TSTP Solution File: SEV002^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV002^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n089.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 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV002^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.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 07:23:46 CDT 2014
% % CPUTime : 300.03
% 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 0x157e950>, <kernel.Type object at 0x157eea8>) 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 ((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)))) (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)))))->(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))))) of role conjecture named cMODULAR_THM_DEF2_pme
% Conjecture to prove = (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((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)))) (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)))))->(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN 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 ((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)))) (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)))))->(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))))']
% Parameter a:Type.
% Trying to prove (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((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)))) (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)))))->(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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 ((JOIN Xx) Xy)) ((JOIN Xx) Xz))):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found (eq_ref0 ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN 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) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((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) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x0:(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Instantiate: b:=((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))):a
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found (eq_ref0 ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% 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 x3000:=(x300 ((JOIN Xx) Xz)):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) ((JOIN Xx) Xz))))
% Found (x300 ((JOIN Xx) Xz)) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((x30 Xy) ((JOIN Xx) Xz)) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found (((x3 Xx) Xy) ((JOIN Xx) Xz)) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found (((x3 Xx) Xy) ((JOIN Xx) Xz)) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found (((x3 Xx) Xy) ((JOIN Xx) Xz)) as proof of (((eq a) ((JOIN Xx) ((MEET 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) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((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) ((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 eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((MEET Xy) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found (eq_ref0 ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((eq_ref a) ((MEET ((JOIN Xx) Xy)) ((JOIN 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) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((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) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref a) b) as proof of (((eq a) b) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found x0:(P ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Instantiate: b:=((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)):a
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found x2:(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Instantiate: b:=((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))):a
% Found x2 as proof of (P0 b)
% Found x1000:=(x100 Xz):(((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) ((JOIN ((MEET ((JOIN Xx) Xy)) Xx)) ((MEET ((JOIN Xx) Xy)) Xz)))
% Found (x100 Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found ((x10 Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found (((x1 ((JOIN Xx) Xy)) Xx) Xz) as proof of (((eq a) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))) b)
% Found x0:(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Instantiate: b:=((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))):a
% Found x0 as proof of (P0 b)
% 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 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b0)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b0)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b0)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b0) as proof of (((eq a) b0) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b0) as proof of (((eq a) b0) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found ((eq_ref a) b0) as proof of (((eq a) b0) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET 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 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found ((eq_ref a) a0) as proof of (((eq a) a0) ((JOIN Xx) Xz))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 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 ((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) ((JOIN Xx) Xz))))->(P ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))))
% Found (eq_ref00 P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found ((eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) P) as proof of (P0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found eq_ref00:=(eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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) ((JOIN Xx) Xz)))):(((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz))))
% Found (eq_ref0 ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) b)
% Found ((eq_ref a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) as proof of (((eq a) ((JOIN Xx) ((MEET 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 ((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 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz)
% EOF
%------------------------------------------------------------------------------