TPTP Problem File: SEV070^5.p
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%------------------------------------------------------------------------------
% File : SEV070^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem THM577
% Version : Especial.
% English : Inductive defn of <= on naturals is transitive.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0476 [Bro09]
% : THM577 [TPS]
% Status : Theorem
% Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 26 ( 0 ~; 0 |; 4 &; 15 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 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/
% : Polymorphic definitions expanded.
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thf(cS,type,
cS: $i > $i ).
thf(cTHM577_pme,conjecture,
! [Xx: $i,Xy: $i,Xz: $i] :
( ( ! [Xp: $i > $o] :
( ( ( Xp @ Xx )
& ! [Xn: $i] :
( ( Xp @ Xn )
=> ( Xp @ ( cS @ Xn ) ) ) )
=> ( Xp @ Xy ) )
& ! [Xp: $i > $o] :
( ( ( Xp @ Xy )
& ! [Xn: $i] :
( ( Xp @ Xn )
=> ( Xp @ ( cS @ Xn ) ) ) )
=> ( Xp @ Xz ) ) )
=> ! [Xp: $i > $o] :
( ( ( Xp @ Xx )
& ! [Xn: $i] :
( ( Xp @ Xn )
=> ( Xp @ ( cS @ Xn ) ) ) )
=> ( Xp @ Xz ) ) ) ).
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