mirror of
https://github.com/RAIRLab/Spectra.git
synced 2024-11-14 05:17:29 -05:00
53 lines
2.3 KiB
Text
53 lines
2.3 KiB
Text
;--------------------------------------------------------------------------
|
|
; File : GRP002-3 : TPTP v2.2.0. Released v1.0.0.
|
|
; Domain : Group Theory
|
|
; Problem : Commutator equals identity in groups of order 3
|
|
; Version : [Ove90] (equality) axioms : Incomplete.
|
|
; English : In a group, if (for all x) the cube of x is the identity
|
|
; (i.e. a group of order 3), then the equation [[x,y],y]=
|
|
; identity holds, where [x,y] is the product of x, y, the
|
|
; inverse of x and the inverse of y (i.e. the commutator
|
|
; of x and y).
|
|
|
|
; 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-1 [Ove90]
|
|
; : THEOREM EQ-1 [LM93]
|
|
; : PROBLEM 1 [Zha93]
|
|
; : comm.in [OTTER]
|
|
|
|
; Status : unsatisfiable
|
|
; Rating : 0.33 v2.2.0, 0.43 v2.1.0, 0.25 v2.0.0
|
|
; Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR)
|
|
; Number of literals : 6 ( 6 equality)
|
|
; Maximal clause size : 1 ( 1 average)
|
|
; Number of predicates : 1 ( 0 propositional; 2-2 arity)
|
|
; Number of functors : 6 ( 3 constant; 0-2 arity)
|
|
; Number of variables : 8 ( 0 singleton)
|
|
; Maximal term depth : 5 ( 2 average)
|
|
|
|
; Comments : Uses an explicit formulation of the commutator.
|
|
; : tptp2X -f kif -t rm_equality:rstfp GRP002-3.p
|
|
;--------------------------------------------------------------------------
|
|
; left_identity, axiom.
|
|
(or (= (multiply identity ?A) ?A))
|
|
|
|
; left_inverse, axiom.
|
|
(or (= (multiply (inverse ?A) ?A) identity))
|
|
|
|
; associativity, axiom.
|
|
(or (= (multiply (multiply ?A ?B) ?C) (multiply ?A (multiply ?B ?C))))
|
|
|
|
; commutator, axiom.
|
|
(or (= (commutator ?A ?B) (multiply ?A (multiply ?B (multiply (inverse ?A) (inverse ?B))))))
|
|
|
|
; x_cubed_is_identity, hypothesis.
|
|
(or (= (multiply ?A (multiply ?A ?A)) identity))
|
|
|
|
; prove_commutator, conjecture.
|
|
(or (/= (commutator (commutator a b) b) identity))
|
|
|
|
;--------------------------------------------------------------------------
|