358 term (continued) first-order, 100 free for substitution for a variable, 129 ground, 101 value for a variable assignment, 112 value in a structure, 111 theorem of H, 54 of ST, 61 of D, 48 theorem proving automated, 254 interactive, 255 theory complete, 90 consistent, 89 first-order, 211 Henkin extension maximal, 216 inconsistent, 89 maximal consistent, 89 model of, 211 propositional, 89 satisfiable, 211 unsatisfiable, 211 Thoralf Skolem, 192 total order, 239 tree height, 38 truth of formula in a structure under a variable assignment, 109, 112 truth assignment falsifying, 12 truth tables, truth valuation, 41 truth value, Index unifiable literals, 196 terms, 196 unifier substitution, 196 union, 232 unique generation, 43 unique readability property, 43, 105 universal closure, 136 universal set, 236 universe, 37 upper bound, 241 least, 241 value of a term for a variable assignment, 112 of term in a structure, 111 variable assignment, 112 bound, 126 existentially, 126 universally, 126 free, 126 individual, 99 propositional, variant assignment, 113 Venn diagram, 153 Verifier, 115 well-ordering, 40, 242 principle, 249 Wilfrid Hodges, 123 William Jevons, 27 witness, 180 Zeno of Citium, 18