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55 lines
2.4 KiB
Text
55 lines
2.4 KiB
Text
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;--------------------------------------------------------------------------
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; File : LCL109-2 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Logic Calculi (Many valued sentential)
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; Problem : MV-4 depends on the Merideth system
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; Version : [Ove90] axioms.
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; Theorem formulation : Wajsberg algebra formulation.
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; English : An axiomatisation of the many valued sentential calculus
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; is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg provided
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; a different axiomatisation. Show that MV-4 depends on the
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; Wajsberg system.
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; Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
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; : [LM92] Lusk & McCune (1992), Experiments with ROO, a Parallel
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; : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
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; : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal
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; : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11
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; : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
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; Source : [Ove90]
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; Names : CADE-11 Competition Eq-5 [Ove90]
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; : Luka-5 [LM92]
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; : MV4 [LW92]
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; : THEOREM EQ-5 [LM93]
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; : PROBLEM 5 [Zha93]
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; Status : unsatisfiable
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; Rating : 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0
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; Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR)
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; Number of literals : 5 ( 5 equality)
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; Maximal clause size : 1 ( 1 average)
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; Number of predicates : 1 ( 0 propositional; 2-2 arity)
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; Number of functors : 5 ( 3 constant; 0-2 arity)
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; Number of variables : 8 ( 0 singleton)
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; Maximal term depth : 4 ( 2 average)
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; Comments :
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; : tptp2X -f kif -t rm_equality:rstfp LCL109-2.p
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; ; 'true' renamed to 'true0' - MES
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;--------------------------------------------------------------------------
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; wajsberg_1, axiom.
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(or (= (implies true0 ?A) ?A))
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; wajsberg_2, axiom.
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(or (= (implies (implies ?A ?B) (implies (implies ?B ?C) (implies ?A ?C))) true0))
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; wajsberg_3, axiom.
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(or (= (implies (implies ?A ?B) ?B) (implies (implies ?B ?A) ?A)))
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; wajsberg_4, axiom.
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(or (= (implies (implies (not ?A) (not ?B)) (implies ?B ?A)) true0))
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; prove_wajsberg_mv_4, conjecture.
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(or (/= (implies (implies (implies a b) (implies b a)) (implies b a)) true0))
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;--------------------------------------------------------------------------
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