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Stock-Based Compensation (Tables)
3 Months Ended
Oct. 31, 2019
Share-based Payment Arrangement [Abstract]  
Common stock options granted, forfeited or expired and exercised

The following is a summary of the common stock options granted, forfeited or expired and exercised under the Plan:

   Options  Weighted Average Exercise Price per Share  Weighted Average Remaining Life (Years)  Aggregate Intrinsic Value
Outstanding - July 31, 2019   7,988,675   $0.84    7.21   $15,961,391 
Granted   1,003,000   $2.09    4.92    —   
Forfeited or expired   (130,000)  $1.11    7.65    —   
Exercised   —      —      —      —   
Outstanding - October 31, 2019   8,861,675   $0.98    6.71   $5,859,392 
Fair value assumptions used in Black-Scholes option-pricing

The following assumptions were used in the Black-Scholes option-pricing model:

   October 31,
2019
Exercise price   $2.01 – 2.09 
Time to expiration   5 years 
Risk-free interest rate   1.51% - 1.59% 
Estimated volatility   153.4%
Expected dividend   —   
Stock price at valuation date   $2.01 – 2.09