% Mizar problem: t1_gate_2,gate_2,51,13 
fof(t1_gate_2,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V] : ~ ( ~ ( ~ v1_xboole_0(A)
          & v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q)))
          & v1_xboole_0(A) )
      & ~ ( ~ v1_xboole_0(B)
          & v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q))
          & v1_xboole_0(B) )
      & ~ ( ~ v1_xboole_0(C)
          & v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q)))
          & v1_xboole_0(C) )
      & ~ ( ~ v1_xboole_0(D)
          & v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q))
          & v1_xboole_0(D) )
      & ~ ( ~ v1_xboole_0(E)
          & v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q)))
          & v1_xboole_0(E) )
      & ~ ( ~ v1_xboole_0(F)
          & v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q))
          & v1_xboole_0(F) )
      & ~ ( ~ v1_xboole_0(G)
          & v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q)))
          & v1_xboole_0(G) )
      & ~ ( ~ v1_xboole_0(H)
          & v1_xboole_0(k8_gate_1(S,R,Q)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(S,R,Q))
          & v1_xboole_0(H) )
      & ~ ( ~ v1_xboole_0(I)
          & v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T)))
          & v1_xboole_0(I) )
      & ~ ( ~ v1_xboole_0(J)
          & v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T))
          & v1_xboole_0(J) )
      & ~ ( ~ v1_xboole_0(K)
          & v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T)))
          & v1_xboole_0(K) )
      & ~ ( ~ v1_xboole_0(L)
          & v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T))
          & v1_xboole_0(L) )
      & ~ ( ~ v1_xboole_0(M)
          & v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T)))
          & v1_xboole_0(M) )
      & ~ ( ~ v1_xboole_0(N)
          & v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T))
          & v1_xboole_0(N) )
      & ~ ( ~ v1_xboole_0(O)
          & v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T))) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T)))
          & v1_xboole_0(O) )
      & ~ ( ~ v1_xboole_0(P)
          & v1_xboole_0(k8_gate_1(V,U,T)) )
      & ~ ( ~ v1_xboole_0(k8_gate_1(V,U,T))
          & v1_xboole_0(P) )
      & ~ ( ~ v1_xboole_0(T)
          & v1_xboole_0(k1_gate_1(Q)) )
      & ~ ( ~ v1_xboole_0(k1_gate_1(Q))
          & v1_xboole_0(T) )
      & ~ ( ~ v1_xboole_0(U)
          & v1_xboole_0(k4_gate_1(Q,R)) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(Q,R))
          & v1_xboole_0(U) )
      & ~ ( ~ v1_xboole_0(V)
          & v1_xboole_0(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S)))) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S))))
          & v1_xboole_0(V) )
      & ~ ( ~ ( ~ v1_xboole_0(J)
              & v1_xboole_0(A) )
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(J) )
          & ~ ( ~ v1_xboole_0(K)
              & v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(B)
              & v1_xboole_0(K) )
          & ~ ( ~ v1_xboole_0(L)
              & v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & v1_xboole_0(L) )
          & ~ ( ~ v1_xboole_0(M)
              & v1_xboole_0(D) )
          & ~ ( ~ v1_xboole_0(D)
              & v1_xboole_0(M) )
          & ~ ( ~ v1_xboole_0(N)
              & v1_xboole_0(E) )
          & ~ ( ~ v1_xboole_0(E)
              & v1_xboole_0(N) )
          & ~ ( ~ v1_xboole_0(O)
              & v1_xboole_0(F) )
          & ~ ( ~ v1_xboole_0(F)
              & v1_xboole_0(O) )
          & ~ ( ~ v1_xboole_0(P)
              & v1_xboole_0(G) )
          & ~ ( ~ v1_xboole_0(G)
              & v1_xboole_0(P) )
          & ~ ( ~ v1_xboole_0(I)
              & v1_xboole_0(H) )
          & ~ ( ~ v1_xboole_0(H)
              & v1_xboole_0(I) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_gate_1,dt_k1_xboole_0,dt_k2_gate_1,dt_k3_gate_1,dt_k4_gate_1,dt_k8_gate_1,t16_gate_1,t4_gate_1,t6_boole,t6_gate_1,t7_boole,t7_gate_1,t8_boole,t8_gate_1]),
    [file(gate_2,t1_gate_2)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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

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_k3_gate_1,axiom,(
    $true ),
    file(gate_1,k3_gate_1),
    []).

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

fof(dt_k8_gate_1,axiom,(
    $true ),
    file(gate_1,k8_gate_1),
    []).

fof(t16_gate_1,axiom,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(k8_gate_1(A,B,C))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) ) ) ),
    file(gate_1,t16_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_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

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_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

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),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

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),
    []).