TPTP Problem File: KLE044-10.p

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% File     : KLE044-10 : TPTP v7.5.0. Released v7.3.0.
% Domain   : Puzzles
% Problem  : Star simplification
% 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   : 0.45 v7.5.0, 0.46 v7.4.0, 0.43 v7.3.0
% Syntax   : Number of clauses     :   21 (   0 non-Horn;  21 unit;   1 RR)
%            Number of atoms       :   21 (  21 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :   13 (   5 constant; 0-4 arity)
%            Number of variables   :   41 (   5 singleton)
%            Maximal term depth    :    5 (   2 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from KLE044+2 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(additive_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(right_distributivity,axiom,
    ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )).

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

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

cnf(left_annihilation,axiom,
    ( multiplication(zero,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(star_unfold_right,axiom,
    ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )).

cnf(star_unfold_left,axiom,
    ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )).

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

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

cnf(goals,negated_conjecture,
    ( tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) )).

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