TPTP Problem File: SEV246^5.p
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% File : SEV246^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from SETS-OF-SETS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0977 [Bro09]
% Status : Theorem
% Rating : 0.25 v9.0.0, 0.58 v8.2.0, 0.55 v8.1.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.75 v7.1.0, 0.71 v7.0.0, 0.62 v6.4.0, 0.71 v6.3.0, 0.67 v6.2.0, 0.50 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.60 v5.4.0, 0.50 v5.2.0, 0.75 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 25 ( 0 ~; 0 |; 2 &; 16 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 11 ( 1 ^; 8 !; 2 ?; 11 :)
% 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(cTHM2A_ONE_pme,conjecture,
! [K: ( $i > $o ) > $i > $o] :
( ! [Xx: $i > $o,Xy: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( Xy @ Xx0 ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K @ Xy @ Xx0 ) ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) ) ) ) ).
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