## TPTP Problem File: KLE145-10.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE145-10 : TPTP v7.5.0. Released v7.3.0.
% Domain   : Puzzles
% Problem  : Finite iteration after strong iteration is strong iteration
% 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   : 0.55 v7.5.0, 0.46 v7.4.0, 0.48 v7.3.0
% Syntax   : Number of clauses     :   23 (   0 non-Horn;  23 unit;   1 RR)
%            Number of atoms       :   23 (  23 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :   12 (   4 constant; 0-4 arity)
%            Number of variables   :   45 (   4 singleton)
%            Maximal term depth    :    5 (   2 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from KLE145+1 to UEQ using [CS18].
%------------------------------------------------------------------------------
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 )).

( 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,

cnf(distributivity2,axiom,

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,
( star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0) )).

%------------------------------------------------------------------------------
```