TPTP Problem File: CAT002-3.p
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%--------------------------------------------------------------------------
% File : CAT002-3 : TPTP v8.2.0. Released v1.0.0.
% Domain : Category Theory
% Problem : X and Y monomorphisms, XY well-defined => XY monomorphism
% Version : [Sco79] axioms : Reduced > Complete.
% English : If x and y are monomorphisms and xy is well-defined then
% xy is a monomorphism.
% Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% Source : [ANL]
% Names : p2.ver3.in [ANL]
% Status : Unsatisfiable
% Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.18 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.10 v5.5.0, 0.35 v5.3.0, 0.28 v5.2.0, 0.25 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.27 v4.0.0, 0.18 v3.7.0, 0.00 v3.3.0, 0.14 v3.2.0, 0.15 v3.1.0, 0.18 v2.7.0, 0.08 v2.6.0, 0.00 v2.5.0, 0.25 v2.4.0, 0.33 v2.3.0, 0.11 v2.2.1, 0.44 v2.2.0, 0.22 v2.1.0, 0.44 v2.0.0
% Syntax : Number of clauses : 23 ( 7 unt; 2 nHn; 18 RR)
% Number of literals : 47 ( 23 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 4 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : Axioms simplified by Art Quaife.
%--------------------------------------------------------------------------
%----Include Scott's axioms for category theory
include('Axioms/CAT003-0.ax').
%--------------------------------------------------------------------------
cnf(assume_ab_exists,hypothesis,
there_exists(compose(a,b)) ).
cnf(cancellation_for_compose1,hypothesis,
( compose(a,X) != Y
| compose(a,Z) != Y
| X = Z ) ).
cnf(cancellation_for_compose2,hypothesis,
( compose(b,X) != Y
| compose(b,Z) != Y
| X = Z ) ).
cnf(assume_h_exists,hypothesis,
there_exists(h) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
%--------------------------------------------------------------------------