% Mizar problem: t3_gate_2,gate_2,165,5 
fof(t3_gate_2, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( ~ ( (v1_xboole_0(k2_gate_1(A, B)) & v1_xboole_0(k3_gate_1(k1_gate_1(A), k1_gate_1(B)))) )  &  ( ( ~ (v1_xboole_0(k3_gate_1(k1_gate_1(A), k1_gate_1(B))))  => v1_xboole_0(k2_gate_1(A, B)))  &  ( ~ ( ( ~ (v1_xboole_0(k3_gate_1(A, B)))  &  ( ~ (v1_xboole_0(k3_gate_1(C, B)))  & v1_xboole_0(k3_gate_1(k2_gate_1(A, C), B))) ) )  &  ( ( ~ (v1_xboole_0(k3_gate_1(k2_gate_1(A, C), B)))  =>  ( ~ (v1_xboole_0(k3_gate_1(A, B)))  &  ~ (v1_xboole_0(k3_gate_1(C, B))) ) )  &  ( ~ ( ( ~ (v1_xboole_0(k3_gate_1(A, B)))  &  ( ~ (v1_xboole_0(k3_gate_1(C, B)))  &  ( ~ (v1_xboole_0(k3_gate_1(D, B)))  & v1_xboole_0(k3_gate_1(k8_gate_1(A, C, D), B))) ) ) )  &  ( ( ~ (v1_xboole_0(k3_gate_1(k8_gate_1(A, C, D), B)))  =>  ( ~ (v1_xboole_0(k3_gate_1(A, B)))  &  ( ~ (v1_xboole_0(k3_gate_1(C, B)))  &  ~ (v1_xboole_0(k3_gate_1(D, B))) ) ) )  &  ~ ( ( ~ (v1_xboole_0(k3_gate_1(A, B)))  &  ( ~ ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(C)) )  &  ( ~ ( ( ~ (v1_xboole_0(C))  & v1_xboole_0(A)) )  & v1_xboole_0(k3_gate_1(C, B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(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_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(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(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)) ) ) ) ) ).
