TPTP Problem File: LCL077-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LCL077-2 : TPTP v8.2.0. Released v1.0.0.
% Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% Problem : CN-39 depends on the Church system
% Version : [ANL] axioms : Augmented.
% English : Axiomatisations of the Implication/Negation 2 valued
% sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
% {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
% {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
% CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
% {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
% Show that CN-39 depends on the Church system.
% Refs : [Mor84] Morgan (1984), Logic Problems
% Source : [ANL]
% Names : morgan.two.ver1.in [ANL]
% Status : Unsatisfiable
% Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v2.1.0, 0.00 v2.0.0
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 10 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 1 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments : Transitivity of implies is supplied as an axiom
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cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(transitivity,axiom,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X1,X3)) ) ).
cnf(prove_cn_39,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)) ).
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