TPTP Problem File: SET041-6.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : SET041-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain : Set Theory
% Problem : Properties of apply for composition of functions, 3 of 3
% Version : [Qua92] axioms.
% English :
% Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : AP11 [Qua92]
% Status : Unknown
% Rating : 1.00 v2.1.0
% Syntax : Number of clauses : 115 ( 40 unt; 8 nHn; 82 RR)
% Number of literals : 221 ( 50 equ; 101 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% Number of functors : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 214 ( 32 sgn)
% SPC : CNF_UNK_RFO_SEQ_NHN
% Comments : This problem has been removed from its position in Quaife's
% order of presentation because it corresponds to one of [BL+86]
% problems. If the user wishes to create augmented versions of
% the Quaife problems, the theorem name above indicates its
% position in Quaife's ordering.
% : Quaife proves all these problems by augmenting the axioms with
% all previously proved theorems. With a few exceptions (the
% problems that correspond to [BL+86] problems), the TPTP has
% retained the order in which Quaife presents the problems. The
% user may create an augmented version of this problem by adding
% all previously proved theorems (the ones that correspond to
% [BL+86] are easily identified and positioned using Quaife's
% naming scheme).
% Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% : v1.2.1 - Fixed prove_application_property11_1.
% : v2.1.0 - Bugfix in SET004-0.ax.
%--------------------------------------------------------------------------
%----Include von Neuman-Bernays-Godel set theory axioms
include('Axioms/SET004-0.ax').
%----Include von Neuman-Bernays-Godel Boolean Algebra definitions
include('Axioms/SET004-1.ax').
%--------------------------------------------------------------------------
cnf(prove_application_property11_1,negated_conjecture,
single_valued_class(xf) ).
cnf(prove_application_property11_2,negated_conjecture,
member(x,domain_of(xf)) ).
cnf(prove_application_property11_3,negated_conjecture,
apply(compose(yf,xf),x) != apply(yf,apply(xf,x)) ).
%--------------------------------------------------------------------------