>(1R)-=A /Symbols allowed. > is highest priority and groups right. pred, func, const /Parameter categories allowed. (Could allow sent too?) mp /First rule is mp (modus ponens). P /It says that from P P>Q /and P->Q :Q /you can infer Q. ti /Everything else in the file is an axiom. The next :gen(p>(q>p)) /three axioms are tautologies from which all other id /tautologies can be derived by modus ponens. They :gen((p>q>r)>(p>q)>(p>r)) /are not really needed since I have also included con /the axiom... :gen((-p>-q)>(-p>q)>p) taut /Tautology. This can be used to justify any gene- :gen(taut) /ralization of a tautology (e.g. Ax(P(x)->P(x))). ui /Universal instantiation. "p[x|a]" means p with :gen(Axp>p[x|a]) /all free x's replaced with some term a. ud :gen(Ax(P>Q)>(AxP>AxQ)) vg :gen(P[x*]>AxP) /P[x*] means x must not occur free in P. ref :gen(x=x) sub :gen(x=y>P>P[x?y,A]) /P[x?y,A] means P, perhaps with SOME free x's replaced by y. Also P must be atomic.