TPTP Problem File: CAT019-3.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : CAT019-3 : TPTP v8.2.0. 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 : [ANL]
% Names : p15.ver3.no2.in [ANL]
% : p15.ver3.no4.in [ANL]
% Status : Unsatisfiable
% Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.18 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.20 v5.3.0, 0.22 v5.2.0, 0.25 v5.1.0, 0.12 v5.0.0, 0.00 v4.0.1, 0.09 v4.0.0, 0.00 v2.5.0, 0.08 v2.4.0, 0.00 v2.1.0, 0.00 v2.0.0
% Syntax : Number of clauses : 20 ( 4 unt; 2 nHn; 15 RR)
% Number of literals : 44 ( 20 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : The ANL set uses very few axioms for this. I'm not sure
% if using them all is OK.
% : Axioms simplified by Art Quaife.
%--------------------------------------------------------------------------
%----Include Scott's axioms for category theory
include('Axioms/CAT003-0.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 ).
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