%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV107^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n107.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 13:33:45 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV107^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.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 08:06:21 CDT 2014
% % CPUTime  : 300.09 
% 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 0x128d7a0>, <kernel.Type object at 0x128e290>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x128dd40>, <kernel.Constant object at 0x128d0e0>) of role type named z
% Using role type
% Declaring z:a
% FOF formula (<kernel.Constant object at 0x128ddd0>, <kernel.DependentProduct object at 0x128e9e0>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula (<kernel.Constant object at 0x128d0e0>, <kernel.DependentProduct object at 0x128e9e0>) of role type named f
% Using role type
% Declaring f:(a->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x128d7a0>, <kernel.DependentProduct object at 0x128efc8>) of role type named cS
% Using role type
% Declaring cS:(fofType->(fofType->Prop))
% FOF formula (((and (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx)))->(((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:fofType) (Xy2:fofType), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:fofType), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))) (forall (Xy:fofType) (Xx1:a) (Xx2:a), (((and (forall (Xw:a), ((or ((f Xx1) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx1) z))))) (forall (Xw:a), ((or ((f Xx2) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx2) z)))))->((cR Xx1) Xx2))))) (forall (Xy:fofType), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))))) of role conjecture named cTHM552B_pme
% Conjecture to prove = (((and (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx)))->(((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:fofType) (Xy2:fofType), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:fofType), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))) (forall (Xy:fofType) (Xx1:a) (Xx2:a), (((and (forall (Xw:a), ((or ((f Xx1) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx1) z))))) (forall (Xw:a), ((or ((f Xx2) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx2) z)))))->((cR Xx1) Xx2))))) (forall (Xy:fofType), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx)))->(((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:fofType) (Xy2:fofType), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:fofType), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))) (forall (Xy:fofType) (Xx1:a) (Xx2:a), (((and (forall (Xw:a), ((or ((f Xx1) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx1) z))))) (forall (Xw:a), ((or ((f Xx2) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx2) z)))))->((cR Xx1) Xx2))))) (forall (Xy:fofType), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z))))))))))']
% Parameter a:Type.
% Parameter z:a.
% Parameter cR:(a->(a->Prop)).
% Parameter fofType:Type.
% Parameter f:(a->(fofType->Prop)).
% Parameter cS:(fofType->(fofType->Prop)).
% Trying to prove (((and (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx)))->(((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:fofType) (Xy2:fofType), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:fofType), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->((and ((and (forall (Xx:a), ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))) (forall (Xy:fofType) (Xx1:a) (Xx2:a), (((and (forall (Xw:a), ((or ((f Xx1) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx1) z))))) (forall (Xw:a), ((or ((f Xx2) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx2) z)))))->((cR Xx1) Xx2))))) (forall (Xy:fofType), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z))))))))))
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (fun (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((cR x1) z)
% Found (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect00 (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found ((and_rect0 ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x2:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x2) x)) ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x2:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x2) x)) ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((cR x3) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found ((and_rect1 ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (fun (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((cR x1) z)
% Found (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect00 (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found ((and_rect0 ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x2:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x2) x)) ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x2:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x2) x)) ((cR x1) z)) (fun (x2:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x3:(forall (Xx:a), ((cR Xx) Xx)))=> (x3 x1))) as proof of ((cR x1) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((cR x3) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found ((and_rect1 ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x30:=(x3 Xx2):((cR Xx2) Xx2)
% Found (x3 Xx2) as proof of ((cR Xx2) Xv)
% Found (x3 Xx2) as proof of ((cR Xx2) Xv)
% Found (x3 Xx2) as proof of ((cR Xx2) Xv)
% Found x30:=(x3 Xx1):((cR Xx1) Xx1)
% Found (x3 Xx1) as proof of ((cR Xx1) Xv)
% Found (x3 Xx1) as proof of ((cR Xx1) Xv)
% Found (x3 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((cR x1) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found ((and_rect1 ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((cR x5) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found ((and_rect2 ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((cR x1) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found ((and_rect1 ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((cR x3) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found ((and_rect1 ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x60:=(x6 Xx2):((cR Xx2) Xx2)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found x60:=(x6 Xx1):((cR Xx1) Xx1)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x30:=(x3 x1):((cR x1) x1)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found (x3 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((cR x5) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found ((and_rect2 ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 Xx2):((cR Xx2) Xx2)
% Found (x5 Xx2) as proof of ((cR Xx2) Xv)
% Found (x5 Xx2) as proof of ((cR Xx2) Xv)
% Found (x5 Xx2) as proof of ((cR Xx2) Xv)
% Found x50:=(x5 Xx1):((cR Xx1) Xx1)
% Found (x5 Xx1) as proof of ((cR Xx1) Xv)
% Found (x5 Xx1) as proof of ((cR Xx1) Xv)
% Found (x5 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found x70:=(x7 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((cR x3) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found ((and_rect2 ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found x60:=(x6 x7):((cR x7) x7)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found (x6 x7) as proof of ((cR x7) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((cR x3) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found ((and_rect1 ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x3) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x3))) as proof of ((cR x3) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 x5):((cR x5) x5)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found (x2 x5) as proof of ((cR x5) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x20:=(x2 x3):((cR x3) x3)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found (x2 x3) as proof of ((cR x3) z)
% Found x6:((f Xx) x5)
% Instantiate: Xx:=Xx0:a;x7:=x5:fofType
% Found x6 as proof of ((f Xx0) x7)
% Found (or_introl00 x6) as proof of ((or ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z)))
% Found ((or_introl0 ((and (((f Xw) x7)->False)) ((cR Xx0) z))) x6) as proof of ((or ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z)))
% Found (((or_introl ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z))) x6) as proof of ((or ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z)))
% Found (fun (Xw:a)=> (((or_introl ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z))) x6)) as proof of ((or ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z)))
% Found (fun (Xw:a)=> (((or_introl ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z))) x6)) as proof of (forall (Xw:a), ((or ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z))))
% Found (ex_intro000 (fun (Xw:a)=> (((or_introl ((f Xx0) x7)) ((and (((f Xw) x7)->False)) ((cR Xx0) z))) x6))) as proof of ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z))))))
% Found ((ex_intro00 x5) (fun (Xw:a)=> (((or_introl ((f Xx0) x5)) ((and (((f Xw) x5)->False)) ((cR Xx0) z))) x6))) as proof of ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z))))))
% Found (((ex_intro0 (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z)))))) x5) (fun (Xw:a)=> (((or_introl ((f Xx0) x5)) ((and (((f Xw) x5)->False)) ((cR Xx0) z))) x6))) as proof of ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z))))))
% Found ((((ex_intro fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z)))))) x5) (fun (Xw:a)=> (((or_introl ((f Xx0) x5)) ((and (((f Xw) x5)->False)) ((cR Xx0) z))) x6))) as proof of ((ex fofType) (fun (Xy:fofType)=> (forall (Xw:a), ((or ((f Xx0) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx0) z))))))
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((cR x3) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found ((and_rect2 ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x60:=(x6 Xx2):((cR Xx2) Xx2)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found (x6 Xx2) as proof of ((cR Xx2) Xv)
% Found x60:=(x6 Xx1):((cR Xx1) Xx1)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found (x6 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((cR x1) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found ((and_rect1 ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((cR x1) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found ((and_rect1 ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((cR x5) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found ((and_rect2 ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found x20:=(x2 x7):((cR x7) x7)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found (x2 x7) as proof of ((cR x7) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((cR x5) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x5) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found ((and_rect2 ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x5) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x5))) as proof of ((cR x5) z)
% Found x40:=(x4 x5):((cR x5) x5)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found (x4 x5) as proof of ((cR x5) z)
% Found x70:=(x7 x5):((cR x5) x5)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found (x7 x5) as proof of ((cR x5) z)
% Found x50:=(x5 x1):((cR x1) x1)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (x5 x1) as proof of ((cR x1) z)
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((cR x1) z)
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z))
% Found (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x1) z)))
% Found (and_rect10 (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found ((and_rect1 ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found (((fun (P:Type) (x4:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x4) x)) ((cR x1) z)) (fun (x4:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x5:(forall (Xx:a), ((cR Xx) Xx)))=> (x5 x1))) as proof of ((cR x1) z)
% Found x50:=(x5 x3):((cR x3) x3)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found (x5 x3) as proof of ((cR x3) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x20:=(x2 Xx2):((cR Xx2) Xx2)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found (x2 Xx2) as proof of ((cR Xx2) Xv)
% Found x20:=(x2 Xx1):((cR Xx1) Xx1)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found (x2 Xx1) as proof of ((cR Xx1) Xv)
% Found x40:=(x4 Xx2):((cR Xx2) Xx2)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found (x4 Xx2) as proof of ((cR Xx2) Xv)
% Found x40:=(x4 Xx1):((cR Xx1) Xx1)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found (x4 Xx1) as proof of ((cR Xx1) Xv)
% Found x40:=(x4 x7):((cR x7) x7)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found (x4 x7) as proof of ((cR x7) z)
% Found x70:=(x7 x3):((cR x3) x3)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (x7 x3) as proof of ((cR x3) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((cR x3) z)
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3)) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->((cR x3) z)))
% Found (and_rect20 (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found ((and_rect2 ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x3))) as proof of ((cR x3) z)
% Found (((fun (P:Type) (x6:((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))->((forall (Xx:a), ((cR Xx) Xx))->P)))=> (((((and_rect (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((cR Xu) Xw)))) (forall (Xx:a), ((cR Xx) Xx))) P) x6) x)) ((cR x3) z)) (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xv)) ((cR Xw) Xv))->((
% EOF
%------------------------------------------------------------------------------