TPTP Problem File: SEV042^5.p
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% File : SEV042^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem THM600
% Version : Especial.
% English : Existence of a symmetric, transitive closure (PER closure).
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0533 [Bro09]
% : THM600 [TPS]
% Status : Theorem
% Rating : 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 : 47 ( 0 ~; 0 |; 7 &; 32 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 19 ( 0 ^; 18 !; 1 ?; 19 :)
% 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/
% : Polymorphic definitions expanded.
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thf(cTHM600_pme,conjecture,
! [Xr: $i > $i > $o] :
? [Xs: $i > $i > $o] :
( ! [Xa: $i,Xb: $i] :
( ( Xr @ Xa @ Xb )
=> ( Xs @ Xa @ Xb ) )
& ! [Xx: $i,Xy: $i] :
( ( Xs @ Xx @ Xy )
=> ( Xs @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( Xs @ Xx @ Xy )
& ( Xs @ Xy @ Xz ) )
=> ( Xs @ Xx @ Xz ) )
& ! [Xt: $i > $i > $o] :
( ( ! [Xa: $i,Xb: $i] :
( ( Xr @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) )
& ! [Xx: $i,Xy: $i] :
( ( Xt @ Xx @ Xy )
=> ( Xt @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( Xt @ Xx @ Xy )
& ( Xt @ Xy @ Xz ) )
=> ( Xt @ Xx @ Xz ) ) )
=> ! [Xa: $i,Xb: $i] :
( ( Xs @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) ) ) ) ).
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