There are three basal aspects of logic:
The Law of Identity
The Law of Non-contradiction
The Law of excluded Middle
If a solipsist were to acknowledge these as real apart from themselves, they would no longer be solipsists. Just look at Identity. If a solipsist were to acknowledge any other entity's identity as true apart from their imagination then... solipsism logically defeated, period.
And, amazingly Adam, the denials will still come. The logic you are using is sound, and the reasoning of a solid foundation. But, the denials will deafen themselves from the weight of their own noise just to remain in denial.
I might suggest the following:
There are several innate principles in the human mind that we do not derive from our senses.
IÃ¢â‚¬â„¢m only going to talk about the principle of Ã¢â‚¬Å“Sufficient ReasonÃ¢â‚¬Â, because, this principle alone is enough to defeat solipsism, and anyone who attempts to defend it. In this principle itÃ¢â‚¬â„¢s stated that Ã¢â‚¬Å“Nothing is without a reasonÃ¢â‚¬Â; or meaning, everything has a reason or cause. This is the grounds of ALL true propositions and it is known to be true analytically. And hereÃ¢â‚¬â„¢s the thing: You cannot deny it without using it. That is, you must have a sufficient reason for even denying the principle of sufficient reason, in which case you affirm it in the very process of denying it.
In other words, the solipsist has to use Ã¢â‚¬Å“Sufficient ReasonÃ¢â‚¬Â to deny the Ã¢â‚¬Å“Sufficient ReasonÃ¢â‚¬Â for reality or for the Ã¢â‚¬Å“Sufficient ReasonÃ¢â‚¬Â that you and I and everyone else actually exists.
I like the following quote:
Ã¢â‚¬Å“Is it not an astonishing set of coincidencesÃ¢â‚¬â€astonishing, that is to anyone who doubts an external worldÃ¢â‚¬â€that everybody sees essentially the same phaneron? We walk the same streets of the same cities. We find the same buildings at the same locations. Two people can see the same spiral galaxy through a telescope. Not only that, they see the same spiral structure. The hypothesis that there is an external world, not dependent on human minds, made of something, is so obviously useful and so strongly confirmed by experience down through the ages that we can say without exaggerating that it is better confirmed than any other empirical hypothesis. So useful is the posit that it is almost impossible for anyone except a madman or a professional metaphysician to comprehend a reason for doubting it.Ã¢â‚¬Â - Martin Gardner
But, remember, the liar will still lie. The denier will still deny, and the time waster will continue to waste time. Ã¢â‚¬Å“Oh what a tangled web we weaveÃ¢â‚¬Â.