## TPTP Problem File: KLE096-10.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE096-10 : TPTP v7.5.0. Released v7.5.0.
% Domain   : Puzzles
% Problem  : Modal operators satisfy a star unfold law
% 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     :   35 (   0 non-Horn;  35 unit;   1 RR)
%            Number of atoms       :   35 (  35 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :   22 (   5 constant; 0-4 arity)
%            Number of variables   :   62 (   5 singleton)
%            Maximal term depth    :    6 (   3 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from KLE096+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 )).

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,

cnf(left_distributivity,axiom,

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

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

cnf(order_1,axiom,

cnf(order,axiom,

cnf(star_unfold_right,axiom,

cnf(star_unfold_left,axiom,

cnf(star_induction_left,axiom,

cnf(star_induction_right,axiom,

cnf(domain1,axiom,
( multiplication(antidomain(X0),X0) = zero )).

cnf(domain2,axiom,

cnf(domain3,axiom,

cnf(domain4,axiom,
( domain(X0) = antidomain(antidomain(X0)) )).

cnf(codomain1,axiom,
( multiplication(X0,coantidomain(X0)) = zero )).

cnf(codomain2,axiom,

cnf(codomain3,axiom,

cnf(codomain4,axiom,
( codomain(X0) = coantidomain(coantidomain(X0)) )).

cnf(complement,axiom,
( c(X0) = antidomain(domain(X0)) )).

cnf(domain_difference,axiom,
( domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)) )).

cnf(forward_diamond,axiom,
( forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )).

cnf(backward_diamond,axiom,
( backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)) )).

cnf(forward_box,axiom,
( forward_box(X0,X1) = c(forward_diamond(X0,c(X1))) )).

cnf(backward_box,axiom,
( backward_box(X0,X1) = c(backward_diamond(X0,c(X1))) )).

cnf(goals,negated_conjecture,