% Mizar problem: t1_gate_2,gate_2,52,5 
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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(commutativity_k2_gate_1, axiom,  (! [A, B] : k2_gate_1(A, B)=k2_gate_1(B, A)) ).
fof(commutativity_k3_gate_1, axiom,  (! [A, B] : k3_gate_1(A, B)=k3_gate_1(B, A)) ).
fof(commutativity_k4_gate_1, axiom,  (! [A, B] : k4_gate_1(A, B)=k4_gate_1(B, A)) ).
fof(dt_k1_gate_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_gate_1, axiom, $true).
fof(dt_k3_gate_1, axiom, $true).
fof(dt_k4_gate_1, axiom, $true).
fof(dt_k8_gate_1, axiom, $true).
fof(fc17_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k8_gate_1(A, B, C))) ) ) ).
fof(fc18_gate_1, axiom,  (! [A, B, C] :  (v1_xboole_0(A) => v1_xboole_0(k8_gate_1(A, B, C))) ) ).
fof(fc19_gate_1, axiom,  (! [A, B, C] :  (v1_xboole_0(A) => v1_xboole_0(k8_gate_1(B, A, C))) ) ).
fof(fc1_gate_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v1_xboole_0(k1_gate_1(A))) ) ) ).
fof(fc20_gate_1, axiom,  (! [A, B, C] :  (v1_xboole_0(A) => v1_xboole_0(k8_gate_1(B, C, A))) ) ).
fof(fc2_gate_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => v1_xboole_0(k1_gate_1(A))) ) ).
fof(fc3_gate_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_gate_1(A, B))) ) ) ).
fof(fc4_gate_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_gate_1(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(fc7_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k4_gate_1(A, B))) ) ) ).
fof(fc8_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k4_gate_1(A, B))) ) ).
fof(fc9_gate_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  => v1_xboole_0(k4_gate_1(A, B))) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_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))) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
