TSTP Solution File: SYO148^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO148^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:45 EDT 2022
% Result : Timeout 289.40s 289.56s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO148^5 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.13 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Computer : n006.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % RAMPerCPU : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % DateTime : Fri Mar 11 16:37:59 EST 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.36 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.36 Python 2.7.5
% 9.13/9.32 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 9.13/9.32 FOF formula (<kernel.Constant object at 0x2b5096e70a70>, <kernel.Type object at 0x2b5096e70b90>) of role type named a_type
% 9.13/9.32 Using role type
% 9.13/9.32 Declaring a:Type
% 9.13/9.32 FOF formula (<kernel.Constant object at 0xce42d8>, <kernel.DependentProduct object at 0x2b5096e70098>) of role type named cZ
% 9.13/9.32 Using role type
% 9.13/9.32 Declaring cZ:(a->Prop)
% 9.13/9.32 FOF formula (<kernel.Constant object at 0x2b5096e70200>, <kernel.DependentProduct object at 0x2b5096e70128>) of role type named cY
% 9.13/9.32 Using role type
% 9.13/9.32 Declaring cY:(a->Prop)
% 9.13/9.32 FOF formula (<kernel.Constant object at 0x2b5096e70950>, <kernel.DependentProduct object at 0x2b5096e75368>) of role type named cX
% 9.13/9.32 Using role type
% 9.13/9.32 Declaring cX:(a->Prop)
% 9.13/9.32 FOF formula ((forall (U:a), ((iff ((cX U)->False)) ((iff (cY U)) (cZ U))))->(((eq (a->Prop)) cX) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))) of role conjecture named cBOOL25
% 9.13/9.32 Conjecture to prove = ((forall (U:a), ((iff ((cX U)->False)) ((iff (cY U)) (cZ U))))->(((eq (a->Prop)) cX) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))):Prop
% 9.13/9.32 Parameter a_DUMMY:a.
% 9.13/9.32 We need to prove ['((forall (U:a), ((iff ((cX U)->False)) ((iff (cY U)) (cZ U))))->(((eq (a->Prop)) cX) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))']
% 9.13/9.32 Parameter a:Type.
% 9.13/9.32 Parameter cZ:(a->Prop).
% 9.13/9.32 Parameter cY:(a->Prop).
% 9.13/9.32 Parameter cX:(a->Prop).
% 9.13/9.32 Trying to prove ((forall (U:a), ((iff ((cX U)->False)) ((iff (cY U)) (cZ U))))->(((eq (a->Prop)) cX) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))
% 9.13/9.32 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 9.13/9.32 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 9.13/9.32 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 9.13/9.32 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 9.13/9.32 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 9.13/9.32 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 9.13/9.32 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found eq_ref00:=(eq_ref0 cX):(((eq (a->Prop)) cX) cX)
% 9.13/9.32 Found (eq_ref0 cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 9.13/9.32 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 9.13/9.32 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 9.13/9.32 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 9.13/9.32 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 9.13/9.32 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 9.13/9.32 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found x00:(P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 9.13/9.32 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 9.13/9.32 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 12.23/12.42 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 12.23/12.42 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 12.23/12.42 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 12.23/12.42 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 12.23/12.42 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 12.23/12.42 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 12.23/12.42 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 12.23/12.42 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 12.23/12.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 12.23/12.42 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 12.23/12.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 12.23/12.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 12.23/12.42 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 12.23/12.42 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 12.23/12.42 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 12.23/12.42 Found (eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 12.23/12.42 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 12.23/12.42 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 12.23/12.42 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 12.23/12.42 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 12.23/12.42 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 12.23/12.42 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 12.23/12.42 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 12.23/12.42 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 22.93/23.09 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 22.93/23.09 Found x10:(P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 22.93/23.09 Found x10:(P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 22.93/23.09 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 22.93/23.09 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.93/23.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 22.93/23.09 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 22.93/23.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.93/23.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 22.93/23.09 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 22.93/23.09 Found x10:(P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 22.93/23.09 Found x10:(P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 22.93/23.09 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 22.93/23.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.93/23.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 22.93/23.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 22.93/23.09 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 22.93/23.09 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 22.93/23.09 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 22.93/23.09 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.23/27.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.23/27.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 27.23/27.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.23/27.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 27.23/27.46 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 27.23/27.46 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 27.23/27.46 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 27.23/27.46 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 27.23/27.46 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 27.23/27.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.23/27.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.23/27.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 27.23/27.46 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 27.23/27.46 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.33/37.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 37.33/37.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.33/37.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 37.33/37.55 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 37.33/37.55 Found x3:(cX U)
% 37.33/37.55 Found x3 as proof of (cX U)
% 37.33/37.55 Found x0:(P cX)
% 37.33/37.55 Instantiate: b:=cX:(a->Prop)
% 37.33/37.55 Found x0 as proof of (P0 b)
% 37.33/37.55 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 37.33/37.55 Found (eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 37.33/37.55 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 37.33/37.55 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 37.33/37.55 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 37.33/37.55 Found x3:(cX U)
% 37.33/37.55 Found x3 as proof of (cX U)
% 37.33/37.55 Found x0:(P cX)
% 37.33/37.55 Instantiate: f:=cX:(a->Prop)
% 37.33/37.55 Found x0 as proof of (P0 f)
% 37.33/37.55 Found x0:(P cX)
% 37.33/37.55 Instantiate: f:=cX:(a->Prop)
% 37.33/37.55 Found x0 as proof of (P0 f)
% 37.33/37.55 Found x4:(cX U)
% 37.33/37.55 Found x4 as proof of (cX U)
% 37.33/37.55 Found x4:(cX U)
% 37.33/37.55 Found x4 as proof of (cX U)
% 37.33/37.55 Found x0:(P cX)
% 37.33/37.55 Instantiate: b:=cX:(a->Prop)
% 37.33/37.55 Found x0 as proof of (P0 b)
% 37.33/37.55 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 37.33/37.55 Found (eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 44.75/44.93 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 44.75/44.93 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 44.75/44.93 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 44.75/44.93 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 44.75/44.93 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 44.75/44.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 44.75/44.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 44.75/44.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 44.75/44.93 Found eq_ref00:=(eq_ref0 cX):(((eq (a->Prop)) cX) cX)
% 44.75/44.93 Found (eq_ref0 cX) as proof of (((eq (a->Prop)) cX) b)
% 44.75/44.93 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 44.75/44.94 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 44.75/44.94 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 44.75/44.94 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 44.75/44.94 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.75/44.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 44.75/44.94 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 44.75/44.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.75/44.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 44.75/44.94 Found x3:(cX U)
% 44.75/44.94 Found x3 as proof of (cX U)
% 44.75/44.94 Found x0:(P cX)
% 44.75/44.94 Instantiate: f:=cX:(a->Prop)
% 44.75/44.94 Found x0 as proof of (P0 f)
% 44.75/44.94 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 44.75/44.94 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (not ((iff (cY x)) (cZ x)))))
% 44.75/44.94 Found x0:(P cX)
% 44.75/44.94 Instantiate: f:=cX:(a->Prop)
% 44.75/44.94 Found x0 as proof of (P0 f)
% 44.75/44.94 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 44.75/44.94 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not ((iff (cY x1)) (cZ x1))))
% 44.75/44.94 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (not ((iff (cY x)) (cZ x)))))
% 44.75/44.94 Found x3:(cX U)
% 44.75/44.94 Found x3 as proof of (cX U)
% 44.75/44.94 Found x4:(cX U)
% 44.75/44.94 Found x4 as proof of (cX U)
% 44.75/44.94 Found eta_expansion_dep000:=(eta_expansion_dep00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 49.47/49.67 Found (eta_expansion_dep00 cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 49.47/49.67 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 49.47/49.67 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 49.47/49.67 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 49.47/49.67 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 49.47/49.67 Found x4:(cX U)
% 49.47/49.67 Found x4 as proof of (cX U)
% 49.47/49.67 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 49.47/49.67 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.47/49.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 49.47/49.67 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 49.47/49.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.47/49.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 49.47/49.67 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 49.47/49.67 Found (eta_expansion_dep00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 49.47/49.67 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 49.47/49.67 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 49.47/49.67 Found x0:(P0 b)
% 49.47/49.67 Instantiate: b:=cX:(a->Prop)
% 49.47/49.67 Found (fun (x0:(P0 b))=> x0) as proof of (P0 cX)
% 49.47/49.67 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 cX))
% 49.47/49.67 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 49.47/49.67 Found x0:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 49.47/49.67 Instantiate: b:=(fun (U:a)=> (((iff (cY U)) (cZ U))->False)):(a->Prop)
% 49.47/49.67 Found x0 as proof of (P0 b)
% 49.47/49.67 Found eq_ref00:=(eq_ref0 cX):(((eq (a->Prop)) cX) cX)
% 49.47/49.67 Found (eq_ref0 cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 49.47/49.67 Found x00:(P cX)
% 57.84/58.06 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 57.84/58.06 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 57.84/58.06 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 57.84/58.06 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found eq_ref00:=(eq_ref0 cX):(((eq (a->Prop)) cX) cX)
% 57.84/58.06 Found (eq_ref0 cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 57.84/58.06 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 57.84/58.06 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 57.84/58.06 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 57.84/58.06 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 57.84/58.06 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 57.84/58.06 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 57.84/58.06 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 57.84/58.06 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b0)
% 57.84/58.06 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b0)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b0)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b0)
% 57.84/58.06 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b0)
% 57.84/58.06 Found x3:(cX U)
% 57.84/58.06 Found x3 as proof of (cX U)
% 57.84/58.06 Found x30:(P cX)
% 57.84/58.06 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 57.84/58.06 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 57.84/58.06 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 57.84/58.06 Found (eta_expansion_dep00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 57.84/58.06 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 57.84/58.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 57.84/58.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 57.84/58.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 57.84/58.06 Found x0:(P0 b)
% 57.84/58.06 Instantiate: b:=cX:(a->Prop)
% 57.84/58.06 Found (fun (x0:(P0 b))=> x0) as proof of (P0 cX)
% 57.84/58.06 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 cX))
% 57.84/58.06 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 57.84/58.06 Found x00:(P cX)
% 57.84/58.06 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 57.84/58.06 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 57.84/58.06 Found eta_expansion_dep000:=(eta_expansion_dep00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 61.74/61.93 Found (eta_expansion_dep00 cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 61.74/61.93 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 61.74/61.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 61.74/61.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 61.74/61.93 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 61.74/61.93 Found x0:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 61.74/61.93 Instantiate: b:=(fun (U:a)=> (not ((iff (cY U)) (cZ U)))):(a->Prop)
% 61.74/61.93 Found x0 as proof of (P0 b)
% 61.74/61.93 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 61.74/61.93 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 61.74/61.93 Found x0:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 61.74/61.93 Instantiate: f:=(fun (U:a)=> (((iff (cY U)) (cZ U))->False)):(a->Prop)
% 61.74/61.93 Found x0 as proof of (P0 f)
% 61.74/61.93 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 61.74/61.93 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cX x)))
% 61.74/61.93 Found x0:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 61.74/61.93 Instantiate: f:=(fun (U:a)=> (((iff (cY U)) (cZ U))->False)):(a->Prop)
% 61.74/61.93 Found x0 as proof of (P0 f)
% 61.74/61.93 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 61.74/61.93 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cX x1))
% 61.74/61.93 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cX x)))
% 61.74/61.93 Found x3:(cX U)
% 61.74/61.93 Found x3 as proof of (cX U)
% 61.74/61.93 Found x3:(cX U)
% 61.74/61.93 Found x3 as proof of (cX U)
% 61.74/61.93 Found x1:(P (cX x0))
% 61.74/61.93 Instantiate: b:=(cX x0):Prop
% 61.74/61.93 Found x1 as proof of (P0 b)
% 61.74/61.93 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 61.74/61.93 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found x1:(P (cX x0))
% 61.74/61.93 Instantiate: b:=(cX x0):Prop
% 61.74/61.93 Found x1 as proof of (P0 b)
% 61.74/61.93 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 61.74/61.93 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 61.74/61.93 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 68.05/68.26 Found x3:(cX U)
% 68.05/68.26 Found x3 as proof of (cX U)
% 68.05/68.26 Found x30:(P cX)
% 68.05/68.26 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 68.05/68.26 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 68.05/68.26 Found x30:(P cX)
% 68.05/68.26 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 68.05/68.26 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 68.05/68.26 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 68.05/68.26 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 68.05/68.26 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 68.05/68.26 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 68.05/68.26 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 68.05/68.26 Found ((eta_expansion_dep0 (fun (x4:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 68.05/68.26 Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 68.05/68.26 Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 68.05/68.26 Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 68.05/68.26 Found x3:(cX U)
% 68.05/68.26 Found x3 as proof of (cX U)
% 68.05/68.26 Found x4:(cX U)
% 68.05/68.26 Found x4 as proof of (cX U)
% 68.05/68.26 Found x4:(cX U)
% 68.05/68.26 Found x4 as proof of (cX U)
% 68.05/68.26 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 68.05/68.26 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 68.05/68.26 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 68.05/68.26 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 68.05/68.26 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 68.05/68.26 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 68.05/68.26 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found x4:(cX U)
% 75.65/75.82 Found x4 as proof of (cX U)
% 75.65/75.82 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 75.65/75.82 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 75.65/75.82 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 75.65/75.82 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 75.65/75.82 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 75.65/75.82 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 75.65/75.82 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 75.65/75.82 Found x00:(P cX)
% 75.65/75.82 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 75.65/75.82 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 75.65/75.82 Found x0:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 75.65/75.82 Instantiate: f:=(fun (U:a)=> (not ((iff (cY U)) (cZ U)))):(a->Prop)
% 75.65/75.82 Found x0 as proof of (P0 f)
% 75.65/75.82 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 75.65/75.82 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cX x)))
% 75.65/75.82 Found x0:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 75.65/75.82 Instantiate: f:=(fun (U:a)=> (not ((iff (cY U)) (cZ U)))):(a->Prop)
% 75.65/75.82 Found x0 as proof of (P0 f)
% 75.65/75.82 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 75.65/75.82 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cX x1))
% 75.65/75.82 Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cX x)))
% 75.65/75.82 Found x3:(cX U)
% 75.65/75.82 Found x3 as proof of (cX U)
% 75.65/75.82 Found x3:(cX U)
% 75.65/75.82 Found x3 as proof of (cX U)
% 75.65/75.82 Found x30:(P cX)
% 75.65/75.82 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 75.65/75.82 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 75.65/75.82 Found x4:(cX U)
% 75.65/75.82 Found x4 as proof of (cX U)
% 75.65/75.82 Found x4:(cX U)
% 75.65/75.82 Found x4 as proof of (cX U)
% 75.65/75.82 Found x1:(P (cX x0))
% 75.65/75.82 Instantiate: b:=(cX x0):Prop
% 75.65/75.82 Found x1 as proof of (P0 b)
% 75.65/75.82 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 75.65/75.82 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found x1:(P (cX x0))
% 75.65/75.82 Instantiate: b:=(cX x0):Prop
% 75.65/75.82 Found x1 as proof of (P0 b)
% 75.65/75.82 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 75.65/75.82 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 75.65/75.82 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 78.85/79.07 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.85/79.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.85/79.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found x00:(P cX)
% 78.85/79.07 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 78.85/79.07 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.85/79.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.85/79.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.85/79.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 78.85/79.07 Found x00:(P cX)
% 78.85/79.07 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 78.85/79.07 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 78.85/79.07 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 78.85/79.07 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 78.85/79.07 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 84.26/84.45 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 84.26/84.45 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 84.26/84.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.26/84.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 84.26/84.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 84.26/84.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 84.26/84.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 84.26/84.45 Found x3:(cX U)
% 84.26/84.45 Found x3 as proof of (cX U)
% 84.26/84.45 Found x3:(cX U)
% 84.26/84.45 Found x3 as proof of (cX U)
% 84.26/84.45 Found x3:(cX U)
% 84.26/84.45 Found x3 as proof of (cX U)
% 84.26/84.45 Found x4:(cX U)
% 84.26/84.45 Found x4 as proof of (cX U)
% 84.26/84.45 Found x5:(cX U)
% 84.26/84.45 Found x5 as proof of (cX U)
% 84.26/84.45 Found x5:(cX U)
% 84.26/84.45 Found x5 as proof of (cX U)
% 84.26/84.45 Found x30:(P cX)
% 84.26/84.45 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 84.26/84.45 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 84.26/84.45 Found x30:(P cX)
% 84.26/84.45 Found (fun (x30:(P cX))=> x30) as proof of (P cX)
% 84.26/84.45 Found (fun (x30:(P cX))=> x30) as proof of (P0 cX)
% 84.26/84.45 Found x4:(cX U)
% 84.26/84.45 Found x4 as proof of (cX U)
% 84.26/84.45 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 84.26/84.45 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 84.26/84.45 Found (eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found ((eta_expansion0 Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 84.26/84.45 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 84.26/84.45 Found (eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found ((eta_expansion0 Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 84.26/84.45 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 84.26/84.45 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 84.26/84.45 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 84.26/84.45 Found (eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 92.67/92.91 Found ((eta_expansion0 Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 92.67/92.91 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 92.67/92.91 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 92.67/92.91 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 92.67/92.91 Found x4:(cX U)
% 92.67/92.91 Found x4 as proof of (cX U)
% 92.67/92.91 Found x4:(cX U)
% 92.67/92.91 Found x4 as proof of (cX U)
% 92.67/92.91 Found x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P2 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P2 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P2 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P1 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P2 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found x3:(cX U)
% 92.67/92.91 Found x3 as proof of (cX U)
% 92.67/92.91 Found x00:(P b)
% 92.67/92.91 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 92.67/92.91 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 92.67/92.91 Found x4:(cX U)
% 92.67/92.91 Found x4 as proof of (cX U)
% 92.67/92.91 Found x4:(cX U)
% 92.67/92.91 Found x4 as proof of (cX U)
% 92.67/92.91 Found x4:(cX U)
% 92.67/92.91 Found x4 as proof of (cX U)
% 92.67/92.91 Found x10:(P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 92.67/92.91 Found x10:(P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 92.67/92.91 Found x10:(P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 92.67/92.91 Found x10:(P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 92.67/92.91 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 92.67/92.91 Found eq_ref00:=(eq_ref0 cX):(((eq (a->Prop)) cX) cX)
% 92.67/92.91 Found (eq_ref0 cX) as proof of (((eq (a->Prop)) cX) b0)
% 92.67/92.91 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b0)
% 92.67/92.91 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b0)
% 92.67/92.91 Found ((eq_ref (a->Prop)) cX) as proof of (((eq (a->Prop)) cX) b0)
% 92.67/92.91 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 92.67/92.91 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 92.67/92.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 92.67/92.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 92.67/92.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 92.67/92.91 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 92.67/92.91 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 98.44/98.65 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 98.44/98.65 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 98.44/98.65 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 98.44/98.65 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 98.44/98.65 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 98.44/98.65 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 98.44/98.65 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 98.44/98.65 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 98.44/98.65 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 98.44/98.65 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 98.44/98.65 Found x4:(cX U)
% 98.44/98.65 Found x4 as proof of (cX U)
% 98.44/98.65 Found x4:(cX U)
% 98.44/98.65 Found x4 as proof of (cX U)
% 98.44/98.65 Found x3:(cX U)
% 98.44/98.65 Found x3 as proof of (cX U)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 98.44/98.65 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 98.44/98.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 98.44/98.65 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 98.44/98.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found x4:(cX U)
% 98.44/98.65 Found x4 as proof of (cX U)
% 98.44/98.65 Found x4:(cX U)
% 98.44/98.65 Found x4 as proof of (cX U)
% 98.44/98.65 Found x00:(P b)
% 98.44/98.65 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 98.44/98.65 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 98.44/98.65 Found x00:(P b)
% 98.44/98.65 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 98.44/98.65 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 98.44/98.65 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 98.44/98.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 98.44/98.65 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 98.44/98.65 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 98.44/98.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.85/106.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 105.85/106.05 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.85/106.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 105.85/106.05 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 105.85/106.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.85/106.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 105.85/106.05 Found x5:(cX U)
% 105.85/106.05 Found x5 as proof of (cX U)
% 105.85/106.05 Found x5:(cX U)
% 105.85/106.05 Found x5 as proof of (cX U)
% 105.85/106.05 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 105.85/106.05 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 105.85/106.05 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 105.85/106.05 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b0)
% 105.85/106.05 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b0)
% 105.85/106.05 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b0)
% 105.85/106.05 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b0)
% 105.85/106.05 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b0)
% 105.85/106.05 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 105.85/106.05 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 105.85/106.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 105.85/106.05 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 105.85/106.05 Found (eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 105.85/106.05 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 109.53/109.69 Found x5:(cX U)
% 109.53/109.69 Found x5 as proof of (cX U)
% 109.53/109.69 Found x5:(cX U)
% 109.53/109.69 Found x5 as proof of (cX U)
% 109.53/109.69 Found x4:(cX U)
% 109.53/109.69 Found x4 as proof of (cX U)
% 109.53/109.69 Found x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P2 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P2 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P2 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found (fun (x00:(P1 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P2 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 109.53/109.69 Found x5:(cX U)
% 109.53/109.69 Found x5 as proof of (cX U)
% 109.53/109.69 Found x5:(cX U)
% 109.53/109.69 Found x5 as proof of (cX U)
% 109.53/109.69 Found x10:(P (cX x0))
% 109.53/109.69 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 109.53/109.69 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 109.53/109.69 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 109.53/109.69 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 109.53/109.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found x10:(P (cX x0))
% 109.53/109.69 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 109.53/109.69 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 109.53/109.69 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 109.53/109.69 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 109.53/109.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 109.53/109.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 109.53/109.69 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 109.53/109.69 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 109.53/109.69 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 109.53/109.69 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 109.53/109.69 Found x1:(P0 b)
% 109.53/109.69 Instantiate: b:=(cX x0):Prop
% 109.53/109.69 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (cX x0))
% 109.53/109.69 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (cX x0)))
% 109.53/109.69 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 109.53/109.69 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 117.94/118.15 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 117.94/118.15 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 117.94/118.15 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 117.94/118.15 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 117.94/118.15 Found x1:(P0 b)
% 117.94/118.15 Instantiate: b:=(cX x0):Prop
% 117.94/118.15 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (cX x0))
% 117.94/118.15 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (cX x0)))
% 117.94/118.15 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 117.94/118.15 Found x4:(cX U)
% 117.94/118.15 Found x4 as proof of (cX U)
% 117.94/118.15 Found x4:(cX U)
% 117.94/118.15 Found x4 as proof of (cX U)
% 117.94/118.15 Found x4:(cX U)
% 117.94/118.15 Found x4 as proof of (cX U)
% 117.94/118.15 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 117.94/118.15 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 117.94/118.15 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 117.94/118.15 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 117.94/118.15 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 117.94/118.15 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 117.94/118.15 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 117.94/118.15 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 117.94/118.15 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 117.94/118.15 Found (eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 117.94/118.15 Found ((eta_expansion0 Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 117.94/118.15 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 117.94/118.15 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 117.94/118.15 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 117.94/118.15 Found x10:(P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 117.94/118.15 Found x10:(P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 117.94/118.15 Found x10:(P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 117.94/118.15 Found x10:(P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P1 (cX x0))
% 117.94/118.15 Found (fun (x10:(P1 (cX x0)))=> x10) as proof of (P2 (cX x0))
% 117.94/118.15 Found x1:(P (((iff (cY x0)) (cZ x0))->False))
% 117.94/118.15 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 117.94/118.15 Found x1 as proof of (P0 b)
% 117.94/118.15 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 117.94/118.15 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found x1:(P (((iff (cY x0)) (cZ x0))->False))
% 117.94/118.15 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 117.94/118.15 Found x1 as proof of (P0 b)
% 117.94/118.15 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 117.94/118.15 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 117.94/118.15 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 117.94/118.15 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) cX)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 129.87/130.02 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) b0)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 129.87/130.02 Found x4:(cX U)
% 129.87/130.02 Found x4 as proof of (cX U)
% 129.87/130.02 Found x4:(cX U)
% 129.87/130.02 Found x4 as proof of (cX U)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 129.87/130.02 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 129.87/130.02 Found (eq_ref0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 (cX x3)):(((eq Prop) (cX x3)) (cX x3))
% 129.87/130.02 Found (eq_ref0 (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.87/130.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found eq_ref00:=(eq_ref0 (cX x3)):(((eq Prop) (cX x3)) (cX x3))
% 129.87/130.02 Found (eq_ref0 (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 129.87/130.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.87/130.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x3)) (cZ x3))->False))
% 129.87/130.02 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 129.87/130.02 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 129.87/130.02 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 129.87/130.02 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (x:a)=> (not ((iff (cY x)) (cZ x)))))
% 129.87/130.02 Found (eta_expansion00 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 129.87/130.02 Found ((eta_expansion0 Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 129.87/130.02 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 129.87/130.02 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 138.15/138.39 Found (((eta_expansion a) Prop) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 138.15/138.39 Found x1:(P (((iff (cY x0)) (cZ x0))->False))
% 138.15/138.39 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 138.15/138.39 Found x1 as proof of (P0 b)
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 138.15/138.39 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found x1:(P (((iff (cY x0)) (cZ x0))->False))
% 138.15/138.39 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 138.15/138.39 Found x1 as proof of (P0 b)
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 138.15/138.39 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 138.15/138.39 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 138.15/138.39 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 138.15/138.39 Found x10:(P (cX x0))
% 138.15/138.39 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 138.15/138.39 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 138.15/138.39 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.15/138.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found x10:(P (cX x0))
% 138.15/138.39 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 138.15/138.39 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 138.15/138.39 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 138.15/138.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.15/138.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 138.15/138.39 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 138.15/138.39 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 138.15/138.39 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 138.15/138.39 Found x1:(P0 b)
% 138.15/138.39 Instantiate: b:=(cX x0):Prop
% 138.15/138.39 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (cX x0))
% 138.15/138.39 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (cX x0)))
% 138.15/138.39 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 138.15/138.39 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 138.15/138.39 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 148.75/148.90 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 148.75/148.90 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 148.75/148.90 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 148.75/148.90 Found x1:(P0 b)
% 148.75/148.90 Instantiate: b:=(cX x0):Prop
% 148.75/148.90 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (cX x0))
% 148.75/148.90 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (cX x0)))
% 148.75/148.90 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 148.75/148.90 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 148.75/148.90 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 148.75/148.90 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 148.75/148.90 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 148.75/148.90 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 148.75/148.90 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 148.75/148.90 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 148.75/148.90 Found x5:(cX U)
% 148.75/148.90 Found x5 as proof of (cX U)
% 148.75/148.90 Found x5:(cX U)
% 148.75/148.90 Found x5 as proof of (cX U)
% 148.75/148.90 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 148.75/148.90 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 148.75/148.90 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 148.75/148.90 Found (eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 148.75/148.90 Found x3:(cX U)
% 148.75/148.90 Found x3 as proof of (cX U)
% 148.75/148.90 Found x3:(cX U)
% 148.75/148.90 Found x3 as proof of (cX U)
% 148.75/148.90 Found x5:(cX U)
% 148.75/148.90 Found x5 as proof of (cX U)
% 148.75/148.90 Found x5:(cX U)
% 148.75/148.90 Found x5 as proof of (cX U)
% 148.75/148.90 Found x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False)))
% 148.75/148.90 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False)))
% 148.75/148.90 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 148.75/148.90 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 148.75/148.90 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 148.75/148.90 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 148.75/148.90 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 148.75/148.90 Found (eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 165.26/165.46 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 165.26/165.46 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 165.26/165.46 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b0)
% 165.26/165.46 Found x1:(P (not ((iff (cY x0)) (cZ x0))))
% 165.26/165.46 Instantiate: b:=(not ((iff (cY x0)) (cZ x0))):Prop
% 165.26/165.46 Found x1 as proof of (P0 b)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 165.26/165.46 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found x1:(P (not ((iff (cY x0)) (cZ x0))))
% 165.26/165.46 Instantiate: b:=(not ((iff (cY x0)) (cZ x0))):Prop
% 165.26/165.46 Found x1 as proof of (P0 b)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 165.26/165.46 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found x00:(P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 165.26/165.46 Found x40:(P (cX x3))
% 165.26/165.46 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P (cX x3))
% 165.26/165.46 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P0 (cX x3))
% 165.26/165.46 Found x40:(P (cX x3))
% 165.26/165.46 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P (cX x3))
% 165.26/165.46 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P0 (cX x3))
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 165.26/165.46 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 165.26/165.46 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 165.26/165.46 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 165.26/165.46 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 165.26/165.46 Found x4:(cX U)
% 165.26/165.46 Found x4 as proof of (cX U)
% 165.26/165.46 Found x4:(cX U)
% 165.26/165.46 Found x4 as proof of (cX U)
% 165.26/165.46 Found x4:(cX U)
% 165.26/165.46 Found x4 as proof of (cX U)
% 165.26/165.46 Found x4:(cX U)
% 165.26/165.46 Found x4 as proof of (cX U)
% 165.26/165.46 Found x00:(P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 165.26/165.46 Found x00:(P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 165.26/165.46 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 165.26/165.46 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 165.26/165.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.26/165.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 165.26/165.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 165.26/165.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 165.26/165.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 165.26/165.46 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 172.46/172.63 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 172.46/172.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 172.46/172.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 172.46/172.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 172.46/172.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 172.46/172.63 Found x3:(cX U)
% 172.46/172.63 Found x3 as proof of (cX U)
% 172.46/172.63 Found x3:(cX U)
% 172.46/172.63 Found x3 as proof of (cX U)
% 172.46/172.63 Found eta_expansion000:=(eta_expansion00 cX):(((eq (a->Prop)) cX) (fun (x:a)=> (cX x)))
% 172.46/172.63 Found (eta_expansion00 cX) as proof of (((eq (a->Prop)) cX) b)
% 172.46/172.63 Found ((eta_expansion0 Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 172.46/172.63 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 172.46/172.63 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 172.46/172.63 Found (((eta_expansion a) Prop) cX) as proof of (((eq (a->Prop)) cX) b)
% 172.46/172.63 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 172.46/172.63 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 172.46/172.63 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 172.46/172.63 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 172.46/172.63 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 172.46/172.63 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))):(((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 172.46/172.63 Found (eq_ref0 (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 172.46/172.63 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 172.46/172.63 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 172.46/172.63 Found ((eq_ref (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) as proof of (((eq (a->Prop)) (fun (U:a)=> (not ((iff (cY U)) (cZ U))))) b)
% 172.46/172.63 Found x1:(P (not ((iff (cY x0)) (cZ x0))))
% 172.46/172.63 Instantiate: b:=(not ((iff (cY x0)) (cZ x0))):Prop
% 172.46/172.63 Found x1 as proof of (P0 b)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 172.46/172.63 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found x1:(P (not ((iff (cY x0)) (cZ x0))))
% 172.46/172.63 Instantiate: b:=(not ((iff (cY x0)) (cZ x0))):Prop
% 172.46/172.63 Found x1 as proof of (P0 b)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 172.46/172.63 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 (cX x3)):(((eq Prop) (cX x3)) (cX x3))
% 172.46/172.63 Found (eq_ref0 (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 172.46/172.63 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 172.46/172.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.58/179.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found eq_ref00:=(eq_ref0 (cX x3)):(((eq Prop) (cX x3)) (cX x3))
% 179.58/179.79 Found (eq_ref0 (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 179.58/179.79 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 179.58/179.79 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 179.58/179.79 Found ((eq_ref Prop) (cX x3)) as proof of (((eq Prop) (cX x3)) b)
% 179.58/179.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.58/179.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x3)) (cZ x3))))
% 179.58/179.79 Found x20:=(x2 x10):((cX U)->False)
% 179.58/179.79 Found (x2 x10) as proof of ((cX U)->False)
% 179.58/179.79 Found (x2 x10) as proof of ((cX U)->False)
% 179.58/179.79 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 179.58/179.79 Found x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False)))
% 179.58/179.79 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False)))
% 179.58/179.79 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x30:(P (fun (U0:a)=> (((iff (cY U0)) (cZ U0))->False))))=> x30) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 179.58/179.79 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 179.58/179.79 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 179.58/179.79 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found x00:(P b)
% 179.58/179.79 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 179.58/179.79 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 179.58/179.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.58/179.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 179.58/179.79 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 179.58/179.79 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 179.58/179.79 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 179.58/179.79 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 179.58/179.79 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 179.58/179.79 Found x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found (fun (x00:(P (fun (U:a)=> (((iff (cY U)) (cZ U))->False))))=> x00) as proof of (P0 (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 179.58/179.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.58/179.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 179.58/179.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 181.35/181.49 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found x00:(P b)
% 181.35/181.49 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 181.35/181.49 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 181.35/181.49 Found x4:(cX U)
% 181.35/181.49 Found x4 as proof of (cX U)
% 181.35/181.49 Found x4:(cX U)
% 181.35/181.49 Found x4 as proof of (cX U)
% 181.35/181.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.35/181.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 181.35/181.49 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.35/181.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 181.35/181.49 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.35/181.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 181.35/181.49 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 181.35/181.49 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 181.35/181.49 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 181.35/181.49 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.46/183.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 183.46/183.70 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.46/183.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 183.46/183.70 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.46/183.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.46/183.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.46/183.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.46/183.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 183.46/183.70 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 183.46/183.70 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 183.46/183.70 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 184.84/185.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 184.84/185.07 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 184.84/185.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 184.84/185.07 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 184.84/185.07 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 184.84/185.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 184.84/185.07 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 184.84/185.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 184.84/185.07 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 184.84/185.07 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 184.84/185.07 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.98/186.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 185.98/186.16 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.98/186.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 185.98/186.16 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.98/186.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found x4:(cX U)
% 185.98/186.16 Found x4 as proof of (cX U)
% 185.98/186.16 Found x4:(cX U)
% 185.98/186.16 Found x4 as proof of (cX U)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 185.98/186.16 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.98/186.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 185.98/186.16 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 185.98/186.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.98/186.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 185.98/186.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 202.05/202.27 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.05/202.27 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 202.05/202.27 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 202.05/202.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.05/202.27 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 202.05/202.27 Found x20:=(x2 x10):((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found x00:(P cX)
% 202.05/202.27 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 202.05/202.27 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 202.05/202.27 Found x20:=(x2 x10):((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found x10:(P b)
% 202.05/202.27 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 202.05/202.27 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 202.05/202.27 Found x10:(P b)
% 202.05/202.27 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 202.05/202.27 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 202.05/202.27 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 202.05/202.27 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 202.05/202.27 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 202.05/202.27 Found x10:(P (cX x0))
% 202.05/202.27 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 202.05/202.27 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 202.05/202.27 Found x10:(P (cX x0))
% 202.05/202.27 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P (cX x0))
% 202.05/202.27 Found (fun (x10:(P (cX x0)))=> x10) as proof of (P0 (cX x0))
% 202.05/202.27 Found x3:(cX U)
% 202.05/202.27 Found x3 as proof of (cX U)
% 202.05/202.27 Found x3:(cX U)
% 202.05/202.27 Found x3 as proof of (cX U)
% 202.05/202.27 Found x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0)))))
% 202.05/202.27 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 202.05/202.27 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 202.05/202.27 Found x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0)))))
% 202.05/202.27 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 202.05/202.27 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 202.05/202.27 Found x4:(cX U)
% 202.05/202.27 Found x4 as proof of (cX U)
% 202.05/202.27 Found x4:(cX U)
% 202.05/202.27 Found x4 as proof of (cX U)
% 202.05/202.27 Found x20:=(x2 x10):((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found (x2 x10) as proof of ((cX U)->False)
% 202.05/202.27 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 202.05/202.27 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 202.05/202.27 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 202.05/202.27 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 202.05/202.27 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 215.44/215.60 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.44/215.60 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found x40:(P (cX x0))
% 215.44/215.60 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P (cX x0))
% 215.44/215.60 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P0 (cX x0))
% 215.44/215.60 Found x40:(P (cX x0))
% 215.44/215.60 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P (cX x0))
% 215.44/215.60 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P0 (cX x0))
% 215.44/215.60 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 215.44/215.60 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 215.44/215.60 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 215.44/215.60 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 215.44/215.60 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 215.44/215.60 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.44/215.60 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x5:(cX U)
% 215.44/215.60 Found x5 as proof of (cX U)
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x5:(cX U)
% 215.44/215.60 Found x5 as proof of (cX U)
% 215.44/215.60 Found x00:(P cX)
% 215.44/215.60 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 215.44/215.60 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 215.44/215.60 Found x00:(P cX)
% 215.44/215.60 Found (fun (x00:(P cX))=> x00) as proof of (P cX)
% 215.44/215.60 Found (fun (x00:(P cX))=> x00) as proof of (P0 cX)
% 215.44/215.60 Found x30:=(x3 x20):((cX U)->False)
% 215.44/215.60 Found (x3 x20) as proof of ((cX U)->False)
% 215.44/215.60 Found (x3 x20) as proof of ((cX U)->False)
% 215.44/215.60 Found x5:(cX U)
% 215.44/215.60 Found x5 as proof of (cX U)
% 215.44/215.60 Found x5:(cX U)
% 215.44/215.60 Found x5 as proof of (cX U)
% 215.44/215.60 Found x20:=(x2 x30):((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x2 x30) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x2 x30) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found x20:=(x2 x10):((cX U)->False)
% 215.44/215.60 Found (x2 x10) as proof of ((cX U)->False)
% 215.44/215.60 Found (x2 x10) as proof of ((cX U)->False)
% 215.44/215.60 Found x40:(P (cX x3))
% 215.44/215.60 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P (cX x3))
% 215.44/215.60 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P0 (cX x3))
% 215.44/215.60 Found x40:(P (cX x3))
% 215.44/215.60 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P (cX x3))
% 215.44/215.60 Found (fun (x40:(P (cX x3)))=> x40) as proof of (P0 (cX x3))
% 215.44/215.60 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x4:(cX U)
% 215.44/215.60 Found x4 as proof of (cX U)
% 215.44/215.60 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 215.44/215.60 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found x10:(P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P1 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found (fun (x10:(P1 (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P2 (((iff (cY x0)) (cZ x0))->False))
% 222.37/222.51 Found x4:(cX U)
% 222.37/222.51 Found x4 as proof of (cX U)
% 222.37/222.51 Found x4:(cX U)
% 222.37/222.51 Found x4 as proof of (cX U)
% 222.37/222.51 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 222.37/222.51 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 222.37/222.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 222.37/222.51 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 222.37/222.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 222.37/222.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found x20:=(x2 x10):(not (cX U))
% 222.37/222.51 Found (x2 x10) as proof of (not (cX U))
% 222.37/222.51 Found (x2 x10) as proof of (not (cX U))
% 222.37/222.51 Found x20:=(x2 x10):((cX U)->False)
% 222.37/222.51 Found (x2 x10) as proof of ((cX U)->False)
% 222.37/222.51 Found (x2 x10) as proof of ((cX U)->False)
% 222.37/222.51 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 222.37/222.51 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 222.37/222.51 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 222.37/222.51 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 222.37/222.51 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 222.37/222.51 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 222.37/222.51 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 222.37/222.51 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 222.37/222.51 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b0)
% 224.57/224.75 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 224.57/224.75 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found (fun (x00:(P (fun (U:a)=> (not ((iff (cY U)) (cZ U))))))=> x00) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 224.57/224.75 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 224.57/224.75 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 224.57/224.75 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 224.57/224.75 Found x20:=(x2 x10):((cX U)->False)
% 224.57/224.75 Found (x2 x10) as proof of ((cX U)->False)
% 224.57/224.75 Found (x2 x10) as proof of ((cX U)->False)
% 224.57/224.75 Found x4:(cX U)
% 224.57/224.75 Found x4 as proof of (cX U)
% 224.57/224.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 224.57/224.75 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 224.57/224.75 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found x4:(cX U)
% 224.57/224.75 Found x4 as proof of (cX U)
% 224.57/224.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 224.57/224.75 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 224.57/224.75 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 224.57/224.75 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 224.57/224.75 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 226.45/226.65 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.45/226.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.45/226.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 226.45/226.65 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.45/226.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 226.45/226.65 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found x30:=(x3 x20):((cX U)->False)
% 226.45/226.65 Found (x3 x20) as proof of ((cX U)->False)
% 226.45/226.65 Found (x3 x20) as proof of ((cX U)->False)
% 226.45/226.65 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 226.45/226.65 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 226.45/226.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.45/226.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.45/226.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 226.45/226.65 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 226.45/226.65 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 227.71/227.94 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 227.71/227.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 227.71/227.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 227.71/227.94 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 227.71/227.94 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 227.71/227.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 227.71/227.94 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 227.71/227.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 227.71/227.94 Found x3:(cX U)
% 227.71/227.94 Found x3 as proof of (cX U)
% 227.71/227.94 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 227.71/227.94 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 227.71/227.94 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.25/229.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 229.25/229.42 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.25/229.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 229.25/229.42 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.25/229.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 229.25/229.42 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.25/229.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 229.25/229.42 Found x3:(cX U)
% 229.25/229.42 Found x3 as proof of (cX U)
% 229.25/229.42 Found x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0)))))
% 229.25/229.42 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 229.25/229.42 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 229.25/229.42 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 229.25/229.42 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 229.25/229.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.25/229.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 236.14/236.31 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.14/236.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 236.14/236.31 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.14/236.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 236.14/236.31 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 236.14/236.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.14/236.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 236.14/236.31 Found x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0)))))
% 236.14/236.31 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 236.14/236.31 Found (fun (x30:(P (fun (U0:a)=> (not ((iff (cY U0)) (cZ U0))))))=> x30) as proof of (P0 (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 236.14/236.31 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 236.14/236.31 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 236.14/236.31 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 236.14/236.31 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 236.14/236.31 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 236.14/236.31 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 236.14/236.31 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 236.14/236.31 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (((iff (cY U)) (cZ U))->False)))
% 236.14/236.31 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 236.14/236.31 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) b0)
% 236.14/236.31 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 236.14/236.31 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 236.14/236.31 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 236.14/236.31 Found x20:=(x2 x10):(not (cX U))
% 236.14/236.31 Found (x2 x10) as proof of (not (cX U))
% 236.14/236.31 Found (x2 x10) as proof of (not (cX U))
% 236.14/236.31 Found x10:(P b)
% 244.14/244.35 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 244.14/244.35 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 244.14/244.35 Found x10:(P b)
% 244.14/244.35 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 244.14/244.35 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 244.14/244.35 Found x20:=(x2 x10):(not (cX U))
% 244.14/244.35 Found (x2 x10) as proof of (not (cX U))
% 244.14/244.35 Found (x2 x10) as proof of (not (cX U))
% 244.14/244.35 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 244.14/244.35 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 244.14/244.35 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x10:(P (b x0))
% 244.14/244.35 Found (fun (x10:(P (b x0)))=> x10) as proof of (P (b x0))
% 244.14/244.35 Found (fun (x10:(P (b x0)))=> x10) as proof of (P0 (b x0))
% 244.14/244.35 Found x10:(P (b x0))
% 244.14/244.35 Found (fun (x10:(P (b x0)))=> x10) as proof of (P (b x0))
% 244.14/244.35 Found (fun (x10:(P (b x0)))=> x10) as proof of (P0 (b x0))
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x5:(cX U)
% 244.14/244.35 Found x5 as proof of (cX U)
% 244.14/244.35 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 244.14/244.35 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 244.14/244.35 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 244.14/244.35 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found x5:(cX U)
% 244.14/244.35 Found x5 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x4:(cX U)
% 244.14/244.35 Found x4 as proof of (cX U)
% 244.14/244.35 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 244.14/244.35 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 244.14/244.35 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.01/256.21 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found x10:(P (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found (fun (x10:(P (((iff (cY x0)) (cZ x0))->False)))=> x10) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 256.01/256.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.01/256.21 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 256.01/256.21 Found x20:=(x2 x10):((cX U)->False)
% 256.01/256.21 Found (x2 x10) as proof of ((cX U)->False)
% 256.01/256.21 Found (x2 x10) as proof of ((cX U)->False)
% 256.01/256.21 Found x5:(cX U)
% 256.01/256.21 Found x5 as proof of (cX U)
% 256.01/256.21 Found x5:(cX U)
% 256.01/256.21 Found x5 as proof of (cX U)
% 256.01/256.21 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 256.01/256.21 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found x1:(P0 b)
% 256.01/256.21 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 256.01/256.21 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((iff (cY x0)) (cZ x0))->False)))
% 256.01/256.21 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 256.01/256.21 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 256.01/256.21 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 256.01/256.21 Found x1:(P0 b)
% 256.01/256.21 Instantiate: b:=(((iff (cY x0)) (cZ x0))->False):Prop
% 256.01/256.21 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((iff (cY x0)) (cZ x0))->False))
% 256.01/256.21 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((iff (cY x0)) (cZ x0))->False)))
% 256.01/256.21 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 256.01/256.21 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 256.01/256.21 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 256.01/256.21 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 256.01/256.21 Found x4:(cX U)
% 256.01/256.21 Found x4 as proof of (cX U)
% 256.01/256.21 Found x30:=(x3 x20):(not (cX U))
% 256.01/256.21 Found (x3 x20) as proof of (not (cX U))
% 256.01/256.21 Found (x3 x20) as proof of (not (cX U))
% 256.01/256.21 Found x4:(cX U)
% 256.01/256.21 Found x4 as proof of (cX U)
% 256.01/256.21 Found x20:=(x2 x30):((iff (cY U)) (cZ U))
% 256.01/256.21 Found (x2 x30) as proof of ((iff (cY U)) (cZ U))
% 256.01/256.21 Found (x2 x30) as proof of ((iff (cY U)) (cZ U))
% 256.01/256.21 Found x20:=(x2 x10):(not (cX U))
% 256.01/256.21 Found (x2 x10) as proof of (not (cX U))
% 256.01/256.21 Found (x2 x10) as proof of (not (cX U))
% 256.01/256.21 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 256.01/256.21 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 256.01/256.21 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 256.01/256.21 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 256.01/256.21 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 256.01/256.21 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 263.47/263.68 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 263.47/263.68 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) cX)
% 263.47/263.68 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 263.47/263.68 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 263.47/263.68 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) cX)
% 263.47/263.68 Found eta_expansion000:=(eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))):(((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) (fun (x:a)=> (((iff (cY x)) (cZ x))->False)))
% 263.47/263.68 Found (eta_expansion00 (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found ((eta_expansion0 Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found (((eta_expansion a) Prop) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) as proof of (((eq (a->Prop)) (fun (U:a)=> (((iff (cY U)) (cZ U))->False))) b)
% 263.47/263.68 Found x40:(P (cX x0))
% 263.47/263.68 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P (cX x0))
% 263.47/263.68 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P0 (cX x0))
% 263.47/263.68 Found x40:(P (cX x0))
% 263.47/263.68 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P (cX x0))
% 263.47/263.68 Found (fun (x40:(P (cX x0)))=> x40) as proof of (P0 (cX x0))
% 263.47/263.68 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 263.47/263.68 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 263.47/263.68 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 263.47/263.68 Found x20:=(x2 x10):(not (cX U))
% 263.47/263.68 Found (x2 x10) as proof of (not (cX U))
% 263.47/263.68 Found (x2 x10) as proof of (not (cX U))
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 263.47/263.68 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 263.47/263.68 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 263.47/263.68 Found x20:=(x2 x10):((cX U)->False)
% 263.47/263.68 Found (x2 x10) as proof of ((cX U)->False)
% 263.47/263.68 Found (x2 x10) as proof of ((cX U)->False)
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x4:(cX U)
% 263.47/263.68 Found x4 as proof of (cX U)
% 263.47/263.68 Found x5:(cX U)
% 263.47/263.68 Found x5 as proof of (cX U)
% 263.47/263.68 Found x5:(cX U)
% 263.47/263.68 Found x5 as proof of (cX U)
% 263.47/263.68 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 263.47/263.68 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x10:(P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P1 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found (fun (x10:(P1 (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P2 (not ((iff (cY x0)) (cZ x0))))
% 280.79/281.00 Found x1:(P (cX x0))
% 280.79/281.00 Instantiate: b:=(cX x0):Prop
% 280.79/281.00 Found x1 as proof of (P0 b)
% 280.79/281.00 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 280.79/281.00 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found x1:(P (cX x0))
% 280.79/281.00 Instantiate: b:=(cX x0):Prop
% 280.79/281.00 Found x1 as proof of (P0 b)
% 280.79/281.00 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 280.79/281.00 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b)
% 280.79/281.00 Found x5:(cX U)
% 280.79/281.00 Found x5 as proof of (cX U)
% 280.79/281.00 Found x5:(cX U)
% 280.79/281.00 Found x5 as proof of (cX U)
% 280.79/281.00 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 280.79/281.00 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 280.79/281.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.79/281.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.79/281.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.79/281.00 Found eq_ref00:=(eq_ref0 (((iff (cY x0)) (cZ x0))->False)):(((eq Prop) (((iff (cY x0)) (cZ x0))->False)) (((iff (cY x0)) (cZ x0))->False))
% 280.79/281.00 Found (eq_ref0 (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b0)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b0)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b0)
% 280.79/281.00 Found ((eq_ref Prop) (((iff (cY x0)) (cZ x0))->False)) as proof of (((eq Prop) (((iff (cY x0)) (cZ x0))->False)) b0)
% 280.79/281.00 Found x20:=(x2 x10):(not (cX U))
% 280.79/281.00 Found (x2 x10) as proof of (not (cX U))
% 280.79/281.00 Found (x2 x10) as proof of (not (cX U))
% 280.79/281.00 Found x30:=(x3 x20):(not (cX U))
% 280.79/281.00 Found (x3 x20) as proof of (not (cX U))
% 280.79/281.00 Found (x3 x20) as proof of (not (cX U))
% 280.79/281.00 Found x20:=(x2 x10):(not (cX U))
% 280.79/281.00 Found (x2 x10) as proof of (not (cX U))
% 280.79/281.00 Found (x2 x10) as proof of (not (cX U))
% 280.79/281.00 Found x4:(cX U)
% 280.79/281.00 Found x4 as proof of (cX U)
% 280.79/281.00 Found x4:(cX U)
% 280.79/281.00 Found x4 as proof of (cX U)
% 280.79/281.00 Found x10:=(x1 x20):((iff (cY U)) (cZ U))
% 280.79/281.00 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 289.40/289.56 Found (x1 x20) as proof of ((iff (cY U)) (cZ U))
% 289.40/289.56 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 289.40/289.56 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) b0)
% 289.40/289.56 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 289.40/289.56 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 289.40/289.56 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% 289.40/289.56 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% 289.40/289.56 Found (eta_expansion_dep00 b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 289.40/289.56 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 289.40/289.56 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 289.40/289.56 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 289.40/289.56 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (U:a)=> (not ((iff (cY U)) (cZ U)))))
% 289.40/289.56 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 289.40/289.56 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.40/289.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 289.40/289.56 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.40/289.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 289.40/289.56 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.40/289.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found eq_ref00:=(eq_ref0 (cX x0)):(((eq Prop) (cX x0)) (cX x0))
% 289.40/289.56 Found (eq_ref0 (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found ((eq_ref Prop) (cX x0)) as proof of (((eq Prop) (cX x0)) b)
% 289.40/289.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.40/289.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((iff (cY x0)) (cZ x0))->False))
% 289.40/289.56 Found x5:(cX U)
% 289.40/289.56 Found x5 as proof of (cX U)
% 289.40/289.56 Found x5:(cX U)
% 289.40/289.56 Found x5 as proof of (cX U)
% 289.40/289.56 Found x4:(cX U)
% 289.40/289.56 Found x4 as proof of (cX U)
% 289.40/289.56 Found x4:(cX U)
% 289.40/289.56 Found x4 as proof of (cX U)
% 289.40/289.56 Found x5:(cX U)
% 292.59/292.76 Found x5 as proof of (cX U)
% 292.59/292.76 Found x5:(cX U)
% 292.59/292.76 Found x5 as proof of (cX U)
% 292.59/292.76 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.59/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.59/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found x5:(cX U)
% 292.59/292.76 Found x5 as proof of (cX U)
% 292.59/292.76 Found x5:(cX U)
% 292.59/292.76 Found x5 as proof of (cX U)
% 292.59/292.76 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.59/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 292.59/292.76 Found x10:(P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (fun (x10:(P (not ((iff (cY x0)) (cZ x0)))))=> x10) as proof of (P0 (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found eq_ref00:=(eq_ref0 (not ((iff (cY x0)) (cZ x0)))):(((eq Prop) (not ((iff (cY x0)) (cZ x0)))) (not ((iff (cY x0)) (cZ x0))))
% 292.59/292.76 Found (eq_ref0 (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 292.59/292.76 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 297.19/297.34 Found ((eq_ref Prop) (not ((iff (cY x0)) (cZ x0)))) as proof of (((eq Prop) (not ((iff (cY x0)) (cZ x0)))) b)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.19/297.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x0))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x0))
% 297.19/297.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 297.19/297.34 Found (eq_ref0 a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 297.19/297.34 Found (eq_ref0 a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 297.19/297.34 Found (eq_ref0 a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 (((iff (cY x3)) (cZ x3))->False)):(((eq Prop) (((iff (cY x3)) (cZ x3))->False)) (((iff (cY x3)) (cZ x3))->False))
% 297.19/297.34 Found (eq_ref0 (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.19/297.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 297.19/297.34 Found (eq_ref0 a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) x0)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.19/297.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found eq_ref00:=(eq_ref0 (((iff (cY x3)) (cZ x3))->False)):(((eq Prop) (((iff (cY x3)) (cZ x3))->False)) (((iff (cY x3)) (cZ x3))->False))
% 297.19/297.34 Found (eq_ref0 (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found x5:(cX U)
% 297.19/297.34 Found x5 as proof of (cX U)
% 297.19/297.34 Found x5:(cX U)
% 297.19/297.34 Found x5 as proof of (cX U)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 (((iff (cY x3)) (cZ x3))->False)):(((eq Prop) (((iff (cY x3)) (cZ x3))->False)) (((iff (cY x3)) (cZ x3))->False))
% 297.19/297.34 Found (eq_ref0 (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found ((eq_ref Prop) (((iff (cY x3)) (cZ x3))->False)) as proof of (((eq Prop) (((iff (cY x3)) (cZ x3))->False)) b)
% 297.19/297.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.19/297.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cX x3))
% 297.19/297.34 Found ((eq_ref Prop) b) as proof of (((eq Prop)
%------------------------------------------------------------------------------