TPTP Problem File: ALG294^5.p
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% File : ALG294^5 : 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_1238 [Bro09]
% Status : Theorem
% Rating : 0.50 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.71 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, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 8 ( 0 unt; 7 typ; 0 def)
% Number of atoms : 29 ( 21 equ; 0 cnn)
% Maximal formula atoms : 15 ( 29 avg)
% Number of connectives : 148 ( 1 ~; 5 |; 29 &; 89 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 24 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 8 ^; 29 !; 17 ?; 54 :)
% 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(cR,type,
cR: a > a ).
thf(cL,type,
cL: a > a ).
thf(cPSI,type,
cPSI: ( a > $o ) > a > $o ).
thf(cP,type,
cP: a > a > a ).
thf(cZ,type,
cZ: a ).
thf(cPHI,type,
cPHI: ( a > $o ) > a > $o ).
thf(cPU_X2310B_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X: a > $o] :
( ? [Xt: a] :
( ( X @ Xt )
& ! [Xu: a] :
( ( X @ Xu )
=> ( X @ ( cL @ Xu ) ) ) )
=> ( X @ cZ ) )
& ! [X: a > $o,Xz: a] :
( ( cPHI @ X @ Xz )
<=> ? [Xx: a] :
( ! [Xx_14: a] :
( ! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_14 ) ) )
=> ( X @ Xx_14 ) )
& ( cPHI
@ ^ [Xy: a] :
! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xy ) ) )
@ Xz ) ) )
& ! [X: a > $o,Xz: a] :
( ( cPSI @ X @ Xz )
<=> ? [Xx: a] :
( ! [Xx_15: a] :
( ! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_15 ) ) )
=> ( X @ Xx_15 ) )
& ( cPSI
@ ^ [Xy: a] :
! [X0: a > $o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xy ) ) )
@ Xz ) ) ) )
=> ( ( ^ [Xu: a] :
( ( Xu = cZ )
| ? [Xx: a,Xy: a] :
( ( Xu
= ( cP @ Xx @ Xy ) )
& ( ( cPHI
@ ^ [Xy0: a] :
! [X: a > $o] :
( ( ( X @ Xx )
& ! [Xz: a] :
( ( X @ Xz )
=> ( X @ ( cL @ Xz ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy )
| ( cPSI
@ ^ [Xy0: a] :
! [X: a > $o] :
( ( ( X @ Xx )
& ! [Xz: a] :
( ( X @ Xz )
=> ( X @ ( cL @ Xz ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) ) ) ) )
= ( ^ [Xz: a] :
( ( Xz = cZ )
| ? [Xx: a,Xy: a] :
( ( Xz
= ( cP @ Xx @ Xy ) )
& ( cPHI
@ ^ [Xy0: a] :
! [X: a > $o] :
( ( ( X @ Xx )
& ! [Xz0: a] :
( ( X @ Xz0 )
=> ( X @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) )
| ( Xz = cZ )
| ? [Xx: a,Xy: a] :
( ( Xz
= ( cP @ Xx @ Xy ) )
& ( cPSI
@ ^ [Xy0: a] :
! [X: a > $o] :
( ( ( X @ Xx )
& ! [Xz0: a] :
( ( X @ Xz0 )
=> ( X @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) ) ) ) ) ) ).
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