 If the contraposition rule and uniform substitution are assumed and implication is transitive, the combination of Conjunctive Simplification and Aristotle’s Theses results in negation inconsistency, i.e., there are formulas A such that A and its negation ~A are both theorems, see, for example, Woods 1968 and Thompson 1991. Non-trivial negation inconsistent logics (with a transitive consequence relation) must be paraconsistent. Using certain three-valued truth tables, Mortensen (1984) pointed out that there are inconsistent but non-trivial systems satisfying both AT′ and Simplification. Examples of non-trivial inconsistent systems of connexive logic satisfying Conjunctive Simplification are presented in section 4.5. The availability of such connexive systems may be appreciated in view of the fact that Zermelo-Fraenkel set theory based on a system of connexive logic with Simplification is inconsistent, see Wiredu 1974. Mortensen (1984) also pointed out that the addition of AT′ to the relevance logic R of Anderson and Belnap has a trivializing effect, a fact shown in Routley et al. 1982 as well.