TPTP Problem File: SYO113^5.p
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% File : SYO113^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem THM350
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0484 [Bro09]
% : THM350 [TPS]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 18 ( 0 equ; 0 cnn)
% Maximal formula atoms : 18 ( 18 avg)
% Number of connectives : 46 ( 0 ~; 1 |; 10 &; 29 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% SPC : TH0_THM_NEQ_NAR
% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% project in the Department of Mathematical Sciences at Carnegie
% Mellon University. Distributed under the Creative Commons copyleft
% license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(cNUMBER,type,
cNUMBER: $i > $o ).
thf(cODD,type,
cODD: $i > $o ).
thf(cEVEN,type,
cEVEN: $i > $o ).
thf(cS,type,
cS: $i > $i ).
thf(c0,type,
c0: $i ).
thf(cTHM350,conjecture,
( ( ( cEVEN @ c0 )
& ! [Xn: $i] :
( ( cEVEN @ Xn )
=> ( cEVEN @ ( cS @ ( cS @ Xn ) ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [Xn: $i] :
( ( cODD @ Xn )
=> ( cODD @ ( cS @ ( cS @ Xn ) ) ) )
& ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [Xx: $i] :
( ( ( cNUMBER @ Xx )
& ( cNUMBER @ ( cS @ Xx ) ) )
=> ( ( cNUMBER @ ( cS @ Xx ) )
& ( cNUMBER @ ( cS @ ( cS @ Xx ) ) ) ) ) )
=> ! [Xx: $i] :
( ( cNUMBER @ Xx )
& ( cNUMBER @ ( cS @ Xx ) ) ) )
& ! [Xn: $i] :
( ( cNUMBER @ Xn )
<=> ( ( cEVEN @ Xn )
| ( cODD @ Xn ) ) ) )
=> ! [Xn: $i] : ( cNUMBER @ Xn ) ) ).
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