TPTP Problem File: SEV378^5.p
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% File : SEV378^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (GvNB)
% Problem : TPS problem from GVB-MB-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0865 [Bro09]
% Status : CounterSatisfiable
% Rating : 0.75 v8.1.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% Number of atoms : 5 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 12 ( 0 ~; 0 |; 2 &; 8 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% Number of variables : 5 ( 0 ^; 2 !; 3 ?; 5 :)
% SPC : TH0_CSA_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(cGVB_APPLY,type,
cGVB_APPLY: $i > $i > $i ).
thf(cGVB_ITERATE,type,
cGVB_ITERATE: $i > $i > $o ).
thf(cGVB_THM15B,conjecture,
! [Xf: $i] :
( ? [Xg: $i] :
( ( cGVB_ITERATE @ Xf @ Xg )
& ? [Xx: $i] :
( ( ( cGVB_APPLY @ Xg @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( cGVB_APPLY @ Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: $i] :
( ( cGVB_APPLY @ Xf @ Xy )
= Xy ) ) ).
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