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%--------------------------------------------------------------------------
% File : CAT004-4 : TPTP v6.4.0. Released v1.0.0.
% Domain : Category Theory
% Problem : X and Y epimorphisms, XY well-defined => XY epimorphism
% Version : [Sco79] axioms : Reduced > Complete.
% English : If x and y are epimorphisms and xy is well-defined, then
% xy is an epimorphism.
% Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% Source : [TPTP]
% Names :
% Status : Unsatisfiable
% Rating : 0.00 v6.1.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.31 v5.4.0, 0.27 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.14 v5.0.0, 0.29 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.17 v2.2.1, 0.33 v2.2.0, 0.14 v2.1.0, 0.40 v2.0.0
% Syntax : Number of clauses : 17 ( 0 non-Horn; 7 unit; 14 RR)
% Number of atoms : 31 ( 15 equality)
% Maximal clause size : 3 ( 2 average)
% Number of predicates : 3 ( 0 propositional; 1-2 arity)
% Number of functors : 7 ( 4 constant; 0-2 arity)
% Number of variables : 25 ( 2 singleton)
% Maximal term depth : 3 ( 2 average)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments : The dependent axioms have been removed.
%--------------------------------------------------------------------------
%----Include Scott's axioms for category theory
include('Axioms/CAT004-0.ax').
%--------------------------------------------------------------------------
cnf(assume_ab_exists,hypothesis,
( there_exists(compose(a,b)) )).
cnf(cancellation_for_product1,hypothesis,
( compose(X,a) != Y
| compose(Z,a) != Y
| X = Z )).
cnf(cancellation_for_product2,hypothesis,
( compose(X,b) != Y
| compose(Z,b) != Y
| X = Z )).
cnf(assume_h_exists,hypothesis,
( there_exists(h) )).
cnf(h_ab_equals_g_ab,hypothesis,
( compose(h,compose(a,b)) = compose(g,compose(a,b)) )).
cnf(prove_h_equals_g,negated_conjecture,
( h != g )).
%--------------------------------------------------------------------------
|
