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% File     : REL029-10 : TPTP v8.2.0. Released v7.3.0.
% Domain   : Puzzles
% Problem  : Distributivity of subidentities
% Version  : Especial.
% English  :

% Refs     : [CS18]  Claessen & Smallbone (2018), Efficient Encodings of Fi
%          : [Sma18] Smallbone (2018), Email to Geoff Sutcliffe
% Source   : [Sma18]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.73 v8.2.0, 0.71 v8.1.0, 0.80 v7.5.0, 0.79 v7.4.0, 0.78 v7.3.0
% Syntax   : Number of clauses     :   19 (  19 unt;   0 nHn;   3 RR)
%            Number of literals    :   19 (  19 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from REL029-4 to UEQ using [CS18].
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cnf(maddux1_join_commutativity_1,axiom,
    join(A,B) = join(B,A) ).

cnf(maddux2_join_associativity_2,axiom,
    join(A,join(B,C)) = join(join(A,B),C) ).

cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
    A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).

cnf(maddux4_definiton_of_meet_4,axiom,
    meet(A,B) = complement(join(complement(A),complement(B))) ).

cnf(composition_associativity_5,axiom,
    composition(A,composition(B,C)) = composition(composition(A,B),C) ).

cnf(composition_identity_6,axiom,
    composition(A,one) = A ).

cnf(composition_distributivity_7,axiom,
    composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).

cnf(converse_idempotence_8,axiom,
    converse(converse(A)) = A ).

cnf(converse_additivity_9,axiom,
    converse(join(A,B)) = join(converse(A),converse(B)) ).

cnf(converse_multiplicativity_10,axiom,
    converse(composition(A,B)) = composition(converse(B),converse(A)) ).

cnf(converse_cancellativity_11,axiom,
    join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).

cnf(def_top_12,axiom,
    top = join(A,complement(A)) ).

cnf(def_zero_13,axiom,
    zero = meet(A,complement(A)) ).

cnf(dedekind_law_14,axiom,
    join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) ).

cnf(modular_law_1_15,axiom,
    join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C) ).

cnf(modular_law_2_16,axiom,
    join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C) ).

cnf(goals_17,negated_conjecture,
    join(sk1,one) = one ).

cnf(goals_18,negated_conjecture,
    join(sk2,one) = one ).

cnf(goals_19,negated_conjecture,
    tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))) ).

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