TPTP Problem File: LCL726^5.p
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% File : LCL726^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logical Calculi
% Problem : TPS problem THM534
% Version : Especial.
% English : AC1 => AC17 from [RR93].
% Refs : [RR93] Rubin & Rubin (1993), Weak Forms of the Axiom of Choic
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0159 [Bro09]
% : THM534 [TPS]
% Status : Theorem
% Rating : 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 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 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 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 : 16 ( 0 ~; 0 |; 0 &; 11 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 9 ( 0 ^; 5 !; 4 ?; 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/
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thf(a_type,type,
a: $tType ).
thf(cTHM534,conjecture,
( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) )
=> ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) ) ).
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