TSTP Solution File: PUZ095^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ095^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n121.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 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:22:30 EDT 2015
% Result : Timeout 293.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.03 % Problem : PUZ095^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.01/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/1.07 % Computer : n121.star.cs.uiowa.edu
% 0.02/1.07 % Model : x86_64 x86_64
% 0.02/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.07 % Memory : 32286.75MB
% 0.02/1.07 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.02/1.07 % CPULimit : 300
% 0.02/1.07 % DateTime : Thu Apr 16 11:43:52 CDT 2015
% 0.02/1.07 % CPUTime :
% 0.02/1.08 Python 2.7.5
% 0.04/1.41 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba62d8>, <kernel.Constant object at 0x1ba6320>) of role type named c1_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring c1:fofType
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba6368>, <kernel.DependentProduct object at 0x163cf80>) of role type named s_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring s:(fofType->fofType)
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba62d8>, <kernel.DependentProduct object at 0x163cfc8>) of role type named cCKB6_BLACK_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring cCKB6_BLACK:(fofType->(fofType->Prop))
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba6368>, <kernel.DependentProduct object at 0x163cdd0>) of role type named cCKB_INF_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring cCKB_INF:((fofType->(fofType->Prop))->Prop)
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba65f0>, <kernel.DependentProduct object at 0x163cef0>) of role type named cCKB_INJ_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring cCKB_INJ:((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)
% 0.04/1.41 FOF formula (<kernel.Constant object at 0x1ba6368>, <kernel.DependentProduct object at 0x163cdd0>) of role type named cCKB_XPL_type
% 0.04/1.41 Using role type
% 0.04/1.41 Declaring cCKB_XPL:((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.04/1.41 FOF formula (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))) of role definition named cCKB6_BLACK_def
% 0.04/1.41 A new definition: (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))))
% 0.04/1.41 Defined: cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))
% 0.04/1.41 FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))) of role definition named cCKB_INJ_def
% 0.04/1.41 A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))))
% 0.04/1.41 Defined: cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))
% 0.04/1.41 FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))) of role definition named cCKB_XPL_def
% 0.04/1.41 A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))))
% 0.04/2.06 Defined: cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))
% 0.04/2.06 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_INF) (fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn)))))))))) of role definition named cCKB_INF_def
% 0.04/2.06 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_INF) (fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn))))))))))
% 0.04/2.06 Defined: cCKB_INF:=(fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn)))))))))
% 0.04/2.06 FOF formula (cCKB_INF cCKB6_BLACK) of role conjecture named cCKB6_L50000
% 0.04/2.06 Conjecture to prove = (cCKB_INF cCKB6_BLACK):Prop
% 0.04/2.06 We need to prove ['(cCKB_INF cCKB6_BLACK)']
% 0.04/2.06 Parameter fofType:Type.
% 0.04/2.06 Parameter c1:fofType.
% 0.04/2.06 Parameter s:(fofType->fofType).
% 0.04/2.06 Definition cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))):(fofType->(fofType->Prop)).
% 0.04/2.06 Definition cCKB_INF:=(fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn))))))))):((fofType->(fofType->Prop))->Prop).
% 0.04/2.06 Definition cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))):((fofType->(fofType->(fofType->(fofType->Prop))))->Prop).
% 0.04/2.06 Definition cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))):((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 0.04/2.06 Trying to prove (cCKB_INF cCKB6_BLACK)
% 0.04/2.06 Found eq_ref000:=(eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))):(((((x Xx2) Xy2) Xu) Xv)->((((x Xx2) Xy2) Xu) Xv))
% 0.04/2.06 Found (eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.06 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.06 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.06 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.07 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.07 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 0.04/2.07 Found (and_rect00 (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 0.04/2.07 Found ((and_rect0 ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 0.04/2.07 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 0.04/2.07 Found (fun (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 0.04/2.07 Found (fun (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 0.04/2.07 Found (fun (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 0.04/2.07 Found (fun (Xy2:fofType) (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xu:fofType) (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 0.04/2.07 Found (fun (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 1.69/2.89 Found eq_ref000:=(eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))):(((((x Xx2) Xy2) Xu) Xv)->((((x Xx2) Xy2) Xu) Xv))
% 1.69/2.89 Found (eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 1.69/2.89 Found (and_rect00 (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 1.69/2.89 Found ((and_rect0 ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 1.69/2.89 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 1.69/2.89 Found (fun (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 1.69/2.89 Found (fun (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 1.69/2.89 Found (fun (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 10.59/11.74 Found (fun (Xy2:fofType) (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xu:fofType) (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 10.59/11.74 Found (fun (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (forall (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 10.59/11.74 Found x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 10.59/11.74 Found (fun (x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> x000) as proof of ((and (((eq fofType) Xx1) Xx2)) ((((x Xx2) Xy2) Xu) Xv))
% 10.59/11.74 Found (fun (x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> x000) as proof of (P ((((x Xx2) Xy2) Xu) Xv))
% 10.59/11.74 Found x3:((Xw c1) c1)
% 10.59/11.74 Instantiate: x0:=c1:fofType;x1:=c1:fofType
% 10.59/11.74 Found (fun (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3) as proof of ((Xw x0) x1)
% 10.59/11.74 Found (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3) as proof of ((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw x0) x1))
% 10.59/11.74 Found (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3) as proof of (((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw x0) x1)))
% 10.59/11.74 Found (and_rect00 (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3)) as proof of ((Xw x0) x1)
% 10.59/11.74 Found ((and_rect0 ((Xw x0) x1)) (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3)) as proof of ((Xw x0) x1)
% 10.59/11.74 Found (((fun (P:Type) (x3:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x3) x2)) ((Xw x0) x1)) (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3)) as proof of ((Xw x0) x1)
% 10.59/11.74 Found (fun (x2:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x3:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x3) x2)) ((Xw x0) x1)) (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3))) as proof of ((Xw x0) x1)
% 10.59/11.74 Found (fun (Xw:(fofType->(fofType->Prop))) (x2:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x3:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x3) x2)) ((Xw x0) x1)) (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3))) as proof of (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw x0) x1))
% 27.90/29.04 Found (fun (Xw:(fofType->(fofType->Prop))) (x2:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x3:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x3) x2)) ((Xw x0) x1)) (fun (x3:((Xw c1) c1)) (x4:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x3))) as proof of ((cCKB6_BLACK x0) x1)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 27.90/29.04 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 27.90/29.04 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 27.90/29.04 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 27.90/29.04 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 27.90/29.04 Found x20:(P Xx1)
% 27.90/29.04 Found (fun (x20:(P Xx1))=> x20) as proof of (P Xx1)
% 27.90/29.04 Found (fun (x20:(P Xx1))=> x20) as proof of (P0 Xx1)
% 27.90/29.04 Found x20:(P Xy1)
% 27.90/29.04 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 27.90/29.04 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 27.90/29.04 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 27.90/29.04 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 27.90/29.04 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 27.90/29.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 27.90/29.04 Found eq_ref00:=(eq_ref0 Xx2):(((eq fofType) Xx2) Xx2)
% 27.90/29.04 Found (eq_ref0 Xx2) as proof of (((eq fofType) Xx2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 27.90/29.04 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 27.90/29.04 Found eq_trans00000:=(eq_trans0000 x01):((((eq fofType) b) Xx2)->(((eq fofType) Xx1) Xx2))
% 27.90/29.04 Found (eq_trans0000 x01) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xx2))
% 27.90/29.04 Found (eq_trans0000 x01) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xx2))
% 33.91/35.03 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01)) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xx2))
% 33.91/35.03 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xx2)))
% 33.91/35.03 Found (and_rect00 (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01))) as proof of (((eq fofType) b) Xx2)
% 33.91/35.03 Found ((and_rect0 (((eq fofType) b) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01))) as proof of (((eq fofType) b) Xx2)
% 33.91/35.03 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01))) as proof of (((eq fofType) b) Xx2)
% 33.91/35.03 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01))) as proof of (((eq fofType) b) Xx2)
% 33.91/35.03 Found ((eq_trans0000 ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (eq_trans0000 x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found (((eq_trans000 Xx1) ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xx1) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((eq_trans000 Xx1) x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found ((((fun (b:fofType)=> ((eq_trans00 b) Xx2)) Xx1) ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xx1) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((fun (b:fofType)=> ((eq_trans00 b) Xx2)) Xx1) x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found ((((fun (b:fofType)=> (((eq_trans0 Xx1) b) Xx2)) Xx1) ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xx1) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((fun (b:fofType)=> (((eq_trans0 Xx1) b) Xx2)) Xx1) x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found ((((fun (b:fofType)=> ((((eq_trans fofType) Xx1) b) Xx2)) Xx1) ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xx1) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((fun (b:fofType)=> ((((eq_trans fofType) Xx1) b) Xx2)) Xx1) x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found ((((fun (b:fofType)=> ((((eq_trans fofType) Xx1) b) Xx2)) Xx1) ((eq_ref fofType) Xx1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xx1) Xx2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((fun (b:fofType)=> ((((eq_trans fofType) Xx1) b) Xx2)) Xx1) x01)))) as proof of (((eq fofType) Xx1) Xx2)
% 33.91/35.03 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 33.91/35.03 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 33.91/35.03 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 33.91/35.03 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 33.91/35.03 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 33.91/35.03 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 33.91/35.03 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 33.91/35.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 33.91/35.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 33.91/35.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 33.91/35.03 Found x20:(P Xy1)
% 33.91/35.03 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 33.91/35.03 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 37.99/39.15 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 37.99/39.15 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 37.99/39.15 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 37.99/39.15 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 37.99/39.15 Found x010:=(x01 (fun (x2:fofType)=> (P Xy1))):((P Xy1)->(P Xy1))
% 37.99/39.15 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 37.99/39.15 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 37.99/39.15 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 37.99/39.15 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 37.99/39.15 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 37.99/39.15 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 37.99/39.15 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found and_rect0000:=(and_rect000 (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))):(((((x Xx2) Xy2) Xu) Xv)->((((x Xx2) Xy2) Xu) Xv))
% 37.99/39.15 Found (and_rect000 (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xy2))
% 37.99/39.15 Found ((and_rect00 eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xy2))
% 37.99/39.15 Found ((and_rect00 eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xy2))
% 37.99/39.15 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((and_rect00 eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xy2))
% 37.99/39.15 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((and_rect00 eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(((eq fofType) b) Xy2)))
% 37.99/39.15 Found (and_rect00 (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((and_rect00 eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found ((and_rect0 (((eq fofType) b) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((and_rect0 (((eq fofType) b) Xy2)) eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of (((eq fofType) b) Xy2)
% 37.99/39.15 Found ((eq_trans0000 ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) b) Xy2)) eq_trans0000) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found (((eq_trans000 Xy1) ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (eq_trans000 Xy1)) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found ((((fun (b:fofType)=> ((eq_trans00 b) Xy2)) Xy1) ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) ((fun (b:fofType)=> ((eq_trans00 b) Xy2)) Xy1)) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found ((((fun (b:fofType)=> (((eq_trans0 Xy1) b) Xy2)) Xy1) ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) ((fun (b:fofType)=> (((eq_trans0 Xy1) b) Xy2)) Xy1)) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found ((((fun (b:fofType)=> ((((eq_trans fofType) Xy1) b) Xy2)) Xy1) ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) ((fun (b:fofType)=> ((((eq_trans fofType) Xy1) b) Xy2)) Xy1)) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found ((((fun (b:fofType)=> ((((eq_trans fofType) Xy1) b) Xy2)) Xy1) ((eq_ref fofType) Xy1)) (((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> ((((fun (P:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P) x2) x00)) (((eq fofType) Xy1) Xy2)) ((fun (b:fofType)=> ((((eq_trans fofType) Xy1) b) Xy2)) Xy1)) (fun (x2:fofType)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of (((eq fofType) Xy1) Xy2)
% 44.20/45.32 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 44.20/45.32 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 44.20/45.32 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 44.20/45.32 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 44.20/45.32 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 44.20/45.32 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 44.20/45.32 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 44.20/45.32 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 44.20/45.32 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 44.20/45.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 44.20/45.32 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 62.50/63.70 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.50/63.70 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 62.50/63.70 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.50/63.70 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 62.50/63.70 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found x20:(P Xy1)
% 62.50/63.70 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 62.50/63.70 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.50/63.70 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 62.50/63.70 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.50/63.70 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 62.50/63.70 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 62.50/63.70 Found x020:=(x02 (fun (x2:fofType)=> (P Xy1))):((P Xy1)->(P Xy1))
% 62.50/63.70 Found (x02 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 62.50/63.70 Found (x02 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 62.50/63.70 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.50/63.70 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 62.50/63.70 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 62.50/63.70 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 62.50/63.70 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 62.50/63.70 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 62.50/63.70 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 75.92/77.07 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.92/77.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 75.92/77.07 Found (fun (x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> x000) as proof of ((and (((eq fofType) Xx1) Xx2)) ((((x Xx2) Xy2) Xu) Xv))
% 75.92/77.07 Found (fun (x000:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> x000) as proof of (P ((((x Xx2) Xy2) Xu) Xv))
% 75.92/77.07 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 75.92/77.07 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 75.92/77.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.92/77.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 75.92/77.07 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 75.92/77.07 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 75.92/77.07 Found iff_sym as proof of b
% 75.92/77.07 Found conj10:=(conj1 ((((x Xx2) Xy2) Xu) Xv)):(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))))
% 75.92/77.07 Found (conj1 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(P b)))
% 75.92/77.07 Found ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(P b)))
% 75.92/77.07 Found ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(P b)))
% 75.92/77.07 Found ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(P b)))
% 75.92/77.07 Found ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->(P b)))
% 75.92/77.07 Found (and_rect00 ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))) as proof of (P b)
% 75.92/77.07 Found ((and_rect0 (P b)) ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))) as proof of (P b)
% 75.92/77.07 Found (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) (P b)) ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))) as proof of (P b)
% 75.92/77.07 Found (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) (P b)) ((conj ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))) as proof of (P b)
% 75.92/77.07 Found x2:(P Xy1)
% 75.92/77.07 Instantiate: b:=Xy1:fofType
% 75.92/77.07 Found x2 as proof of (P0 b)
% 75.92/77.07 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 75.92/77.07 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 75.92/77.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 75.92/77.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 75.92/77.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 83.52/84.66 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 83.52/84.66 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 83.52/84.66 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 83.52/84.66 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 83.52/84.66 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 83.52/84.66 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 83.52/84.66 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 83.52/84.66 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 83.52/84.66 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 83.52/84.66 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) Xy1) Xy2))->(P0 (((eq fofType) Xy1) Xy2)))
% 83.52/84.66 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) Xy1) Xy2))->(P0 (((eq fofType) Xy1) Xy2)))
% 83.52/84.66 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 83.52/84.66 Found (eq_ref0 b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 83.52/84.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 83.52/84.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 83.52/84.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 83.52/84.66 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 83.52/84.66 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 83.52/84.66 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 83.52/84.66 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 83.52/84.66 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/104.49 Found (eq_ref0 b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 103.33/104.49 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 103.33/104.49 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 103.33/104.49 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 103.33/104.49 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 103.33/104.49 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 103.33/104.49 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 103.33/104.49 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 103.33/104.49 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 103.33/104.49 Found x2:(P0 b)
% 103.33/104.49 Instantiate: b:=Xy1:fofType
% 103.33/104.49 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 103.33/104.49 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 103.33/104.49 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 103.33/104.49 Found x20:(P Xy1)
% 103.33/104.49 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 103.33/104.49 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 103.33/104.49 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 103.33/104.49 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 103.33/104.49 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b0)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 103.33/104.49 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 103.33/104.49 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 103.33/104.49 Found x2:(P Xy2)
% 103.33/104.49 Instantiate: b:=Xy2:fofType
% 103.33/104.49 Found x2 as proof of (P0 b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 103.33/104.49 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 103.33/104.49 Found x2:(P Xy1)
% 103.33/104.49 Instantiate: b:=Xy1:fofType
% 103.33/104.49 Found x2 as proof of (P0 b)
% 103.33/104.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/104.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 103.33/104.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 116.32/117.47 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 116.32/117.47 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.32/117.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 116.32/117.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 116.32/117.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 116.32/117.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 116.32/117.47 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 116.32/117.47 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 116.32/117.47 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 116.32/117.47 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 116.32/117.47 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found x20:(P b)
% 116.32/117.47 Found (fun (x20:(P b))=> x20) as proof of (P b)
% 116.32/117.47 Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 116.32/117.47 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 116.32/117.47 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 116.32/117.47 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 116.32/117.47 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 116.32/117.47 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 116.32/117.47 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 116.32/117.47 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 116.32/117.47 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found x010:=(x01 (fun (x2:fofType)=> (P Xy1))):((P Xy1)->(P Xy1))
% 130.63/131.72 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 130.63/131.72 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 130.63/131.72 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 130.63/131.72 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 130.63/131.72 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 130.63/131.72 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 130.63/131.72 Found x20:(P Xy2)
% 130.63/131.72 Found (fun (x20:(P Xy2))=> x20) as proof of (P Xy2)
% 130.63/131.72 Found (fun (x20:(P Xy2))=> x20) as proof of (P0 Xy2)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 130.63/131.72 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 130.63/131.72 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 130.63/131.72 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found x2:(P0 b)
% 130.63/131.72 Instantiate: b:=Xy1:fofType
% 130.63/131.72 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 130.63/131.72 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 130.63/131.72 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 130.63/131.72 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 130.63/131.72 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 130.63/131.72 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 130.63/131.72 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 130.63/131.72 Found x2:(P0 b)
% 130.63/131.72 Instantiate: b:=Xy1:fofType
% 130.63/131.72 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 130.63/131.72 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 130.63/131.72 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 130.63/131.72 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 130.63/131.72 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 130.63/131.72 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 146.73/147.87 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 146.73/147.87 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 146.73/147.87 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 146.73/147.87 Found x2:(P Xy2)
% 146.73/147.87 Instantiate: b:=Xy2:fofType
% 146.73/147.87 Found x2 as proof of (P0 b)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 146.73/147.87 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found x2:(P Xy2)
% 146.73/147.87 Instantiate: b:=Xy2:fofType
% 146.73/147.87 Found x2 as proof of (P0 b)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 146.73/147.87 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 146.73/147.87 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 146.73/147.87 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 146.73/147.87 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 146.73/147.87 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 146.73/147.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 146.73/147.87 Found eq_ref000:=(eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))):(((((x Xx2) Xy2) Xu) Xv)->((((x Xx2) Xy2) Xu) Xv))
% 146.73/147.87 Found (eq_ref00 (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b))
% 146.73/147.87 Found ((eq_ref0 b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b))
% 146.73/147.87 Found (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b))
% 146.73/147.87 Found (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b))
% 146.73/147.87 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b))
% 146.73/147.87 Found (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))) as proof of (((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->((and (((eq fofType) Xx1) Xx2)) b)))
% 146.73/147.87 Found (and_rect00 (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) b)
% 146.73/147.87 Found ((and_rect0 ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) b)
% 146.73/147.87 Found (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) b)
% 147.03/148.10 Found (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of ((and (((eq fofType) Xx1) Xx2)) b)
% 147.03/148.10 Found (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))) as proof of (P b)
% 147.03/148.10 Found ((eq_sym0000 ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 147.03/148.10 Found ((eq_sym0000 ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 147.03/148.10 Found (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) b))=> ((eq_sym000 x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) b)) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) b) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 147.03/148.10 Found (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> (((eq_sym00 (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 147.03/148.10 Found (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> ((((eq_sym0 (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 147.03/148.10 Found (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> (((((eq_sym Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv)))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 152.03/153.12 Found (fun (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> (((((eq_sym Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))))) as proof of ((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))
% 152.03/153.12 Found (fun (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> (((((eq_sym Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))))) as proof of (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))
% 152.03/153.12 Found (fun (Xu:fofType) (Xv:fofType) (x00:((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)))=> (((fun (x2:(((eq Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))))=> (((((eq_sym Prop) (((eq fofType) Xy1) Xy2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) x2) (and (((eq fofType) Xx1) Xx2)))) ((eq_ref Prop) (((eq fofType) Xy1) Xy2))) (((fun (P0:Type) (x2:(((((x Xx1) Xy1) Xu) Xv)->(((((x Xx2) Xy2) Xu) Xv)->P0)))=> (((((and_rect ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv)) P0) x2) x00)) ((and (((eq fofType) Xx1) Xx2)) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2))))) (fun (x01:((((x Xx1) Xy1) Xu) Xv))=> (((eq_ref Prop) (forall (P:(fofType->Prop)), ((P Xy1)->(P Xy2)))) (fun (x2:Prop)=> ((((x Xx2) Xy2) Xu) Xv))))))) as proof of (forall (Xv:fofType), (((and ((((x Xx1) Xy1) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))
% 152.03/153.12 Found x2:(P Xy1)
% 152.03/153.12 Instantiate: b:=Xy1:fofType
% 152.03/153.12 Found x2 as proof of (P0 b)
% 152.03/153.12 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 152.03/153.12 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 152.03/153.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 152.03/153.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 152.03/153.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 152.03/153.12 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 152.03/153.12 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 152.03/153.12 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 152.03/153.12 Found x20:(P Xy2)
% 152.03/153.12 Found (fun (x20:(P Xy2))=> x20) as proof of (P Xy2)
% 152.03/153.12 Found (fun (x20:(P Xy2))=> x20) as proof of (P0 Xy2)
% 152.03/153.12 Found eq_ref00:=(eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))):(((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))
% 159.13/160.24 Found (eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) b)
% 159.13/160.24 Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) b)
% 159.13/160.24 Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) b)
% 159.13/160.24 Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))) b)
% 159.13/160.24 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 159.13/160.24 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 159.13/160.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 159.13/160.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 159.13/160.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 159.13/160.24 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 159.13/160.24 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 159.13/160.24 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 159.13/160.24 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 159.13/160.24 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 159.13/160.24 Found x020:=(x02 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% 159.13/160.24 Found (x02 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% 159.13/160.24 Found (x02 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% 159.13/160.24 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) Xy1) Xy2))->(P0 (((eq fofType) Xy1) Xy2)))
% 159.13/160.24 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 159.13/160.24 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 159.13/160.24 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 159.13/160.24 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 159.13/160.24 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) Xy1) Xy2))->(P0 (((eq fofType) Xy1) Xy2)))
% 159.13/160.24 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found ((eq_ref0 (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found (((eq_ref Prop) (((eq fofType) Xy1) Xy2)) P0) as proof of (P1 (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.23/174.39 Found (eq_ref0 b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.23/174.39 Found (eq_ref0 b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((((x Xx2) Xy2) Xu) Xv))
% 173.23/174.39 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 173.23/174.39 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 173.23/174.39 Found x020:=(x02 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% 173.23/174.39 Found (x02 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% 173.23/174.39 Found (x02 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% 173.23/174.39 Found x010:=(x01 (fun (x2:fofType)=> (P Xy2))):((P Xy2)->(P Xy2))
% 173.23/174.39 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 173.23/174.39 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 173.23/174.39 Found x2:(P Xy2)
% 173.23/174.39 Instantiate: b:=Xy2:fofType
% 173.23/174.39 Found x2 as proof of (P0 b)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 173.23/174.39 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 173.23/174.39 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 173.23/174.39 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 173.23/174.39 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 173.23/174.39 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 173.23/174.39 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 173.23/174.39 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 173.23/174.39 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 184.75/185.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 184.75/185.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 184.75/185.88 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found x010:=(x01 (fun (x2:fofType)=> (P Xy2))):((P Xy2)->(P Xy2))
% 184.75/185.88 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 184.75/185.88 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 184.75/185.88 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 184.75/185.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 184.75/185.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 184.75/185.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 184.75/185.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 184.75/185.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 184.75/185.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found x2:(P0 b)
% 184.75/185.88 Instantiate: b:=Xy1:fofType
% 184.75/185.88 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 184.75/185.88 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 184.75/185.88 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 184.75/185.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 184.75/185.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 184.75/185.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 184.75/185.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.95/202.07 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 200.95/202.07 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 200.95/202.07 Found x20:(P Xy1)
% 200.95/202.07 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 200.95/202.07 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 200.95/202.07 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.95/202.07 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 200.95/202.07 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 200.95/202.07 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 200.95/202.07 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 200.95/202.07 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found x2:(P Xy2)
% 200.95/202.07 Instantiate: b:=Xy2:fofType
% 200.95/202.07 Found x2 as proof of (P0 b)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 200.95/202.07 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 200.95/202.07 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 200.95/202.07 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 200.95/202.07 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 200.95/202.07 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 200.95/202.07 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 200.95/202.07 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy2)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.65/220.78 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 219.65/220.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 219.65/220.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 219.65/220.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 219.65/220.78 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 219.65/220.78 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 219.65/220.78 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 219.65/220.78 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 219.65/220.78 Found x010:=(x01 (fun (x2:fofType)=> (P Xy2))):((P Xy2)->(P Xy2))
% 219.65/220.78 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 219.65/220.78 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 219.65/220.78 Found x2:(P Xy1)
% 219.65/220.78 Instantiate: b:=Xy1:fofType
% 219.65/220.78 Found x2 as proof of (P0 b)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.65/220.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 219.65/220.78 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.65/220.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 219.65/220.78 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.65/220.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 219.65/220.78 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.65/220.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) Xy1) Xy2))
% 219.65/220.78 Found eq_ref00:=(eq_ref0 ((((x Xx2) Xy2) Xu) Xv)):(((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) ((((x Xx2) Xy2) Xu) Xv))
% 219.65/220.78 Found (eq_ref0 ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 219.65/220.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 229.65/230.78 Found ((eq_ref Prop) ((((x Xx2) Xy2) Xu) Xv)) as proof of (((eq Prop) ((((x Xx2) Xy2) Xu) Xv)) b)
% 229.65/230.78 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 229.65/230.78 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 229.65/230.78 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 229.65/230.78 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 229.65/230.78 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 229.65/230.78 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 229.65/230.78 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 229.65/230.78 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 229.65/230.78 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 229.65/230.78 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 229.65/230.78 Found x010:=(x01 (fun (x2:fofType)=> (P Xy2))):((P Xy2)->(P Xy2))
% 229.65/230.78 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 229.65/230.78 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 229.65/230.78 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) (fun (x2:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) x0)) (((eq fofType) Xv) x1))->False))))))
% 229.65/230.78 Found (eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 229.65/230.78 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 229.65/230.78 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 229.65/230.78 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 229.65/230.78 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) (fun (x2:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) x0)) (((eq fofType) Xv) x1))->False))))))
% 245.75/246.89 Found (eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))) b)
% 245.75/246.89 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 245.75/246.89 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 245.75/246.89 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 245.75/246.89 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 245.75/246.89 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 245.75/246.89 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 245.75/246.89 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 245.75/246.89 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 245.75/246.89 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 245.75/246.89 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 245.75/246.89 Found x2:(P Xy2)
% 245.75/246.89 Instantiate: b:=Xy2:fofType
% 245.75/246.89 Found x2 as proof of (P0 b)
% 245.75/246.89 Found x010:=(x01 (fun (x2:fofType)=> (P Xy2))):((P Xy2)->(P Xy2))
% 245.75/246.89 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 245.75/246.89 Found (x01 (fun (x2:fofType)=> (P Xy2))) as proof of (P0 Xy2)
% 245.75/246.89 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 245.75/246.89 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 245.75/246.89 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 245.75/246.89 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 245.75/246.89 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 257.46/258.54 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 257.46/258.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 257.46/258.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 257.46/258.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 257.46/258.54 Found x20:(P b)
% 257.46/258.54 Found (fun (x20:(P b))=> x20) as proof of (P b)
% 257.46/258.54 Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% 257.46/258.54 Found x20:(P Xy1)
% 257.46/258.54 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 257.46/258.54 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 257.46/258.54 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 257.46/258.54 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 257.46/258.54 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 274.06/275.13 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found x010:=(x01 (fun (x2:fofType)=> (P Xy1))):((P Xy1)->(P Xy1))
% 274.06/275.13 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 274.06/275.13 Found (x01 (fun (x2:fofType)=> (P Xy1))) as proof of (P0 Xy1)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 274.06/275.13 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.06/275.13 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 274.06/275.13 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.06/275.13 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 274.06/275.13 Found x20:(P Xy2)
% 274.06/275.13 Found (fun (x20:(P Xy2))=> x20) as proof of (P Xy2)
% 274.06/275.13 Found (fun (x20:(P Xy2))=> x20) as proof of (P0 Xy2)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.06/275.13 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 274.06/275.13 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found x20:(P Xy2)
% 274.06/275.13 Found (fun (x20:(P Xy2))=> x20) as proof of (P Xy2)
% 274.06/275.13 Found (fun (x20:(P Xy2))=> x20) as proof of (P0 Xy2)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.06/275.13 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 274.06/275.13 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 274.06/275.13 Found eq_ref00:=(eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))):(((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and
% ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))))
% 274.06/275.14 Found (eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and
% ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 274.06/275.14 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 274.06/275.14 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 276.87/277.90 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 276.87/277.90 Found eq_ref00:=(eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))):(((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and
% ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))))))
% 276.87/277.90 Found (eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and
% ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 276.87/277.90 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 276.87/277.90 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 293.06/294.19 Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and
% ((and ((((x (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((x (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) x0)) (((eq fofType) Xv) x1))->False)))))))))) b)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 293.06/294.19 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found x2:(P0 b)
% 293.06/294.19 Instantiate: b:=Xy1:fofType
% 293.06/294.19 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 293.06/294.19 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 293.06/294.19 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 293.06/294.19 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 293.06/294.19 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 293.06/294.19 Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy1)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 293.06/294.19 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b0)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 293.06/294.19 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 293.06/294.19 Found x2:(P0 b)
% 293.06/294.19 Instantiate: b:=Xy1:fofType
% 293.06/294.19 Found (fun (x2:(P0 b))=> x2) as proof of (P0 Xy1)
% 293.06/294.19 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 Xy1))
% 293.06/294.19 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 293.06/294.19 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 293.06/294.19 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b0)
% 293.06/294.19 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 293.06/294.19 Found (eq_ref0 b0)
%------------------------------------------------------------------------------