TPTP Problem File: LCL024-1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LCL024-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Logic Calculi (Equivalential)
% Problem : PYO depends on XGK
% Version : [Ove90] axioms.
% English : Show that Kalman's shortest single axiom for the
% equivalential calculus, XGK, can be derived from the Meredith
% single axiom PYO.
% Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
% : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal
% : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11
% Source : [Ove90]
% Names : Test Problem 16 [Wos88]
% : XGK and Equivalential Calculus [Wos88]
% : CADE-11 Competition 4 [Ove90]
% : THEOREM 4 [LM93]
% Status : Unsatisfiable
% Rating : 0.07 v9.0.0, 0.18 v8.2.0, 0.14 v8.1.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.50 v6.0.0, 0.11 v5.5.0, 0.50 v5.4.0, 0.56 v5.3.0, 0.65 v5.2.0, 0.46 v5.1.0, 0.56 v5.0.0, 0.60 v4.0.1, 0.29 v3.4.0, 0.20 v3.3.0, 0.00 v3.2.0, 0.33 v2.7.0, 0.38 v2.6.0, 0.43 v2.5.0, 0.29 v2.4.0, 0.29 v2.3.0, 0.43 v2.2.1, 0.78 v2.2.0, 0.89 v2.1.0, 0.75 v2.0.0
% Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% Number of literals : 5 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments :
%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
%----Axiom by Kalman
cnf(xgk,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))) ).
%----Axiom by Meredith
cnf(prove_pyo,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) ).
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