CONTENTS Introduction.................................................................................................................... 6 Chapter I. Theorem-proving system § 1. Theory...................................................................................................................... 7 § 2. Fundamental theory $T_ƒ$ ................................................................................ 8 § 3. Theorem-proving system.................................................................................... 16 Chapter II. Theorem-proving process § 1. Diagram of a formula........................................................................................... 20 § 2. The set T of partial diagrams.............................................................................. 20 § 3. Properties of the set T of partial diagram......................................................... 22 § 4. Theorem-proving process........................................................................ 27 Chapter III. Properties of theorem-proving systems § 1. Existence and uniqueness of an unextendable process.............................. 32 § 2. Properties of the set of theorem-proving processes..................................... 33 § 3. C- systems............................................................................................................. 36 § 4. Equivalence of theorem-proving systems........................................................ 38 § 5. Theorem-proving algorithms.............................................................................. 43 References.................................................................................................................... 48