TPTP Problem File: PUZ137^1.p
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%------------------------------------------------------------------------------
% File : PUZ137^1 : TPTP v9.0.0. Released v5.3.0.
% Domain : Puzzles
% Problem : Peter the liar says everything
% Version : Especial.
% English : Peter says that everything he says is false. Show that Peter says
% everything.
% Refs : [Bro11] Brown (2011), Email to G. Sutcliffe
% Source : [Bro11]
% Names :
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.1.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.25 v5.3.0
% Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 0 def)
% Number of atoms : 3 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 1 ~; 0 |; 0 &; 6 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% SPC : TH0_THM_NEQ_NAR
% Comments : This is PUZ082^1 with a different conjecture. The idea of using
% truth values ($o) to interpret statements seems to go back to
% Frege. One criticism of this idea is that it can lead to
% unexpected consequences, often due to extensionality. In addition
% to being a theorem of extensional simple type theory, it's also
% an example of why assigning a type ($i > $o > $o) to a relation
% like 'says' may be dangerous.
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%----Signature
thf(peter,type,
peter: $i ).
thf(says,type,
says: $i > $o > $o ).
%----Axioms
thf(ax1,axiom,
( says @ peter
@ ! [X: $o] :
( ( says @ peter @ X )
=> ~ X ) ) ).
thf(thm,conjecture,
! [X: $o] : ( says @ peter @ X ) ).
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