%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV067^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n179.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 13:33:41 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV067^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 07:53:31 CDT 2014
% % CPUTime  : 300.10 
% 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 0x1597fc8>, <kernel.Type object at 0x1597560>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x15974d0>, <kernel.DependentProduct object at 0x1972b48>) of role type named cS
% Using role type
% Declaring cS:(a->Prop)
% FOF formula (<kernel.Constant object at 0x1597908>, <kernel.DependentProduct object at 0x1972a28>) of role type named cT
% Using role type
% Declaring cT:(a->Prop)
% FOF formula (<kernel.Constant object at 0x1597fc8>, <kernel.DependentProduct object at 0x1972b00>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula (((and ((and ((and ((and ((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))) (forall (Xx:a), ((cR Xx) Xx)))) (forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))) (forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cS Xv))->(cS Xu))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cT Xv))->(cT Xu))))->((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))) of role conjecture named cTHM553_pme
% Conjecture to prove = (((and ((and ((and ((and ((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))) (forall (Xx:a), ((cR Xx) Xx)))) (forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))) (forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cS Xv))->(cS Xu))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cT Xv))->(cT Xu))))->((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(((and ((and ((and ((and ((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))) (forall (Xx:a), ((cR Xx) Xx)))) (forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))) (forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cS Xv))->(cS Xu))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cT Xv))->(cT Xu))))->((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx)))))']
% Parameter a:Type.
% Parameter cS:(a->Prop).
% Parameter cT:(a->Prop).
% Parameter cR:(a->(a->Prop)).
% Trying to prove (((and ((and ((and ((and ((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))) (forall (Xx:a), ((cR Xx) Xx)))) (forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))) (forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cS Xv))->(cS Xu))))) (forall (Xu:a) (Xv:a), (((and ((cR Xu) Xv)) (cT Xv))->(cT Xu))))->((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x90:=(x9 Xx):((cR Xx) Xx)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found x90:=(x9 Xx):((cR Xx) Xx)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))):(((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) (forall (Xx:a), ((cT Xx)->(cS Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cT Xx)->(cS Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cS Xx)->(cT Xx)))):((or (forall (Xx:a), ((cS Xx)->(cT Xx)))) (not (forall (Xx:a), ((cS Xx)->(cT Xx)))))
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))):(((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) (forall (Xx:a), ((cS Xx)->(cT Xx))))
% Found (eq_ref0 (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) as proof of (((eq Prop) (forall (Xx:a), ((cS Xx)->(cT Xx)))) b)
% Found classic0:=(classic (forall (Xx:a), ((cT Xx)->(cS Xx)))):((or (forall (Xx:a), ((cT Xx)->(cS Xx)))) (not (forall (Xx:a), ((cT Xx)->(cS Xx)))))
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found (classic (forall (Xx:a), ((cT Xx)->(cS Xx)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x90:=(x9 Xx):((cR Xx) Xx)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found x90:=(x9 Xx):((cR Xx) Xx)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found (x9 Xx) as proof of ((cR Xx) Xv)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x100:=(x10 Xx):((cR Xx) Xx)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (x10 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x10:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x10 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->P)))=> (((((and_rect (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (forall (Xx0:a), ((cR Xx0) Xx0))) P) x9) x7)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found x110:=(x11 Xx):((cR Xx) Xx)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (x11 Xx) as proof of ((cR Xx) Xv)
% Found (fun (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((cR Xx) Xv)
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv))
% Found (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx)) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))->((forall (Xx0:a), ((cR Xx0) Xx0))->((cR Xx) Xv)))
% Found (and_rect40 (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found ((and_rect4 ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))) (forall (Xx:a), ((cR Xx) Xx))) P) x9) x6)) ((cR Xx) Xv)) (fun (x9:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((cR Xx0) Xy)) ((cR Xy) Xz))->((cR Xx0) Xz)))) (x11:(forall (Xx0:a), ((cR Xx0) Xx0)))=> (x11 Xx))) as proof of ((cR Xx) Xv)
% Found (((fun (P:Type) (x9:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cR Xx) Xy)) ((cR Xy) Xz))->((cR Xx) Xz)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((
% EOF
%------------------------------------------------------------------------------