The following valid arguments come in pairs. The validity of the first of the pair makes crucial use of the meanings of the blocks language predicates, whereas the second adds one or more premises, making the result a first-order valid argument. For the latter, give a proof that does not make use of Ana Con. For the former, give a proof that uses Ana Con but only where the premises and conclusions of the citation are literals (including ). You may use Taut Con but do not use FO Con in any of the proofs

given: x (Dodec(x) SameCol(x, a)) SameCol(a, c)

prove : x (Dodec(x) SameCol(x, c))

givens: x (Dodec(x) SameCol(x, a)) SameCol(a, c) and x y z ((SameCol(x, y) SameCol(y, z)) SameCol(x, z))

prove: x (Dodec(x) SameCol(x, c))