TPTP Problem File: ALG292^5.p
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% File : ALG292^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : General Algebra (Domain theory)
% Problem : TPS problem from PU-LAMBDA-MODEL-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1198 [Bro09]
% Status : Theorem
% Rating : 0.80 v8.2.0, 0.85 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.86 v6.1.0, 0.57 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 10 ( 10 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 83 ( 1 ~; 0 |; 17 &; 49 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 23 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 33 ( 0 ^; 25 !; 8 ?; 33 :)
% SPC : TH0_THM_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(a_type,type,
a: $tType ).
thf(cPU_X238A_pme,conjecture,
! [Z: a,P: a > a > a,L: a > a,R: a > a,F: a > $o] :
( ( ( ( L @ Z )
= Z )
& ( ( R @ Z )
= Z )
& ! [Xx: a,Xy: a] :
( ( L @ ( P @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( R @ ( P @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != Z )
<=> ( Xt
= ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) )
& ! [X: a > $o] :
( ? [Xt: a] :
( ( X @ Xt )
& ! [Xu: a] :
( ( X @ Xu )
=> ( X @ ( L @ Xu ) ) ) )
=> ( X @ Z ) ) )
=> ! [X: a > $o,Xz: a] :
( ? [Xx: a] :
( ! [Xx_5: a] :
( ! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( L @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( R @ Xv )
= Xx_5 ) ) )
=> ( X @ Xx_5 ) )
& ( F @ ( P @ Xx @ Xz ) ) )
<=> ? [Xx: a] :
( ! [Xx_6: a] :
( ! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( L @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( R @ Xv )
= Xx_6 ) ) )
=> ( X @ Xx_6 ) )
& ? [Xx_8: a] :
( ! [Xx_7: a] :
( ! [X0: a > $o] :
( ( ( X0 @ Xx_8 )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( L @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( R @ Xv )
= Xx_7 ) ) )
=> ! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( L @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( R @ Xv )
= Xx_7 ) ) ) )
& ( F @ ( P @ Xx_8 @ Xz ) ) ) ) ) ) ).
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