NOT logic gate with two inputs
As a theoretical logic diagram this is pure nonsense. Inverter has only one input and connecting 2 outputs together means nothing.

As practical circuit diagram this can be valid. the special 2 input inverters can really be disconnect-able by the disabling signals. In practice we say "they have 3-state outputs". The  3rd state is called "high-Z" and that means "disconnected by internal electronic switch."

The rightmost a and c should not be the same as the leftmost a and c.

But if you really have this as written and 0 means "disabled" for the special inverters, then you have the following truth table:

a b c .....out

0 0 0 .....undefined (=no proper input to the rightmost inverter)

0 0 1......0

0 1 0 .....undefined

0 1 1 .....0

1 0 0......0

1 0 1 .....smoke (=a short circuit)

1 1 0.....0

1 1 1 ....1