TPTP Problem File: SEU992^5.p
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% File : SEU992^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem from GRAPHS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1097 [Bro09]
% Status : Theorem
% Rating : 1.00 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 1.00 v4.0.0
% Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% Number of atoms : 3 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 34 ( 0 ~; 0 |; 7 &; 21 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 13 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 20 ( 0 ^; 13 !; 7 ?; 20 :)
% SPC : TH0_THM_EQU_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(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(cTHM608_pme,conjecture,
( ? [Xc: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xc @ X ) ) )
=> ( ? [R: a > b > $o] :
( ! [Xx: a] :
? [Xy: b] : ( R @ Xx @ Xy )
& ! [Xy: b] :
? [Xx: a] : ( R @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( R @ Xx @ Xy1 )
& ( R @ Xx @ Xy2 ) )
=> ( Xy1 = Xy2 ) ) )
=> ? [S: b > a > $o] :
( ! [Xx: b] :
? [Xy: a] : ( S @ Xx @ Xy )
& ! [Xx: b,Xy1: a,Xy2: a] :
( ( ( S @ Xx @ Xy1 )
& ( S @ Xx @ Xy2 ) )
=> ( Xy1 = Xy2 ) )
& ! [Xx1: b,Xx2: b,Xy: a] :
( ( ( S @ Xx1 @ Xy )
& ( S @ Xx2 @ Xy ) )
=> ( Xx1 = Xx2 ) ) ) ) ) ).
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