% Mizar problem: t40_gate_1,gate_1,703,5 
fof(t40_gate_1, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (! [H] :  (! [I] :  (! [J] :  (! [K] :  (! [L] :  (! [M] :  (! [N] :  (! [O] :  (! [P] :  (! [Q] :  (! [R] :  (! [S] :  ~ ( ( ~ ( ( ~ (v1_xboole_0(k11_gate_1(B, F, A)))  & v1_xboole_0(J)) )  &  ( ~ ( ( ~ (v1_xboole_0(k11_gate_1(C, G, J)))  & v1_xboole_0(K)) )  &  ( ~ ( ( ~ (v1_xboole_0(k11_gate_1(D, H, K)))  & v1_xboole_0(L)) )  &  ( ~ ( ( ~ (v1_xboole_0(k11_gate_1(E, I, L)))  & v1_xboole_0(M)) )  &  ( ~ ( ( ~ (v1_xboole_0(N))  & v1_xboole_0(k3_gate_1(B, F))) )  &  ( ~ ( ( ~ (v1_xboole_0(O))  & v1_xboole_0(k3_gate_1(C, G))) )  &  ( ~ ( ( ~ (v1_xboole_0(P))  & v1_xboole_0(k3_gate_1(D, H))) )  &  ( ~ ( ( ~ (v1_xboole_0(Q))  & v1_xboole_0(k3_gate_1(E, I))) )  &  ( ~ ( ( ~ (v1_xboole_0(R))  & v1_xboole_0(k18_gate_1(A, N, O, P, Q))) )  &  ( ~ ( ( ~ (v1_xboole_0(S))  & v1_xboole_0(k3_gate_1(M, R))) )  &  ( ~ ( ( ~ (v1_xboole_0(k3_gate_1(M, R)))  & v1_xboole_0(S)) )  &  ~ ( ( ~ ( ( ~ (v1_xboole_0(M))  & v1_xboole_0(S)) )  &  ~ ( ( ~ (v1_xboole_0(S))  & v1_xboole_0(M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(commutativity_k3_gate_1, axiom,  (! [A, B] : k3_gate_1(A, B)=k3_gate_1(B, A)) ).
fof(d18_gate_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  ( ~ ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  &  ( ~ (v1_xboole_0(E))  &  ~ (k18_gate_1(A, B, C, D, E)=k1_gate_1(k1_xboole_0)) ) ) ) ) ) )  &  ( ~ ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  &  ~ (v1_xboole_0(E)) ) ) ) ) )  => k18_gate_1(A, B, C, D, E)=k1_xboole_0) ) ) ) ) ) ) ).
fof(dt_k11_gate_1, axiom, $true).
fof(dt_k18_gate_1, axiom, $true).
fof(dt_k1_gate_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k3_gate_1, axiom, $true).
fof(fc1_gate_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v1_xboole_0(k1_gate_1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_gate_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => v1_xboole_0(k1_gate_1(A))) ) ).
fof(fc33_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k11_gate_1(A, B, C))) ) ) ).
fof(fc34_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k11_gate_1(A, C, B))) ) ) ).
fof(fc35_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k11_gate_1(C, A, B))) ) ) ).
fof(fc36_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k11_gate_1(A, B, C))) ) ).
fof(fc37_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k11_gate_1(A, C, B))) ) ).
fof(fc38_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k11_gate_1(C, A, B))) ) ).
fof(fc5_gate_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k3_gate_1(A, B))) ) ) ).
fof(fc6_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k3_gate_1(A, B))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
