TPTP Problem File: SEV254^5.p
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% File : SEV254^5 : TPTP v8.2.0. 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_1170 [Bro09]
% : tps_1171 [Bro09]
% Status : Theorem
% Rating : 0.17 v8.2.0, 0.18 v8.1.0, 0.42 v7.5.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.1, 0.67 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 : 71 ( 0 ~; 0 |; 9 &; 46 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 28 ( 5 ^; 15 !; 8 ?; 28 :)
% 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(cTHM2C_pme,conjecture,
! [K: ( $i > $o ) > $i > $o] :
( ( ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) )
& ( ! [Xx: $i] :
( ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) ) )
=> ! [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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