%--------------------------------------------------------------------------
% File     : CAT019-4 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Category Theory
% Problem  : Axiom of Indiscernibles
% Version  : [Sco79] axioms : Reduced > Complete.
% English  : [all z (x=z <-> y=z)] -> x=y.

% Refs     : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% Source   : [TPTP]
% Names    :

% Status   : Satisfiable
% Rating   : 0.56 v9.0.0, 0.50 v8.2.0, 0.70 v8.1.0, 0.62 v7.5.0, 0.67 v7.4.0, 0.64 v7.3.0, 0.67 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.29 v6.3.0, 0.25 v6.2.0, 0.30 v6.1.0, 0.44 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0, 0.78 v5.2.0, 0.80 v5.0.0, 0.78 v4.1.0, 0.71 v4.0.1, 0.80 v4.0.0, 0.50 v3.7.0, 0.33 v3.4.0, 0.50 v3.3.0, 0.33 v3.2.0, 0.80 v3.1.0, 0.67 v2.7.0, 0.33 v2.6.0, 0.86 v2.5.0, 0.50 v2.4.0, 0.67 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :   14 (   4 unt;   0 nHn;  11 RR)
%            Number of literals    :   28 (  12 equ;  15 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   21 (   2 sgn)
% SPC      : CNF_SAT_RFO_EQU_NUE

% Comments : The dependent axioms have been removed.
%          : The ANL set uses very few axioms for this. I'm not sure
%            if using them all is OK.
%--------------------------------------------------------------------------
%----Include Scott's axioms for category theory
include('Axioms/CAT004-0.ax').
%--------------------------------------------------------------------------
%----Denial of the axiom of indiscernibles
cnf(equality_of_a_and_b1,hypothesis,
    ( ~ there_exists(Z)
    | a != Z
    | b = Z ) ).

cnf(equality_of_a_and_b2,hypothesis,
    ( ~ there_exists(Z)
    | a = Z
    | b != Z ) ).

cnf(prove_a_equals_b,negated_conjecture,
    a != b ).

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