%------------------------------------------------------------------------------
% File     : NUN135-1.028 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Number Theory
% Problem  : Find a perfect number X >= 7. The smallest is X = 28.
% Version  : Especial
% English  : 

% Refs     : [Sai24] Saito (2024), Email to Geoff Sutcliffe
% Source   : [Sai24]
% Names    : perfect28.p [Sai24]

% Status   : Unsatisfiable
% Rating   : 0.94 v9.3.0
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;   2 RR)
%            Number of literals    :   14 (  14 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-4 aty)
%            Number of variables   :   25 (  10 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : The rules are of TRS_Standard/HirokawaMiddeldorp_04/#t003.ari from
%            TPDB.
%------------------------------------------------------------------------------
% find a perfect number X >= 7. the smallest is 28.
cnf(rule1,axiom,
    minus(X,zero) = X ).

cnf(rule2,axiom,
    minus(s(X),s(Y)) = minus(X,Y) ).

cnf(rule3,axiom,
    '<='(zero,Y) = true ).

cnf(rule4,axiom,
    '<='(s(X),zero) = false ).

cnf(rule5,axiom,
    '<='(s(X),s(Y)) = '<='(X,Y) ).

cnf(rule6,axiom,
    if(true,X,Y) = X ).

cnf(rule7,axiom,
    if(false,X,Y) = Y ).

cnf(rule8,axiom,
    perfectp(zero) = false ).

cnf(rule9,axiom,
    perfectp(s(X)) = f(X,s(zero),s(X),s(X)) ).

cnf(rule10,axiom,
    f(zero,Y,zero,U) = true ).

cnf(rule11,axiom,
    f(zero,Y,s(Z),U) = false ).

cnf(rule12,axiom,
    f(s(X),zero,Z,U) = f(X,U,minus(Z,s(X)),U) ).

cnf(rule13,axiom,
    f(s(X),s(Y),Z,U) = if('<='(X,Y),f(s(X),minus(Y,X),Z,U),f(X,U,Z,U)) ).

cnf(goal,negated_conjecture,
    perfectp(s(s(s(s(s(s(s(X)))))))) != true ).

%------------------------------------------------------------------------------