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pseudo code of the xor-DPLL

Does anyone here understand the code and is able to answer a few of my question towards it?

For info: to_examine is a queue and saves variables which are recently assigned. var is obviously a variable, it's going to be examined whether it causes a conflict, a propagation or nothing.

What I don't understand is how DPLL(var) is returning a clause in line 3, I thought DPLL can just return true or false.

And how/why does the DPLL algorithm accepts just a single variable in line 3?

The source of this pseudo code is the PHD thesis of Mate Soos from 2009.

random-user
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    [Mate Soos](https://www.msoos.org/about/) might be prepared to answer this question. – Axel Kemper Jan 29 '18 at 18:51
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    `clause` is the *conflict-clause* associated with the `unsat-core` that is found by the DPLL when the stack of formulas is unsatisfiable. The notation `DPLL(var)` likely denotes the fact that `var` is decided as an assumption by the DPLL solver. – Patrick Trentin Feb 01 '18 at 22:13

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