% Mizar problem: t1_gate_1,gate_1,45,36 
fof(t1_gate_1, conjecture,  (k1_gate_1(k1_tarski(k1_xboole_0))=k1_xboole_0 & k1_gate_1(k1_xboole_0)=k1_tarski(k1_xboole_0)) ).
fof(dt_k1_gate_1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, 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(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(d1_gate_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  => k1_gate_1(A)=k1_xboole_0)  &  (v1_xboole_0(A) => k1_gate_1(A)=k1_tarski(k1_xboole_0)) ) ) ).
