%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV001^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n186.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:31 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV001^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:23:41 CDT 2014
% % CPUTime  : 300.02 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x14e0c68>, <kernel.Type object at 0x14e0638>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))->((iff (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))))))) of role conjecture named cDISTRIB_THM_pme
% Conjecture to prove = (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))->((iff (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))->((iff (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))))))']
% Parameter a:Type.
% Trying to prove (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))->((iff (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))))))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found x0000:=(x000 Xz):(((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) ((MEET ((JOIN ((MEET Xx) Xy)) Xx)) ((JOIN ((MEET Xx) Xy)) Xz)))
% Found (x000 Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((x00 Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found x0000:=(x000 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x000 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x00 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found x2000:=(x200 Xz):(((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) ((MEET ((JOIN ((MEET Xx) Xy)) Xx)) ((JOIN ((MEET Xx) Xy)) Xz)))
% Found (x200 Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((x20 Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x2 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x2 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x2 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found x2000:=(x200 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x200 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x20 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x2 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x2 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x2 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET Xx) ((JOIN Xy) Xz)))
% Found x0000:=(x000 Xz):(((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) ((MEET ((JOIN ((MEET Xx) Xy)) Xx)) ((JOIN ((MEET Xx) Xy)) Xz)))
% Found (x000 Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((x00 Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found (((x0 ((MEET Xx) Xy)) Xx) Xz) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) Xz)))
% Found x0000:=(x000 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x000 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x00 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found x1:(P ((JOIN Xx) ((MEET Xy) Xz)))
% Instantiate: b:=((JOIN Xx) ((MEET Xy) Xz)):a
% Found x1 as proof of (P0 b)
% Found x1:(P ((MEET Xx) ((JOIN Xy) Xz)))
% Instantiate: b:=((MEET Xx) ((JOIN Xy) Xz)):a
% Found x1 as proof of (P0 b)
% Found x0000:=(x000 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x000 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x00 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x0 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found eq_ref00:=(eq_ref0 ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))):(((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found (eq_ref0 ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((eq_ref a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((eq_ref a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found ((eq_ref a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) as proof of (((eq a) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) Xz)))->(P ((JOIN Xx) ((MEET Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((MEET Xx) ((JOIN Xy) Xz)))->(P ((MEET Xx) ((JOIN Xy) Xz))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found ((eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found (((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) P) as proof of (P0 ((MEET Xx) ((JOIN Xy) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN ((MEET Xx) Xy)) ((MEET Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))):(((eq a) ((JOIN Xx) ((MEET Xy) Xz))) ((JOIN Xx) ((MEET Xy) Xz)))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) Xz))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref00:=(eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))):(((eq a) ((MEET Xx) ((JOIN Xy) Xz))) ((MEET Xx) ((JOIN Xy) Xz)))
% Found (eq_ref0 ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found ((eq_ref a) ((MEET Xx) ((JOIN Xy) Xz))) as proof of (((eq a) ((MEET Xx) ((JOIN Xy) Xz))) b)
% Found eq_ref00:=(eq_ref0
% EOF
%------------------------------------------------------------------------------