TPTP Problem File: SYO501^1.p
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% File : SYO501^1 : TPTP v9.0.0. Released v4.1.0.
% Domain : Syntactic
% Problem : An unsatisfiable normal set with embedded formulas
% Version : Especial.
% English :
% Refs : [BS09a] Brown & Smolka (2009), Terminating Tableaux for the Ba
% : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : Example 3.1 [BS09a]
% : basic6 [Bro09]
% 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 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0
% Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% Number of atoms : 4 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 10 ( 3 ~; 1 |; 0 &; 6 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% SPC : TH0_THM_NEQ_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(x,type,
x: $i ).
thf(y,type,
y: $o ).
thf(f,type,
f: $i > $o > $i ).
thf(p,type,
p: $i > $o ).
thf(claim,conjecture,
( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ) ).
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