F))
              & v1_xboole_0(K) )
          & ~ ( ~ v1_xboole_0(L)
              & v1_xboole_0(k13_gate_5(A,B,C,D,E,F)) )
          & ~ ( ~ v1_xboole_0(k13_gate_5(A,B,C,D,E,F))
              & v1_xboole_0(L) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d10_gate_5,d11_gate_5,d12_gate_5,d13_gate_5,d37_gate_1,d38_gate_1,d39_gate_1,d40_gate_1,d5_gate_5,d6_gate_5,d7_gate_5,d8_gate_5,d9_gate_5,dt_k10_gate_1,dt_k10_gate_5,dt_k11_gate_1,dt_k11_gate_5,dt_k12_gate_5,dt_k13_gate_5,dt_k1_xboole_0,dt_k2_gate_1,dt_k35_gate_1,dt_k36_gate_1,dt_k37_gate_1,dt_k38_gate_1,dt_k4_gate_1,dt_k5_gate_5,dt_k6_gate_5,dt_k7_gate_5,dt_k8_gate_5,dt_k9_gate_5,fc1_xboole_0,l1_gate_5,l2_gate_5,rc1_xboole_0,rc2_xboole_0,t18_gate_1,t19_gate_1,t6_gate_1,t8_gate_1]),
    [file(gate_5,t2_gate_5)]).

fof(d10_gate_5,axiom,(
    ! [A,B,C,D,E,F] : k10_gate_5(A,B,C,D,E,F) = k10_gate_1(k7_gate_5(A,B,C,D,E),k2_gate_1(A,F),k1_xboole_0) ),
    file(gate_5,d10_gate_5),
    []).

fof(d11_gate_5,axiom,(
    ! [A,B,C,D,E,F] : k11_gate_5(A,B,C,D,E,F) = k35_gate_1(k7_gate_5(A,B,C,D,E),k2_gate_1(A,F),k8_gate_5(A,B,C,D,E),k2_gate_1(B,F),k1_xboole_0) ),
    file(gate_5,d11_gate_5),
    []).

fof(d12_gate_5,axiom,(
    ! [A,B,C,D,E,F] : k12_gate_5(A,B,C,D,E,F) = k37_gate_1(k7_gate_5(A,B,C,D,E),k2_gate_1(A,F),k8_gate_5(A,B,C,D,E),k2_gate_1(B,F),k9_gate_5(A,B,C,D,E),k2_gate_1(C,F),k1_xboole_0) ),
    file(gate_5,d12_gate_5),
    []).

fof(d13_gate_5,axiom,(
    ! [A,B,C,D,E,F] : k13_gate_5(A,B,C,D,E,F) = k38_gate_1(k7_gate_5(A,B,C,D,E),k2_gate_1(A,F),k8_gate_5(A,B,C,D,E),k2_gate_1(B,F),k9_gate_5(A,B,C,D,E),k2_gate_1(C,F),k1_xboole_0) ),
    file(gate_5,d13_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(d39_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] : k37_gate_1(A,B,C,D,E,F,G) = k10_gate_1(E,F,k36_gate_1(A,B,C,D,G)) ),
    file(gate_1,d39_gate_1),
    []).

fof(d40_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] : k38_gate_1(A,B,C,D,E,F,G) = k11_gate_1(E,F,k36_gate_1(A,B,C,D,G)) ),
    file(gate_1,d40_gate_1),
    []).

fof(d5_gate_5,axiom,(
    ! [A,B,C,D,E] : k5_gate_5(A,B,C,D,E) = k2_gate_1(A,D) ),
    file(gate_5,d5_gate_5),
    []).

fof(d6_gate_5,axiom,(
    ! [A,B,C,D,E] : k6_gate_5(A,B,C,D,E) = k10_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0) ),
    file(gate_5,d6_gate_5),
    []).

fof(d7_gate_5,axiom,(
    ! [A,B,C,D,E] : k7_gate_5(A,B,C,D,E) = k35_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0) ),
    file(gate_5,d7_gate_5),
    []).

fof(d8_gate_5,axiom,(
    ! [A,B,C,D,E] : k8_gate_5(A,B,C,D,E) = k37_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0,k2_gate_1(C,E),k1_xboole_0) ),
    file(gate_5,d8_gate_5),
    []).

fof(d9_gate_5,axiom,(
    ! [A,B,C,D,E] : k9_gate_5(A,B,C,D,E) = k38_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k2_gate_1(C,D),k2_gate_1(B,E),k1_xboole_0,k2_gate_1(C,E),k1_xboole_0) ),
    file(gate_5,d9_gate_5),
    []).

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

fof(dt_k10_gate_5,axiom,(
    $true ),
    file(gate_5,k10_gate_5),
    []).

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

fof(dt_k11_gate_5,axiom,(
    $true ),
    file(gate_5,k11_gate_5),
    []).

fof(dt_k12_gate_5,axiom,(
    $true ),
    file(gate_5,k12_gate_5),
    []).

fof(dt_k13_gate_5,axiom,(
    $true ),
    file(gate_5,k13_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_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_k37_gate_1,axiom,(
    $true ),
    file(gate_1,k37_gate_1),
    []).

fof(dt_k38_gate_1,axiom,(
    $true ),
    file(gate_1,k38_gate_1),
    []).

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

fof(dt_k5_gate_5,axiom,(
    $true ),
    file(gate_5,k5_gate_5),
    []).

fof(dt_k6_gate_5,axiom,(
    $true ),
    file(gate_5,k6_gate_5),
    []).

fof(dt_k7_gate_5,axiom,(
    $true ),
    file(gate_5,k7_gate_5),
    []).

fof(dt_k8_gate_5,axiom,(
    $true ),
    file(gate_5,k8_gate_5),
    []).

fof(dt_k9_gate_5,axiom,(
    $true ),
    file(gate_5,k9_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(t18_gate_1,axiom,(
    ! [A,B,C] : 
      ( ~ ( ~ v1_xboole_0(k10_gate_1(A,B,C))
          & ~ ( ( ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
                | ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) ) )
              & v1_xboole_0(C) )
          & ~ ( ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
              & ~ ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ v1_xboole_0(C) ) )
      & ~ ( ( ( ( ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
                | ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) ) )
              & v1_xboole_0(C) )
            | ( ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
              & ~ ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ v1_xboole_0(C) ) )
          & v1_xboole_0(k10_gate_1(A,B,C)) ) ) ),
    file(gate_1,t18_gate_1),
    []).

fof(t19_gate_1,axiom,(
    ! [A,B,C] : 
      ( ~ ( ~ v1_xboole_0(k11_gate_1(A,B,C))
          & ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & ~ v1_xboole_0(A) ) )
      & ~ ( ~ ( ~ ( ~ v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ ( ~ v1_xboole_0(B)
                  & ~ v1_xboole_0(C) )
              & ~ ( ~ v1_xboole_0(C)
                  & ~ v1_xboole_0(A) ) )
          & v1_xboole_0(k11_gate_1(A,B,C)) ) ) ),
    file(gate_1,t19_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),
    []).