TPTP Problem File: SEU980^6.p
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% File : SEU980^6 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem from COINDUCTIVE-PU-ALG-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1236 [Bro09]
% : tps_1235 [Bro09]
% Status : Unknown
% Rating : 1.00 v5.1.0
% Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% Number of atoms : 22 ( 22 equ; 0 cnn)
% Maximal formula atoms : 22 ( 22 avg)
% Number of connectives : 174 ( 1 ~; 0 |; 29 &; 124 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 19 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 28 !; 6 ?; 34 :)
% SPC : TH0_UNK_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/
% : Renamed from SEU981^5
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thf(cR,type,
cR: $i > $i ).
thf(cP,type,
cP: $i > $i > $i ).
thf(cL,type,
cL: $i > $i ).
thf(cZ,type,
cZ: $i ).
thf(cPU_LEM2_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: $i,Xy: $i] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: $i,Xy: $i] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: $i] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X: $i > $o] :
( ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ? [X: $i > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
& ? [X: $i > $o] :
( ( X @ ( cP @ Xy @ Xz ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) )
=> ? [X: $i > $o] :
( ( X @ ( cP @ Xx @ Xz ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) )
& ! [Xx: $i] :
? [X: $i > $o] :
( ( X @ ( cP @ Xx @ Xx ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ? [X: $i > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
& ? [X: $i > $o] :
( ( X @ ( cP @ Xy @ Xx ) )
& ! [Xt: $i,Xu: $i] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) )
=> ( Xx = Xy ) ) ) ) ).
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