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98 lines
3.2 KiB
Text
98 lines
3.2 KiB
Text
;--------------------------------------------------------------------------
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; File : GRP002-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Group Theory
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; Problem : Commutator equals identity in groups of order 3
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; Version : [MOW76] axioms.
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; English : In a group, if (for all x) the cube of x is the identity
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; (i.e. a group of order 3), then the equation [[x,y],y]=
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; identity holds, where [x,y] is the product of x, y, the
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; inverse of x and the inverse of y (i.e. the commutator
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; of x and y).
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; Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
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; : [OMW76] Overbeek et al. (1976), Complexity and Related Enhance
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; : [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 : [MOW76]
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; Names : G6 [MOW76]
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; : Theorem 1 [OMW76]
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; : Test Problem 2 [Wos88]
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; : Commutator Theorem [Wos88]
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; : CADE-11 Competition 2 [Ove90]
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; : THEOREM 2 [LM93]
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; : commutator.ver1.in [ANL]
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; Status : unsatisfiable
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; Rating : 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0
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; Syntax : Number of clauses : 16 ( 0 non-Horn; 11 unit; 11 RR)
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; Number of literals : 26 ( 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 : 10 ( 8 constant; 0-2 arity)
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; Number of variables : 26 ( 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 GRP002-1.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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; x_cubed_is_identity_1, hypothesis.
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(or (not (product ?A ?A ?B))
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(product ?A ?B identity))
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; x_cubed_is_identity_2, hypothesis.
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(or (not (product ?A ?A ?B))
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(product ?B ?A identity))
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; a_times_b_is_c, conjecture.
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(or (product a b c))
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; c_times_inverse_a_is_d, conjecture.
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(or (product c (inverse a) d))
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; d_times_inverse_b_is_h, conjecture.
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(or (product d (inverse b) h))
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; h_times_b_is_j, conjecture.
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(or (product h b j))
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; j_times_inverse_h_is_k, conjecture.
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(or (product j (inverse h) k))
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; prove_k_times_inverse_b_is_e, conjecture.
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(or (not (product k (inverse b) identity)))
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;--------------------------------------------------------------------------
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