TPTP Problem File: KLE161-10.p

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%------------------------------------------------------------------------------
% File     : KLE161-10 : TPTP v7.5.0. Released v7.5.0.
% Domain   : Puzzles
% Problem  : Data refinement
% 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   : 1.00 v7.5.0
% Syntax   : Number of clauses     :   28 (   0 non-Horn;  28 unit;   6 RR)
%            Number of atoms       :   28 (  28 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :   19 (  11 constant; 0-4 arity)
%            Number of variables   :   45 (   4 singleton)
%            Maximal term depth    :    6 (   2 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from KLE161+1 to UEQ using [CS18].
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cnf(ifeq_axiom,axiom,
    ( ifeq3(A,A,B,C) = B )).

cnf(ifeq_axiom_001,axiom,
    ( ifeq2(A,A,B,C) = B )).

cnf(ifeq_axiom_002,axiom,
    ( ifeq(A,A,B,C) = B )).

cnf(additive_commutativity,axiom,
    ( addition(A,B) = addition(B,A) )).

cnf(additive_associativity,axiom,
    ( addition(A,addition(B,C)) = addition(addition(A,B),C) )).

cnf(additive_identity,axiom,
    ( addition(A,zero) = A )).

cnf(idempotence,axiom,
    ( addition(A,A) = A )).

cnf(multiplicative_associativity,axiom,
    ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )).

cnf(multiplicative_right_identity,axiom,
    ( multiplication(A,one) = A )).

cnf(multiplicative_left_identity,axiom,
    ( multiplication(one,A) = A )).

cnf(distributivity1,axiom,
    ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )).

cnf(distributivity2,axiom,
    ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )).

cnf(left_annihilation,axiom,
    ( multiplication(zero,A) = zero )).

cnf(star_unfold1,axiom,
    ( addition(one,multiplication(A,star(A))) = star(A) )).

cnf(star_unfold2,axiom,
    ( addition(one,multiplication(star(A),A)) = star(A) )).

cnf(star_induction1,axiom,
    ( ifeq(leq(addition(multiplication(A,C),B),C),true,leq(multiplication(star(A),B),C),true) = true )).

cnf(star_induction2,axiom,
    ( ifeq(leq(addition(multiplication(C,A),B),C),true,leq(multiplication(B,star(A)),C),true) = true )).

cnf(infty_unfold1,axiom,
    ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )).

cnf(infty_coinduction,axiom,
    ( ifeq(leq(C,addition(multiplication(A,C),B)),true,leq(C,multiplication(strong_iteration(A),B)),true) = true )).

cnf(isolation,axiom,
    ( strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) )).

cnf(order_1,axiom,
    ( ifeq2(leq(A,B),true,addition(A,B),B) = B )).

cnf(order,axiom,
    ( ifeq3(addition(A,B),B,leq(A,B),true) = true )).

cnf(goals,negated_conjecture,
    ( strong_iteration(sK2_goals_X7) = star(sK2_goals_X7) )).

cnf(goals_1,negated_conjecture,
    ( leq(multiplication(sK1_goals_X0,sK5_goals_X4),sK6_goals_X3) = true )).

cnf(goals_2,negated_conjecture,
    ( leq(multiplication(sK1_goals_X0,sK3_goals_X6),multiplication(sK4_goals_X5,sK1_goals_X0)) = true )).

cnf(goals_3,negated_conjecture,
    ( leq(multiplication(sK1_goals_X0,sK2_goals_X7),sK1_goals_X0) = true )).

cnf(goals_4,negated_conjecture,
    ( leq(sK7_goals_X2,multiplication(sK8_goals_X1,sK1_goals_X0)) = true )).

cnf(goals_5,negated_conjecture,
    ( leq(multiplication(sK7_goals_X2,multiplication(strong_iteration(addition(sK3_goals_X6,sK2_goals_X7)),sK5_goals_X4)),multiplication(sK8_goals_X1,multiplication(strong_iteration(sK4_goals_X5),sK6_goals_X3))) != true )).

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