Automatic theorem prover for proving simple theorems?

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Is there a simple software that I could use to practice proving theorems in my course of mathematical logic? Basically what I need is ability to 1) define what axioms and laws I am allowed to use in proving theorem and 2) the theorem itself. What I want to see is steps how this theorem is proved. I looked at Jape. However presentation of proving steps seem to me unclear. And there is almost no documentation for that software. Any suggestions?

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In my course of mathematical logic we use this: http://www.spass-prover.org/