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79 lines
2.6 KiB
Text
79 lines
2.6 KiB
Text
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;--------------------------------------------------------------------------
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; File : GRP001-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Group Theory
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; Problem : X^2 = identity => commutativity
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; Version : [MOW76] axioms.
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; English : If the square of every element is the identity, the system
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; is commutative.
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; Refs : [Rob63] Robinson (1963), Theorem Proving on the Computer
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; : [Wos65] Wos (1965), Unpublished Note
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; : [MOW76] McCharen et al. (1976), Problems and Experiments for a
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; : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
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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 : [MOW76]
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; Names : - [Rob63]
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; : wos10 [WM76]
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; : G1 [MOW76]
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; : CADE-11 Competition 1 [Ove90]
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; : THEOREM 1 [LM93]
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; : xsquared.ver1.in [ANL]
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; Status : unsatisfiable
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; Rating : 0.00 v2.0.0
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; Syntax : Number of clauses : 11 ( 0 non-Horn; 8 unit; 5 RR)
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; Number of literals : 19 ( 1 equality)
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; Maximal clause size : 4 ( 1 average)
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; Number of predicates : 2 ( 0 propositional; 2-3 arity)
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; Number of functors : 6 ( 4 constant; 0-2 arity)
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; Number of variables : 23 ( 0 singleton)
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; Maximal term depth : 2 ( 1 average)
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; Comments :
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; : tptp2X -f kif -t rm_equality:rstfp GRP001-1.p
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;--------------------------------------------------------------------------
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; left_identity, axiom.
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(or (product identity ?A ?A))
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; right_identity, axiom.
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(or (product ?A identity ?A))
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; left_inverse, axiom.
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(or (product (inverse ?A) ?A identity))
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; right_inverse, axiom.
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(or (product ?A (inverse ?A) identity))
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; total_function1, axiom.
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(or (product ?A ?B (multiply ?A ?B)))
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; total_function2, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?A ?B ?D))
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(= ?C ?D))
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; associativity1, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?B ?D ?E))
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(not (product ?C ?D ?F))
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(product ?A ?E ?F))
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; associativity2, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?B ?D ?E))
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(not (product ?A ?E ?F))
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(product ?C ?D ?F))
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; square_element, hypothesis.
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(or (product ?A ?A identity))
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; a_times_b_is_c, hypothesis.
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(or (product a b c))
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; prove_b_times_a_is_c, conjecture.
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(or (not (product b a c)))
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;--------------------------------------------------------------------------
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