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**1 - 2**of**2**### Human-Oriented Proof Techniques are Relevant for Proof Tutoring (Extended Abstract)

"... Automated theorem proving techniques are increasingly used within interactive environments for the teaching of proof techniques. Examples are the Advanced Geometry Tutor (Matsuda and VanLehn, 2005), the geometry learning environment ANGLE (Koedinger and Anderson, 1993), the EPGY theorem proving envi ..."

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Automated theorem proving techniques are increasingly used within interactive environments for the teaching of proof techniques. Examples are the Advanced Geometry Tutor (Matsuda and VanLehn, 2005), the geometry learning environment ANGLE (Koedinger and Anderson, 1993), the EPGY theorem proving environment (McMath et al., 2001), the Baghera platform (Trgalova and Chaachoua, 2009) for the assessment of proofs in geometry, the Carnegie Proof Lab (Sieg, 2007), the educational variant of the TPS system ETPS (Andrews et al., 2004), the ProofWeb (Kaliszyk et al., 2008) system for practicing natural deduction proofs, the P-Logic tutor (Lukins et al., 2002), the EASy (Gruttmann et al., 2008) system for the e-assessment for mathematical proofs, the tutorial proof checker Tutch (Abel et al., 2001) and the RISC proof navigator (Schreiner, 2006) for education in proof verification. Most of these systems use automated proof mechanisms based on natural deduction or resolution calculi. Often, the users are required to stick to the employed calculi step by step. Evaluations of several among the above mentioned systems have revealed this as a severe limitation for teaching common mathematical practice. Gruttmann et al. (2008, p. 613) report that “EASy requires small steps to be executed one by one, which normally could be combined in a paper-based proof. Some students mentioned that a computer-supported proof could lead to a reduction of mathematical skills. ” Lukins et al. (2002)

### Under consideration for publication in Formal Aspects of Computing The RISC ProofNavigator: A Proving Assistant for Program Verification in the Classroom

"... Abstract. This paper gives an overview on the RISC ProofNavigator, an interactive proving assistant for the area of program verification. The assistant combines the user-guided top-down decomposition of proofs with the automatic simplification and closing of proof states by an external satisfiabilit ..."

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Abstract. This paper gives an overview on the RISC ProofNavigator, an interactive proving assistant for the area of program verification. The assistant combines the user-guided top-down decomposition of proofs with the automatic simplification and closing of proof states by an external satisfiability solver. The software exhibits a modern graphical user interface which has been developed with a focus on simplicity in order to make the software suitable for educational scenarios. Nevertheless, some use cases of a certain level of complexity demonstrate that it may be also appropriate for various realistic applications.