mirror of
https://github.com/RAIRLab/Spectra.git
synced 2024-09-19 15:25:12 -04:00
47 lines
1.9 KiB
Text
47 lines
1.9 KiB
Text
;--------------------------------------------------------------------------
|
|
; 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))
|
|
|
|
;--------------------------------------------------------------------------
|