TPTP Problem File: SYO039^1.p
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% File : SYO039^1 : TPTP v9.0.0. Released v4.0.0.
% Domain : Syntactic
% Problem : Unsatisfiable basic formula 1
% Version : Especial.
% English :
% Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% Source : [BS09a]
% Names :
% Status : Unsatisfiable
% Rating : 0.00 v5.3.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% Number of atoms : 5 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 5 avg)
% Number of connectives : 6 ( 2 ~; 0 |; 0 &; 4 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% SPC : TH0_UNS_EQU_NAR
% Comments : The fragment of simple type theory that restricts equations to
% base types and disallows lambda abstraction and quantification is
% decidable. This is an example.
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thf(h,type,
h: $o > $i ).
thf(1,axiom,
( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
!= ( h @ $false ) ) ).
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