%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV096^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n104.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 13:33:44 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  : SEV096^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n104.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 08:02:31 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 0x1fb2b48>, <kernel.Type object at 0x1b81b00>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1fb2680>, <kernel.Type object at 0x1b813b0>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1fb2638>, <kernel.Constant object at 0x1b817a0>) of role type named z
% Using role type
% Declaring z:a
% FOF formula (<kernel.Constant object at 0x1fb2680>, <kernel.DependentProduct object at 0x1b81a70>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula (<kernel.Constant object at 0x1fb2638>, <kernel.DependentProduct object at 0x1b818c0>) of role type named f
% Using role type
% Declaring f:(a->(b->Prop))
% FOF formula (<kernel.Constant object at 0x1fb2b48>, <kernel.DependentProduct object at 0x1b81b00>) of role type named cS
% Using role type
% Declaring cS:(b->(b->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 b) (fun (Xy:b)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->(forall (Xy:b), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z))))))))) of role conjecture named cTHM552E_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 b) (fun (Xy:b)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->(forall (Xy:b), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z))))))))):Prop
% Parameter b_DUMMY:b.
% 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 b) (fun (Xy:b)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->(forall (Xy:b), ((ex a) (fun (Xx:a)=> (forall (Xw:a), ((or ((f Xx) Xy)) ((and (((f Xw) Xy)->False)) ((cR Xx) z)))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter z:a.
% Parameter cR:(a->(a->Prop)).
% Parameter f:(a->(b->Prop)).
% Parameter cS:(b->(b->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 b) (fun (Xy:b)=> ((f Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((f Xx) Xy1)) ((f Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((f Xx1) Xy)) ((f Xx2) Xy))->((cR Xx1) Xx2))))->(forall (Xy:b), ((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 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 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 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 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 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 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 (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 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 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 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 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 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 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 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 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 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 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 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 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 (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 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 (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 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 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 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 (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 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 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 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 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 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 (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 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 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 (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 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 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 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 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 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 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 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 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 (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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 (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 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 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 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 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 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 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 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 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 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 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 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 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 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 (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 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 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 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 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 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 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 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 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 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 (x5 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 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 (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 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 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 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 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 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 (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 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 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 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 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 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 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 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 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 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 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 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 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 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 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 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 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 (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 x1):((cR x1) x1)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (x7 x1) as proof of ((cR x1) z)
% Found (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 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 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 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 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 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 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 (x5 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 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 (fun (x7:(forall (Xx:a), ((cR Xx) Xx)))=> (x7 x1)) as proof of ((cR x1) 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 x1)) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((cR x1) 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 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_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 x1))) as proof of ((cR x1) z)
% Found ((and_rect2 ((cR x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) 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 x1) 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 x1))) as proof of ((cR x1) z)
% Found x20:=(x2 x9):((cR x9) x9)
% Found (x2 x9) as proof of ((cR x9) z)
% Found (x2 x9) as proof of ((cR x9) z)
% Found (x2 x9) as proof of ((cR x9) z)
% Found x40:=(x4 x9):((cR x9) x9)
% Found (x4 x9) as proof of ((cR x9) z)
% Found (x4 x9) as proof of ((cR x9) z)
% Found (x4 x9) as proof of ((cR x9) z)
% Found x60:=(x6 x9):((cR x9) x9)
% Found (x6 x9) as proof of ((cR x9) z)
% Found (x6 x9) as proof of ((cR x9) z)
% Found (x6 x9) as proof of ((cR x9) 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 x80:=(x8 x9):((cR x9) x9)
% Found (x8 x9) as proof of ((cR x9) z)
% Found (x8 x9) as proof of ((cR x9) z)
% Found (x8 x9) as proof of ((cR x9) z)
% Found x20:=(x2 x9):((cR x9) x9)
% Found (x2 x9) as proof of ((cR x9) z)
% Found (x2 x9) as proof of ((cR x9) z)
% Found (x2 x9) as proof of ((cR x9) 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 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 x90:=(x9 x7):((cR x7) x7)
% Found (x9 x7) as proof of ((cR x7) z)
% Found (x9 x7) as proof of ((cR x7) z)
% Found (x9 x7) as proof of ((cR x7) z)
% Found x40:=(x4 x9):((cR x9) x9)
% Found (x4 x9) as proof of ((cR x9) z)
% Found (x4 x9) as proof of ((cR x9) z)
% Found (x4 x9) as proof of ((cR x9) 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 x60:=(x6 x9):((cR x9) x9)
% Found (x6 x9) as proof of ((cR x9) z)
% Found (x6 x9) as proof of ((cR x9) z)
% Found (x6 x9) as proof of ((cR x9) 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 x80:=(x8 x9):((cR x9) x9)
% Found (x8 x9) as proof of ((cR x9) z)
% Found (x8 x9) as proof of ((cR x9) z)
% Found (x8 x9) as proof of ((cR x9) z)
% Found x90:=(x9 x7):((cR x7) x7)
% Found (x9 x7) as proof of ((cR x7) z)
% Found (x9 x7) as proof of ((cR x7) z)
% Found (x9 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 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 x90:=(x9 x5):((cR x5) x5)
% Found (x9 x5) as proof of ((cR x5) z)
% Found (x9 x5) as proof of ((cR x5) z)
% Found (x9 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
% EOF
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