TPTP Problem File: SYO103^5.p
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% File : SYO103^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem THM147
% Version : Especial.
% English : Theorem 211 on page 120 of [Chu56].
% Refs : [Chu56] Church (1956), Introduction to Mathematical Logic I
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0367 [Bro09]
% : THM147 [TPS]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% Number of atoms : 7 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 45 ( 4 ~; 2 |; 4 &; 35 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 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(imp,type,
imp: $i > $i > $i ).
thf(cT,type,
cT: $i > $o ).
thf(nt,type,
nt: $i > $i ).
thf(cTHM147,conjecture,
~ ( ! [Xp: $i,Xq: $i] :
( ~ ( cT @ ( imp @ Xp @ Xq ) )
| ~ ( cT @ Xp )
| ( cT @ Xq ) )
& ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
& ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
& ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
& ? [Xa: $i] :
~ ( cT @ ( imp @ Xa @ Xa ) ) ) ).
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