;--------------------------------------------------------------------------
; File     : BOO002-1 : TPTP v2.2.0. Released v1.0.0.
; Domain   : Boolean Algebra (Ternary)
; Problem  : In B3 algebra, X * X^-1 * Y = Y
; Version  : [OTTER] (equality) axioms : Reduced > Incomplete.
; English  : 

; Refs     : [LO85]  Lusk & Overbeek (1985), Reasoning about Equality
;          : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
;          : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal 
;          : [LM93]  Lusk & McCune (1993), Uniform Strategies: The CADE-11 
;          : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
; Source   : [Ove90]
; Names    : Problem 5 [LO85]
;          : CADE-11 Competition Eq-3 [Ove90]
;          : THEOREM EQ-3 [LM93]
;          : PROBLEM 3 [Zha93]

; Status   : unsatisfiable
; Rating   : 0.33 v2.2.0, 0.43 v2.1.0, 0.38 v2.0.0
; Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   1 RR)
;            Number of literals   :    5 (   5 equality)
;            Maximal clause size  :    1 (   1 average)
;            Number of predicates :    1 (   0 propositional; 2-2 arity)
;            Number of functors   :    4 (   2 constant; 0-3 arity)
;            Number of variables  :   11 (   2 singleton)
;            Maximal term depth   :    3 (   2 average)

; Comments : 
;          : tptp2X -f kif -t rm_equality:rstfp BOO002-1.p 
;--------------------------------------------------------------------------
; associativity, axiom.
(or (= (multiply (multiply ?A ?B ?C) ?D (multiply ?A ?B ?E)) (multiply ?A ?B (multiply ?C ?D ?E))))

; ternary_multiply_1, axiom.
(or (= (multiply ?A ?B ?B) ?B))

; ternary_multiply_2, axiom.
(or (= (multiply ?A ?A ?B) ?A))

; left_inverse, axiom.
(or (= (multiply (inverse ?A) ?A ?B) ?B))

; prove_equation, conjecture.
(or (/= (multiply a (inverse a) b) b))

;--------------------------------------------------------------------------