%------------------------------------------------------------------------------
% File     : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Domain   : Software Verification
% Problem  : Faulty property about multiplication of natural numbers
% Version  : Especial.
% English  :

% Refs     : [CST26] Claessen et al. (2026), Email to Geoff Sutcliffe
% Source   : [CST26]
% Names    : Nat_mul_idem.p [CST26]

% Status   : Unsatisfiable
% Rating   : 0.17 v9.3.0
% Syntax   : Number of clauses     :   13 (  13 unt;   0 nHn;   3 RR)
%            Number of literals    :   13 (  13 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   4 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
    x2(z,Y) = Y ).

cnf(axiom_001,axiom,
    x2(s(N),Y) = s(x2(N,Y)) ).

cnf(axiom_002,axiom,
    x22(z,Y) = z ).

cnf(axiom_003,axiom,
    x22(s(N),Y) = x2(Y,x22(N,Y)) ).

cnf(axiom_004,axiom,
    mul_idem(X) = eq(x22(X,X),X) ).

cnf(axiom_005,axiom,
    eq2(bfalse,btrue) = bfalse ).

cnf(axiom_006,axiom,
    eq2(btrue,bfalse) = bfalse ).

cnf(axiom_007,axiom,
    eq(s(X),s(Y)) = eq(X,Y) ).

cnf(axiom_008,axiom,
    eq(z,s(X)) = bfalse ).

cnf(axiom_009,axiom,
    eq(s(X),z) = bfalse ).

cnf(axiom_010,axiom,
    eq(X,X) = btrue ).

cnf(axiom_011,axiom,
    eq2(X,X) = btrue ).

cnf(goal,negated_conjecture,
    eq2(mul_idem(X),bfalse) != btrue ).

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