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129 lines
3.7 KiB
Text
129 lines
3.7 KiB
Text
;--------------------------------------------------------------------------
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; File : RNG008-6 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Ring Theory
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; Problem : Boolean rings are commutative
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; Version : [MOW76] axioms : Augmented.
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; English : Given a ring in which for all x, x * x = x, prove that for
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; all x and y, x * y = y * x.
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; Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
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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 : CADE-11 Competition 3 [Ove90]
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; : THEOREM 3 [LM93]
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; Status : unsatisfiable
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; Rating : 0.67 v2.2.0, 0.71 v2.1.0, 0.75 v2.0.0
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; Syntax : Number of clauses : 22 ( 0 non-Horn; 11 unit; 13 RR)
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; Number of literals : 55 ( 2 equality)
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; Maximal clause size : 5 ( 2 average)
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; Number of predicates : 3 ( 0 propositional; 2-3 arity)
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; Number of functors : 7 ( 4 constant; 0-2 arity)
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; Number of variables : 74 ( 2 singleton)
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; Maximal term depth : 2 ( 1 average)
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; Comments : Supplies multiplication to identity as lemmas
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; : tptp2X -f kif -t rm_equality:rstfp RNG008-6.p
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;--------------------------------------------------------------------------
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; additive_identity1, axiom.
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(or (sum additive_identity ?A ?A))
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; additive_identity2, axiom.
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(or (sum ?A additive_identity ?A))
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; closure_of_multiplication, axiom.
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(or (product ?A ?B (multiply ?A ?B)))
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; closure_of_addition, axiom.
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(or (sum ?A ?B (add ?A ?B)))
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; left_inverse, axiom.
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(or (sum (additive_inverse ?A) ?A additive_identity))
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; right_inverse, axiom.
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(or (sum ?A (additive_inverse ?A) additive_identity))
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; associativity_of_addition1, axiom.
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(or (not (sum ?A ?B ?C))
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(not (sum ?B ?D ?E))
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(not (sum ?C ?D ?F))
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(sum ?A ?E ?F))
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; associativity_of_addition2, axiom.
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(or (not (sum ?A ?B ?C))
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(not (sum ?B ?D ?E))
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(not (sum ?A ?E ?F))
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(sum ?C ?D ?F))
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; commutativity_of_addition, axiom.
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(or (not (sum ?A ?B ?C))
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(sum ?B ?A ?C))
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; associativity_of_multiplication1, 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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; associativity_of_multiplication2, 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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; distributivity1, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?A ?D ?E))
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(not (sum ?B ?D ?F))
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(not (product ?A ?F ?G))
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(sum ?C ?E ?G))
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; distributivity2, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?A ?D ?E))
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(not (sum ?B ?D ?F))
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(not (sum ?C ?E ?G))
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(product ?A ?F ?G))
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; distributivity3, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?D ?B ?E))
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(not (sum ?A ?D ?F))
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(not (product ?F ?B ?G))
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(sum ?C ?E ?G))
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; distributivity4, axiom.
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(or (not (product ?A ?B ?C))
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(not (product ?D ?B ?E))
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(not (sum ?A ?D ?F))
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(not (sum ?C ?E ?G))
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(product ?F ?B ?G))
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; addition_is_well_defined, axiom.
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(or (not (sum ?A ?B ?C))
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(not (sum ?A ?B ?D))
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(= ?C ?D))
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; multiplication_is_well_defined, 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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; x_times_identity_x_is_identity, axiom.
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(or (product ?A additive_identity additive_identity))
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; identity_times_x_is_identity, axiom.
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(or (product additive_identity ?A additive_identity))
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; x_squared_is_x, hypothesis.
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(or (product ?A ?A ?A))
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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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