TPTP Problem File: NUM019-1.p
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%--------------------------------------------------------------------------
% File : NUM019-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Domain : Number Theory
% Problem : Symmetry of equality can be derived
% Version : [LS74] axioms : Incomplete.
% English :
% Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : ls41 [LS74]
% : Problem 41 [LS74]
% : ls41 [WM76]
% Status : Unsatisfiable
% Rating : 0.00 v7.2.0, 0.25 v6.2.0, 0.17 v6.1.0, 0.07 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.07 v4.1.0, 0.13 v4.0.1, 0.14 v4.0.0
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 15 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 2 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments :
% Bugfixes : v4.0.0 - Bugfix in NUM001-0.ax
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%----Include recursive function + and * axioms
include('Axioms/NUM001-0.ax').
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cnf(reflexivity,hypothesis,
equalish(X,X) ).
cnf(transitivity,hypothesis,
( ~ equalish(X,Y)
| ~ equalish(X,Z)
| equalish(Y,Z) ) ).
cnf(zero_is_the_first_number,hypothesis,
~ equalish(successor(A),n0) ).
cnf(a_equals_aa,hypothesis,
equalish(a,aa) ).
cnf(prove_b_equals_a,negated_conjecture,
~ equalish(aa,a) ).
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