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45 lines
2 KiB
Text
45 lines
2 KiB
Text
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;--------------------------------------------------------------------------
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; File : LCL024-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Logic Calculi (Equivalential)
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; Problem : PYO depends on XGK
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; Version : [Ove90] axioms.
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; English : Show that Kalman's shortest single axiom for the
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; equivalential calculus, XGK, can be derived from the Meredith
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; single axiom PYO.
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; Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
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; : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
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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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; Source : [Ove90]
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; Names : Test Problem 16 [Wos88]
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; : XGK and Equivalential Calculus [Wos88]
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; : CADE-11 Competition 4 [Ove90]
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; : THEOREM 4 [LM93]
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; Status : unsatisfiable
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; Rating : 0.78 v2.2.0, 0.89 v2.1.0, 0.75 v2.0.0
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; Syntax : Number of clauses : 3 ( 0 non-Horn; 2 unit; 2 RR)
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; Number of literals : 5 ( 0 equality)
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; Maximal clause size : 3 ( 1 average)
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; Number of predicates : 1 ( 0 propositional; 1-1 arity)
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; Number of functors : 4 ( 3 constant; 0-2 arity)
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; Number of variables : 5 ( 0 singleton)
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; Maximal term depth : 5 ( 2 average)
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; Comments :
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; : tptp2X -f kif -t rm_equality:rstfp LCL024-1.p
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;--------------------------------------------------------------------------
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; condensed_detachment, axiom.
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(or (not (is_a_theorem (equivalent ?A ?B)))
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(not (is_a_theorem ?A))
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(is_a_theorem ?B))
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; prove_xgk, axiom.
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(or (is_a_theorem (equivalent ?A (equivalent (equivalent ?B (equivalent ?C ?A)) (equivalent ?C ?B)))))
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; prove_pyo, conjecture.
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(or (not (is_a_theorem (equivalent (equivalent (equivalent a (equivalent b c)) c) (equivalent b a)))))
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;--------------------------------------------------------------------------
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