% Mizar problem: t1_gate_5,gate_5,65,5 
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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(commutativity_k2_gate_1, axiom,  (! [A, B] : k2_gate_1(A, B)=k2_gate_1(B, A)) ).
fof(d1_gate_5, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k1_gate_5(A, B, C, D)=k2_gate_1(A, C)) ) ) ) ).
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)) ) ) ) ).
fof(d35_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))) ) ) ) ) ).
fof(d36_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))) ) ) ) ) ).
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)) ) ) ) ).
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)) ) ) ) ).
fof(dt_k10_gate_1, axiom, $true).
fof(dt_k11_gate_1, axiom, $true).
fof(dt_k1_gate_5, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_gate_1, axiom, $true).
fof(dt_k2_gate_5, axiom, $true).
fof(dt_k35_gate_1, axiom, $true).
fof(dt_k36_gate_1, axiom, $true).
fof(dt_k3_gate_5, axiom, $true).
fof(dt_k4_gate_5, axiom, $true).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc25_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) &  (v1_xboole_0(B) & v1_xboole_0(C)) )  => v1_xboole_0(k10_gate_1(A, B, C))) ) ).
fof(fc26_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) &  (v1_xboole_0(B) &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k10_gate_1(A, B, C))) ) ) ).
fof(fc27_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) &  (v1_xboole_0(B) &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k10_gate_1(A, C, B))) ) ) ).
fof(fc28_gate_1, axiom,  (! [A, B, C] :  ( (v1_xboole_0(A) &  (v1_xboole_0(B) &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k10_gate_1(C, A, B))) ) ) ).
fof(fc29_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & v1_xboole_0(C)) )  => v1_xboole_0(k10_gate_1(A, B, C))) ) ).
fof(fc30_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & v1_xboole_0(C)) )  => v1_xboole_0(k10_gate_1(A, C, B))) ) ).
fof(fc31_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & v1_xboole_0(C)) )  => v1_xboole_0(k10_gate_1(C, A, B))) ) ).
fof(fc32_gate_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k10_gate_1(A, B, C))) ) ) ).
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(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(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
