Rule logic.propositional.buggy.distrnot

Parameters
Buggy	yes
Rewrite rule	yes
Siblings

Rewrite rule

(¬p) ∧ (q ∨ r)   ⇏   ((¬p) ∧ q) ∨ (p ∧ r)
(¬p) ∧ (q ∨ r)   ⇏   (p ∧ q) ∨ ((¬p) ∧ r)
(p ∨ q) ∧ (¬r)   ⇏   (p ∧ (¬r)) ∨ (q ∧ r)
(p ∨ q) ∧ (¬r)   ⇏   (p ∧ r) ∨ (q ∧ (¬r))
(¬p) ∨ (q ∧ r)   ⇏   ((¬p) ∨ q) ∧ (p ∨ r)
(¬p) ∨ (q ∧ r)   ⇏   (p ∨ q) ∧ ((¬p) ∨ r)
(p ∧ q) ∨ (¬r)   ⇏   (p ∨ (¬r)) ∧ (q ∨ r)
(p ∧ q) ∨ (¬r)   ⇏   (p ∨ r) ∧ (q ∨ (¬r))

Formal Mathematical Properties

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$2"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$2"/></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$1"/><OMA><OMS cd="logic1" name="not"/><OMV name="$2"/></OMA></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>