mirror of
https://github.com/RAIRLab/Spectra.git
synced 2024-11-12 12:30:46 -05:00
38 lines
1.9 KiB
Text
38 lines
1.9 KiB
Text
;--------------------------------------------------------------------------
|
|
; File : GRP014-1 : TPTP v2.2.0. Released v1.0.0.
|
|
; Domain : Group Theory
|
|
; Problem : Product is associative in this group theory
|
|
; Version : [Ove90] (equality) axioms : Incomplete.
|
|
; English : The group theory specified by the axiom given implies the
|
|
; associativity of multiply.
|
|
|
|
; Refs : [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 : CADE-11 Competition Eq-4 [Ove90]
|
|
; : THEOREM EQ-4 [LM93]
|
|
; : PROBLEM 4 [Zha93]
|
|
|
|
; Status : unsatisfiable
|
|
; Rating : 0.33 v2.2.0, 0.43 v2.1.0, 0.50 v2.0.0
|
|
; Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR)
|
|
; Number of literals : 2 ( 2 equality)
|
|
; Maximal clause size : 1 ( 1 average)
|
|
; Number of predicates : 1 ( 0 propositional; 2-2 arity)
|
|
; Number of functors : 5 ( 3 constant; 0-2 arity)
|
|
; Number of variables : 4 ( 0 singleton)
|
|
; Maximal term depth : 9 ( 4 average)
|
|
|
|
; Comments : The group_axiom is in fact a single axiom for group theory
|
|
; [LM93].
|
|
; : tptp2X -f kif -t rm_equality:rstfp GRP014-1.p
|
|
;--------------------------------------------------------------------------
|
|
; group_axiom, axiom.
|
|
(or (= (multiply ?A (inverse (multiply (multiply (inverse (multiply (inverse ?B) (multiply (inverse ?A) ?C))) ?D) (inverse (multiply ?B ?D))))) ?C))
|
|
|
|
; prove_associativity, conjecture.
|
|
(or (/= (multiply a (multiply b c)) (multiply (multiply a b) c)))
|
|
|
|
;--------------------------------------------------------------------------
|