% Here are some sample intuitionistic formulas to use to test the % propositional theorem prover. Not all are provable. % Thanks to Bob Constable for some of the more interesting ones. % Sample use: % % ?- propositional --o test --o test. % 1 % 2 % 3 % 3 ... % MODULE test. prop 1 (imp a a). prop 2 (imp (or a b) (or b a)). prop 3 (imp (and a b) (and b a)). prop 4 (imp a (imp b a)). prop 5 (imp (imp a (imp b c)) (imp (imp a b) (imp a c))). prop 6 (imp (imp (imp a b) a) (imp (imp a b) b)). prop 7 (imp (imp (imp a b) a) a). prop 8 (imp (and (imp a b) (imp c a)) (imp c b)). prop 9 (imp (or a b) (imp (imp a c) (imp (imp b c) c))). prop 10 (imp (or a b) (imp (imp a c) (imp (imp (and b d) c) (imp d c)))). prop 11 (imp (or (imp a b) (imp a c)) (imp a (or b c))). prop 12 (imp (or a b) (imp (imp a c) (imp (imp b (imp d c)) (imp d c)))). prop 13 (imp (and (and a a) (imp a b)) b). prop 14 (imp a (imp a (imp (imp a b) b))). prop 15 (imp (or c (imp c false)) (imp (and (imp a b) (imp (imp a c) b)) b)). prop 16 (imp (or b (imp b false)) (imp (and (a imp b) (imp (imp a c) b)) b)). prop 17 (imp (or a (imp a false)) (imp (and (a imp b) (imp (imp a c) b)) b)). prop 18 (imp (imp b (imp b false)) (imp (imp (imp b false) false) b)). test :- prop A B, pv B, write A, nl, fail.