TPTP Problem File: CAT005-3.p
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%--------------------------------------------------------------------------
% File : CAT005-3 : TPTP v8.2.0. Released v1.0.0.
% Domain : Category Theory
% Problem : Domain is the unique right identity
% Version : [Sco79] axioms : Reduced > Complete.
% English : domain(x) is the unique identity i such that xi is defined.
% Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% Source : [ANL]
% Names : p5.ver3.in [ANL]
% Status : Unsatisfiable
% Rating : 0.10 v8.2.0, 0.05 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.21 v6.0.0, 0.10 v5.5.0, 0.25 v5.4.0, 0.20 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.08 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0, 0.23 v3.1.0, 0.27 v2.7.0, 0.25 v2.6.0, 0.30 v2.5.0, 0.25 v2.4.0, 0.22 v2.3.0, 0.33 v2.2.0, 0.44 v2.1.0, 0.56 v2.0.0
% Syntax : Number of clauses : 21 ( 5 unt; 2 nHn; 16 RR)
% Number of literals : 43 ( 18 equ; 20 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 : Axioms simplified by Art Quaife.
%--------------------------------------------------------------------------
%----Include Scott's axioms for category theory
include('Axioms/CAT003-0.ax').
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%----Denial of the theorem: d is an identity not equal to dom(a),
cnf(ad_exists,hypothesis,
there_exists(compose(a,d)) ).
cnf(xd_equals_x,hypothesis,
( ~ there_exists(compose(X,d))
| compose(X,d) = X ) ).
cnf(dy_equals_y,hypothesis,
( ~ there_exists(compose(d,Y))
| compose(d,Y) = Y ) ).
cnf(prove_domain_of_a_is_d,negated_conjecture,
domain(a) != d ).
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