TSTP Solution File: SYO215^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO215^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 00:50:55 EDT 2022
% Result : Timeout 290.29s 290.62s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO215^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 19:12:07 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 6.75/6.92 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 6.75/6.92 FOF formula (((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))->(forall (U:fofType), ((ex fofType) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))) of role conjecture named cTHM26
% 6.75/6.92 Conjecture to prove = (((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))->(forall (U:fofType), ((ex fofType) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))):Prop
% 6.75/6.92 Parameter fofType_DUMMY:fofType.
% 6.75/6.92 We need to prove ['(((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))->(forall (U:fofType), ((ex fofType) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))))']
% 6.75/6.92 Parameter fofType:Type.
% 6.75/6.92 Trying to prove (((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))->(forall (U:fofType), ((ex fofType) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))))
% 6.75/6.92 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))))
% 6.75/6.92 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found ((eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found (((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found (((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))))
% 6.75/6.92 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found ((eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found (((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found (((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->((ex fofType) (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 6.75/6.92 Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 6.75/6.92 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 6.75/6.92 Instantiate: b:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 6.75/6.92 Found x as proof of (P b)
% 6.75/6.92 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 6.75/6.92 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 8.90/9.15 Instantiate: f:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 8.90/9.15 Found x as proof of (P f)
% 8.90/9.15 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.90/9.15 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 8.90/9.15 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 8.90/9.15 Instantiate: f:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 8.90/9.15 Found x as proof of (P f)
% 8.90/9.15 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.90/9.15 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not (((eq fofType) x0) U)))
% 8.90/9.15 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 8.90/9.15 Found x1:((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 8.90/9.15 Instantiate: b:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 8.90/9.15 Found x1 as proof of (P b)
% 8.90/9.15 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 8.90/9.15 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 8.90/9.15 Found x1:((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 8.90/9.15 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 8.90/9.15 Found x1 as proof of (P f)
% 8.90/9.15 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 8.90/9.15 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 8.90/9.15 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 8.90/9.15 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 10.22/10.37 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 10.22/10.37 Found x1:((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 10.22/10.37 Found x1 as proof of (P f)
% 10.22/10.37 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 10.22/10.37 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 10.22/10.37 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 10.22/10.37 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 10.22/10.37 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x2) U)))
% 10.22/10.37 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 10.22/10.37 Found eq_ref00:=(eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found (eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 10.22/10.37 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 10.22/10.37 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 10.22/10.37 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 10.22/10.37 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 10.22/10.37 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 10.22/10.37 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->((ex fofType) (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 10.22/10.37 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found ((eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found (((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found ((((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found ((((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (ex fofType)) as proof of (P (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 10.22/10.37 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 10.22/10.37 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 10.22/10.37 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 15.22/15.42 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 15.22/15.42 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 15.22/15.42 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 15.22/15.42 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 15.22/15.42 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 15.22/15.42 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 15.22/15.42 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 15.22/15.42 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 15.22/15.42 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 15.22/15.42 Instantiate: b:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 15.22/15.42 Found x as proof of (P b)
% 15.22/15.42 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 15.22/15.42 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 15.22/15.42 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 15.22/15.42 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 15.22/15.42 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 15.22/15.42 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 15.22/15.42 Found x1:((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 15.22/15.42 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 15.22/15.42 Found x1 as proof of (P f)
% 15.22/15.42 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 15.22/15.42 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 15.22/15.42 Found x1:((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 15.22/15.42 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 15.22/15.42 Found x1 as proof of (P f)
% 15.22/15.42 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 15.22/15.42 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (not (((eq fofType) x4) U)))
% 15.22/15.42 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x) U))))
% 15.22/15.42 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 15.22/15.42 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 18.81/19.02 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 18.81/19.02 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 18.81/19.02 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 18.81/19.02 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 18.81/19.02 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 18.81/19.02 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 18.81/19.02 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 18.81/19.02 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 18.81/19.02 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 18.81/19.02 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 18.81/19.02 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 22.03/22.21 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 22.03/22.21 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 22.03/22.21 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 22.03/22.21 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 22.03/22.21 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 22.03/22.21 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 22.03/22.21 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 22.03/22.21 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 22.03/22.21 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 22.03/22.21 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 23.38/23.55 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 23.38/23.55 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.38/23.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.38/23.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 23.38/23.55 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 23.38/23.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.38/23.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 23.38/23.55 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 34.44/34.63 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 34.44/34.63 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 34.44/34.63 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 34.44/34.63 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 34.44/34.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.44/34.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 34.44/34.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 34.44/34.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 34.44/34.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 34.44/34.63 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 34.44/34.63 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 34.44/34.63 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 34.44/34.63 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 34.44/34.63 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 34.44/34.63 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 34.44/34.63 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 37.35/37.57 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 37.35/37.57 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 37.35/37.57 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 37.35/37.57 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.57 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.57 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.57 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 37.35/37.58 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 37.35/37.58 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 37.35/37.58 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 37.35/37.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 48.20/48.39 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found x5:(((eq fofType) x4) U)
% 48.20/48.39 Instantiate: b:=U:fofType;x4:=x0:fofType
% 48.20/48.39 Found x5 as proof of (((eq fofType) x0) b)
% 48.20/48.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 48.20/48.39 Found (eq_ref0 b) as proof of (((eq fofType) b) x2)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 48.20/48.39 Found x50:=(x5 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 48.20/48.39 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found x10:=(x1 (fun (x6:fofType)=> (P x2))):((P x2)->(P x2))
% 48.20/48.39 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 48.20/48.39 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 48.20/48.39 Found x30:=(x3 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 48.20/48.39 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 48.20/48.39 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 48.20/48.39 Found x5:(((eq fofType) x0) U)
% 48.20/48.39 Instantiate: x0:=x1:fofType;b:=U:fofType
% 48.20/48.39 Found x5 as proof of (((eq fofType) x1) b)
% 48.20/48.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 48.20/48.39 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found x30:=(x3 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 48.20/48.39 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 48.20/48.39 Found x5:(((eq fofType) x2) U)
% 48.20/48.39 Instantiate: x2:=x0:fofType;b:=U:fofType
% 48.20/48.39 Found x5 as proof of (((eq fofType) x0) b)
% 48.20/48.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 48.20/48.39 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 48.20/48.39 Found x1:(((eq fofType) x0) U)
% 48.20/48.39 Instantiate: x0:=x2:fofType;b:=U:fofType
% 48.20/48.39 Found x1 as proof of (((eq fofType) x2) b)
% 48.20/48.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 48.20/48.39 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 48.20/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 48.20/48.39 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 48.20/48.39 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 48.20/48.39 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 48.20/48.39 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 48.20/48.39 Found x3:(((eq fofType) x0) U)
% 49.56/49.76 Instantiate: x0:=x1:fofType;b:=U:fofType
% 49.56/49.76 Found x3 as proof of (((eq fofType) x1) b)
% 49.56/49.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 49.56/49.76 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 49.56/49.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 49.56/49.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 49.56/49.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 49.56/49.76 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 49.56/49.76 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 49.56/49.76 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 49.56/49.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.56/49.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.56/49.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 49.56/49.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.56/49.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.56/49.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 49.56/49.76 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 49.56/49.76 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found x3:(((eq fofType) x2) U)
% 50.45/50.69 Instantiate: x2:=x0:fofType;b:=U:fofType
% 50.45/50.69 Found x3 as proof of (((eq fofType) x0) b)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 50.45/50.69 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 50.45/50.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 50.45/50.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 50.45/50.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 50.45/50.69 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 50.45/50.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 50.45/50.69 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 50.45/50.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 50.45/50.69 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 50.45/50.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 50.45/50.69 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 50.45/50.69 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 50.45/50.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 50.45/50.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found x5:(((eq fofType) x4) U)
% 79.25/79.48 Instantiate: b:=U:fofType;x4:=x2:fofType
% 79.25/79.48 Found x5 as proof of (((eq fofType) x2) b)
% 79.25/79.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 79.25/79.48 Found (eq_ref0 b) as proof of (((eq fofType) b) x0)
% 79.25/79.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 79.25/79.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 79.25/79.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 79.25/79.48 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 79.25/79.48 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 79.25/79.48 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 79.25/79.48 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 79.25/79.48 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 79.25/79.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 79.25/79.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 79.25/79.48 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 79.25/79.48 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 79.25/79.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 79.25/79.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 85.85/86.06 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 85.85/86.06 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 85.85/86.06 Found x5:(((eq fofType) x0) U)
% 85.85/86.06 Instantiate: x0:=x3:fofType;b:=U:fofType
% 85.85/86.06 Found x5 as proof of (((eq fofType) x3) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found x1:(((eq fofType) x0) U)
% 85.85/86.06 Instantiate: x0:=x4:fofType;b:=U:fofType
% 85.85/86.06 Found x1 as proof of (((eq fofType) x4) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq fofType) b) x2)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 85.85/86.06 Found x5:(((eq fofType) x2) U)
% 85.85/86.06 Instantiate: x2:=x3:fofType;b:=U:fofType
% 85.85/86.06 Found x5 as proof of (((eq fofType) x3) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found x3:(((eq fofType) x0) U)
% 85.85/86.06 Instantiate: x0:=x4:fofType;b:=U:fofType
% 85.85/86.06 Found x3 as proof of (((eq fofType) x4) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 85.85/86.06 Found x3:(((eq fofType) x2) U)
% 85.85/86.06 Instantiate: x2:=x4:fofType;b:=U:fofType
% 85.85/86.06 Found x3 as proof of (((eq fofType) x4) b)
% 85.85/86.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.85/86.06 Found (eq_ref0 b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 85.85/86.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% 112.01/112.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.01/112.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 112.01/112.28 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.01/112.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 112.01/112.28 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.01/112.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 112.01/112.28 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.01/112.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 112.01/112.28 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 112.01/112.28 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 112.01/112.28 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 112.01/112.28 Instantiate: a:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 112.01/112.28 Found x as proof of (P a)
% 112.01/112.28 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 112.01/112.28 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 112.01/112.28 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 116.67/116.88 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 116.67/116.88 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 116.67/116.88 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 116.67/116.88 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 116.67/116.88 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.67/116.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.67/116.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 116.67/116.88 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 116.67/116.88 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 116.67/116.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.67/116.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.67/116.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 116.67/116.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 135.61/135.85 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 135.61/135.85 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 135.61/135.85 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 135.61/135.85 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 135.61/135.85 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 135.61/135.85 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 135.61/135.85 Instantiate: a:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 135.61/135.85 Found x as proof of (P a)
% 135.61/135.85 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 135.61/135.85 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 135.61/135.85 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 135.61/135.85 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 135.61/135.85 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 135.61/135.85 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found (((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 135.61/135.85 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 135.61/135.85 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 135.61/135.85 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 135.61/135.85 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 139.13/139.36 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 139.13/139.36 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 139.13/139.36 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 139.13/139.36 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 139.13/139.36 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 139.13/139.36 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 139.13/139.36 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 139.13/139.36 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 139.13/139.36 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 139.13/139.36 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 139.13/139.36 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 139.13/139.36 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 139.13/139.36 Found (eta_expansion000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found (((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 139.13/139.36 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 148.44/148.69 Found ((((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 148.44/148.69 Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% 148.44/148.69 Found (eq_ref00 P0) as proof of (P1 (f x0))
% 148.44/148.69 Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% 148.44/148.69 Found (eq_ref00 P0) as proof of (P1 (f x0))
% 148.44/148.69 Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 148.44/148.69 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 148.44/148.69 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 148.44/148.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 148.44/148.69 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 148.44/148.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 148.44/148.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 148.44/148.69 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 148.44/148.69 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 148.44/148.69 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 148.44/148.69 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 148.44/148.69 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 148.44/148.69 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 148.44/148.69 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 148.44/148.69 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 148.44/148.69 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 148.44/148.69 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 151.72/151.95 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 151.72/151.95 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 151.72/151.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 151.72/151.95 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 151.72/151.95 Found (eq_ref0 b) as proof of (P0 b)
% 151.72/151.95 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 151.72/151.95 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 151.72/151.95 Found (eta_expansion_dep00 b) as proof of (P0 b)
% 151.72/151.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 151.72/151.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 151.72/151.95 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 151.72/151.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 155.74/156.01 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 155.74/156.01 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 155.74/156.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 155.74/156.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 155.74/156.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 155.74/156.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 155.74/156.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found x:((ex fofType) (fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))))
% 155.74/156.01 Instantiate: a:=(fun (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> (not (((eq fofType) X) Y))))):(fofType->Prop)
% 155.74/156.01 Found x as proof of (P a)
% 155.74/156.01 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 155.74/156.01 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 155.74/156.01 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 155.74/156.01 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 155.74/156.01 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 155.74/156.01 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 155.74/156.01 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 155.74/156.01 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 155.74/156.01 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 157.64/157.89 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Instantiate: b:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 157.64/157.89 Found x1 as proof of (P1 b)
% 157.64/157.89 Found eq_ref00:=(eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 157.64/157.89 Found (eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 157.64/157.89 Instantiate: b:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 157.64/157.89 Found x1 as proof of (P1 b)
% 157.64/157.89 Found eq_ref00:=(eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 157.64/157.89 Found (eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 157.64/157.89 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 157.64/157.89 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 157.64/157.89 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 157.64/157.89 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 160.99/161.23 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 160.99/161.23 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.99/161.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.99/161.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.99/161.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 160.99/161.23 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 160.99/161.23 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 160.99/161.23 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 174.87/175.15 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 174.87/175.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.87/175.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 174.87/175.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 174.87/175.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 174.87/175.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 174.87/175.15 Found x5:(((eq fofType) x4) U)
% 174.87/175.15 Found x5 as proof of (((eq fofType) x4) b)
% 174.87/175.15 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 174.87/175.15 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found x5:(((eq fofType) x0) U)
% 174.87/175.15 Found x5 as proof of (((eq fofType) x0) b)
% 174.87/175.15 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 b)->(P0 (fun (x:fofType)=> (b x))))
% 174.87/175.15 Found (eta_expansion_dep000 P0) as proof of (P1 b)
% 174.87/175.15 Found ((eta_expansion_dep00 b) P0) as proof of (P1 b)
% 174.87/175.15 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 b)->(P0 (fun (x:fofType)=> (b x))))
% 174.87/175.15 Found (eta_expansion_dep000 P0) as proof of (P1 b)
% 174.87/175.15 Found ((eta_expansion_dep00 b) P0) as proof of (P1 b)
% 174.87/175.15 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) P0) as proof of (P1 b)
% 174.87/175.15 Found x1:(((eq fofType) x0) U)
% 174.87/175.15 Found x1 as proof of (((eq fofType) x0) b)
% 174.87/175.15 Found x5:(((eq fofType) x2) U)
% 174.87/175.15 Found x5 as proof of (((eq fofType) x2) b)
% 174.87/175.15 Found x3:(((eq fofType) x0) U)
% 174.87/175.15 Found x3 as proof of (((eq fofType) x0) b)
% 174.87/175.15 Found eq_ref00:=(eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 174.87/175.15 Found (eq_ref0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 174.87/175.15 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 174.87/175.15 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 174.87/175.15 Found ((eq_ref (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 174.87/175.15 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 174.87/175.15 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 174.87/175.15 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 175.70/176.02 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 175.70/176.02 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 175.70/176.02 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 175.70/176.02 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 175.70/176.02 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b0)
% 175.70/176.02 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 175.70/176.02 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Instantiate: f:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 175.70/176.02 Found x1 as proof of (P1 f)
% 175.70/176.02 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 175.70/176.02 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x0) x))))
% 175.70/176.02 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Instantiate: f:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 175.70/176.02 Found x1 as proof of (P1 f)
% 175.70/176.02 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 175.70/176.02 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x0) x))))
% 175.70/176.02 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Instantiate: f:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 175.70/176.02 Found x1 as proof of (P1 f)
% 175.70/176.02 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 175.70/176.02 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 175.70/176.02 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x0) x))))
% 175.70/176.02 Found x1:(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 175.70/176.02 Instantiate: f:=(fun (Z:fofType)=> (not (((eq fofType) Z) U))):(fofType->Prop)
% 175.70/176.02 Found x1 as proof of (P1 f)
% 175.70/176.02 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 181.59/181.86 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 181.59/181.86 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 181.59/181.86 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 181.59/181.86 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (not (((eq fofType) x0) x2)))
% 181.59/181.86 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (not (((eq fofType) x0) x))))
% 181.59/181.86 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 181.59/181.86 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 181.59/181.86 Found eq_ref00:=(eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found (eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 181.59/181.86 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 181.59/181.86 Found x3:(((eq fofType) x2) U)
% 181.59/181.86 Found x3 as proof of (((eq fofType) x2) b)
% 181.59/181.86 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 181.59/181.86 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 181.59/181.86 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 181.59/181.86 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) b0)
% 181.59/181.86 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 181.59/181.86 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 181.59/181.86 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 181.59/181.86 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 181.59/181.86 Found x2:(P0 (not (((eq fofType) x0) x1)))
% 181.59/181.86 Instantiate: b:=(not (((eq fofType) x0) x1)):Prop
% 181.59/181.86 Found x2 as proof of (P1 b)
% 181.59/181.86 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 181.59/181.86 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 181.59/181.86 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 181.59/181.86 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 181.59/181.86 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 181.59/181.86 Found x2:(P0 (not (((eq fofType) x0) x1)))
% 181.59/181.86 Instantiate: b:=(not (((eq fofType) x0) x1)):Prop
% 181.59/181.86 Found x2 as proof of (P1 b)
% 181.59/181.86 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 181.59/181.86 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found x2:(P0 (not (((eq fofType) x0) x1)))
% 184.75/185.01 Instantiate: b:=(not (((eq fofType) x0) x1)):Prop
% 184.75/185.01 Found x2 as proof of (P1 b)
% 184.75/185.01 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 184.75/185.01 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found x2:(P0 (not (((eq fofType) x0) x1)))
% 184.75/185.01 Instantiate: b:=(not (((eq fofType) x0) x1)):Prop
% 184.75/185.01 Found x2 as proof of (P1 b)
% 184.75/185.01 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 184.75/185.01 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 184.75/185.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 184.75/185.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 184.75/185.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 184.75/185.01 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 184.75/185.01 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 184.75/185.01 Found (eq_ref00 P0) as proof of (P1 b)
% 184.75/185.01 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 184.75/185.01 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 184.75/185.01 Found (eq_ref00 P0) as proof of (P1 b)
% 184.75/185.01 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 184.75/185.01 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 191.67/191.95 Found (eq_ref00 P0) as proof of (P1 b)
% 191.67/191.95 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 191.67/191.95 Found (eq_ref00 P0) as proof of (P1 b)
% 191.67/191.95 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 191.67/191.95 Found (eq_ref00 P0) as proof of (P1 b)
% 191.67/191.95 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 191.67/191.95 Found (eq_ref00 P0) as proof of (P1 b)
% 191.67/191.95 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found (((eq_ref (fofType->Prop)) b) P0) as proof of (P1 b)
% 191.67/191.95 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 191.67/191.95 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 191.67/191.95 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 191.67/191.95 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 191.67/191.95 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 191.67/191.95 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 191.67/191.95 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 191.67/191.95 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 191.67/191.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 191.67/191.95 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 191.67/191.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 191.67/191.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 192.33/192.60 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 192.33/192.60 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 192.33/192.60 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 192.33/192.60 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 192.33/192.60 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 192.33/192.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 203.49/203.80 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 203.49/203.80 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 203.49/203.80 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 203.49/203.80 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 203.49/203.80 Found eq_ref000:=(eq_ref00 P0):((P0 (f x2))->(P0 (f x2)))
% 203.49/203.80 Found (eq_ref00 P0) as proof of (P1 (f x2))
% 203.49/203.80 Found ((eq_ref0 (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found eq_ref000:=(eq_ref00 P0):((P0 (f x2))->(P0 (f x2)))
% 203.49/203.80 Found (eq_ref00 P0) as proof of (P1 (f x2))
% 203.49/203.80 Found ((eq_ref0 (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% 203.49/203.80 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 203.49/203.80 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.49/203.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 203.49/203.80 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% 203.49/203.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.49/203.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x2) U)))
% 203.49/203.80 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 203.49/203.80 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 207.80/208.06 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 207.80/208.06 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 207.80/208.06 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 207.80/208.06 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 207.80/208.06 Found eq_ref00:=(eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 207.80/208.06 Found (eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 207.80/208.06 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 207.80/208.06 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 207.80/208.06 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 207.80/208.06 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 207.80/208.06 Instantiate: b:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 207.80/208.06 Found x1 as proof of (P1 b)
% 207.80/208.06 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 207.80/208.06 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) U)))->(P0 (not (((eq fofType) x0) U))))
% 207.80/208.06 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found ((eq_ref0 (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found (((eq_ref Prop) (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found (((eq_ref Prop) (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) U)))->(P0 (not (((eq fofType) x0) U))))
% 207.80/208.06 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found ((eq_ref0 (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found (((eq_ref Prop) (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found (((eq_ref Prop) (not (((eq fofType) x0) U))) P0) as proof of (P1 (not (((eq fofType) x0) U)))
% 207.80/208.06 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 207.80/208.06 Instantiate: b:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 207.80/208.06 Found x1 as proof of (P1 b)
% 207.80/208.06 Found eq_ref00:=(eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 207.80/208.06 Found (eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 207.80/208.06 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 212.93/213.19 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 212.93/213.19 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 212.93/213.19 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 212.93/213.19 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 212.93/213.19 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 212.93/213.19 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 212.93/213.19 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 212.93/213.19 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 212.93/213.19 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 215.09/215.36 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 215.09/215.36 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 215.09/215.36 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 215.09/215.36 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 215.09/215.36 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 215.09/215.36 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 215.09/215.36 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 215.09/215.36 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 215.09/215.36 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 216.96/217.24 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x0) x1)))->(P0 (not (((eq fofType) x0) x1))))
% 216.96/217.24 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found ((eq_ref0 (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found (((eq_ref Prop) (not (((eq fofType) x0) x1))) P0) as proof of (P1 (not (((eq fofType) x0) x1)))
% 216.96/217.24 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 216.96/217.24 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))))
% 216.96/217.24 Found (eq_ref00 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found ((eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found (((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 216.96/217.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.96/217.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) U))):(((eq Prop) (not (((eq fofType) x0) U))) (not (((eq fofType) x0) U)))
% 216.96/217.24 Found (eq_ref0 (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) U))):(((eq Prop) (not (((eq fofType) x0) U))) (not (((eq fofType) x0) U)))
% 216.96/217.24 Found (eq_ref0 (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b)
% 216.96/217.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.96/217.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 216.96/217.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 217.63/217.91 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 217.63/217.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 217.63/217.91 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 217.63/217.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 217.63/217.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 217.63/217.91 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 217.63/217.91 Found (eta_expansion_dep00 b) as proof of (P0 b)
% 217.63/217.91 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 217.63/217.91 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 217.63/217.91 Found (eq_ref0 b) as proof of (P0 b)
% 217.63/217.91 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found ((eq_ref (fofType->Prop)) b) as proof of (P0 b)
% 217.63/217.91 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 217.63/217.91 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 217.63/217.91 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 218.52/218.78 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 218.52/218.78 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 218.52/218.78 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) b)
% 218.52/218.78 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 218.52/218.78 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.52/218.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 218.52/218.78 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.52/218.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 218.52/218.78 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.52/218.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 218.52/218.78 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 218.52/218.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.52/218.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 218.52/218.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 220.17/220.44 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 220.17/220.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) x1))):(((eq Prop) (not (((eq fofType) x0) x1))) (not (((eq fofType) x0) x1)))
% 220.17/220.44 Found (eq_ref0 (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) x1))) as proof of (((eq Prop) (not (((eq fofType) x0) x1))) b)
% 220.17/220.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 220.17/220.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x1) U)))
% 220.17/220.44 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) U))):(((eq Prop) (not (((eq fofType) x0) U))) (not (((eq fofType) x0) U)))
% 220.17/220.44 Found (eq_ref0 (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x0) U))):(((eq Prop) (not (((eq fofType) x0) U))) (not (((eq fofType) x0) U)))
% 220.17/220.44 Found (eq_ref0 (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found ((eq_ref Prop) (not (((eq fofType) x0) U))) as proof of (((eq Prop) (not (((eq fofType) x0) U))) b0)
% 220.17/220.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 220.17/220.44 Found eta_expansion000:=(eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 220.17/220.44 Found (eta_expansion00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 220.17/220.44 Found ((eta_expansion0 Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 220.17/220.44 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found (((eta_expansion fofType) Prop) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 227.57/227.90 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))):(((eq (fofType->Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) (fun (x:fofType)=> (not (((eq fofType) x0) x))))
% 227.57/227.90 Found (eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) as proof of (P0 b)
% 227.57/227.90 Found eq_ref00:=(eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 227.57/227.90 Found (eq_ref0 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b)
% 227.57/227.90 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 227.57/227.90 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 227.57/227.90 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 227.57/227.90 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 227.57/227.90 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 227.57/227.90 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 227.57/227.90 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 228.85/229.11 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 228.85/229.11 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 228.85/229.11 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 228.85/229.11 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 228.85/229.11 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 228.85/229.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 244.25/244.55 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x0) x)))))
% 244.25/244.55 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((eta_expansion_dep00 (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Y:fofType)=> (not (((eq fofType) x0) Y)))) P0) as proof of (P1 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 244.25/244.55 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 244.25/244.55 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 244.25/244.55 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 244.25/244.55 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 244.25/244.55 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 244.25/244.55 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 244.25/244.55 Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% 244.25/244.55 Found (eq_ref00 P0) as proof of (P1 (f x0))
% 244.25/244.55 Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% 244.25/244.55 Found (eq_ref00 P0) as proof of (P1 (f x0))
% 244.25/244.55 Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% 244.25/244.55 Found x5:(((eq fofType) x4) U)
% 244.25/244.55 Instantiate: b:=U:fofType;x4:=x0:fofType
% 244.25/244.55 Found x5 as proof of (((eq fofType) x0) b)
% 244.25/244.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 244.25/244.55 Found (eq_ref0 b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found x5:(((eq fofType) x4) U)
% 244.25/244.55 Instantiate: b:=U:fofType;x4:=x0:fofType
% 244.25/244.55 Found x5 as proof of (((eq fofType) x0) b)
% 244.25/244.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 244.25/244.55 Found (eq_ref0 b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x2)
% 244.25/244.55 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 260.20/260.49 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 260.20/260.49 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 260.20/260.49 Found (((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 260.20/260.49 Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 260.20/260.49 Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 260.20/260.49 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 260.20/260.49 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.20/260.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 260.20/260.49 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 260.20/260.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.20/260.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) U)))
% 260.20/260.49 Found x50:=(x5 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 260.20/260.49 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 260.20/260.49 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 260.20/260.49 Found x50:=(x5 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 260.20/260.49 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 260.20/260.49 Found (x5 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 260.20/260.49 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 260.20/260.49 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 260.20/260.49 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 260.20/260.49 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 260.20/260.49 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 260.20/260.49 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 260.20/260.49 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 260.20/260.49 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 260.20/260.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 260.20/260.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 260.20/260.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 270.69/271.03 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 270.69/271.03 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 270.69/271.03 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 270.69/271.03 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 270.69/271.03 Found eta_expansion000:=(eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 270.69/271.03 Found (eta_expansion00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found ((eta_expansion0 Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found (((eta_expansion fofType) Prop) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 270.69/271.03 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 270.69/271.03 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found x10:=(x1 (fun (x6:fofType)=> (P x2))):((P x2)->(P x2))
% 270.69/271.03 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 270.69/271.03 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 270.69/271.03 Found x50:=(x5 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 270.69/271.03 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found (x5 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found x5:(((eq fofType) x0) U)
% 270.69/271.03 Instantiate: x0:=x1:fofType;b:=U:fofType
% 270.69/271.03 Found x5 as proof of (((eq fofType) x1) b)
% 270.69/271.03 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 270.69/271.03 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found x30:=(x3 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 270.69/271.03 Found x5:(((eq fofType) x0) U)
% 270.69/271.03 Instantiate: x0:=x1:fofType;b:=U:fofType
% 270.69/271.03 Found x5 as proof of (((eq fofType) x1) b)
% 270.69/271.03 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 270.69/271.03 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found x10:=(x1 (fun (x6:fofType)=> (P x2))):((P x2)->(P x2))
% 270.69/271.03 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 270.69/271.03 Found (x1 (fun (x6:fofType)=> (P x2))) as proof of (P0 x2)
% 270.69/271.03 Found x30:=(x3 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 270.69/271.03 Found x5:(((eq fofType) x2) U)
% 270.69/271.03 Instantiate: x2:=x0:fofType;b:=U:fofType
% 270.69/271.03 Found x5 as proof of (((eq fofType) x0) b)
% 270.69/271.03 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 270.69/271.03 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 270.69/271.03 Found x30:=(x3 (fun (x6:fofType)=> (P x1))):((P x1)->(P x1))
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 270.69/271.03 Found (x3 (fun (x6:fofType)=> (P x1))) as proof of (P0 x1)
% 270.69/271.03 Found x5:(((eq fofType) x2) U)
% 270.69/271.03 Instantiate: x2:=x0:fofType;b:=U:fofType
% 270.69/271.03 Found x5 as proof of (((eq fofType) x0) b)
% 270.69/271.03 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 270.69/271.03 Found (eq_ref0 b) as proof of (((eq fofType) b) x3)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x3)
% 275.03/275.33 Found x1:(((eq fofType) x0) U)
% 275.03/275.33 Instantiate: x0:=x2:fofType;b:=U:fofType
% 275.03/275.33 Found x1 as proof of (((eq fofType) x2) b)
% 275.03/275.33 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 275.03/275.33 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found x3:(((eq fofType) x0) U)
% 275.03/275.33 Instantiate: x0:=x1:fofType;b:=U:fofType
% 275.03/275.33 Found x3 as proof of (((eq fofType) x1) b)
% 275.03/275.33 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 275.03/275.33 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 275.03/275.33 Found x30:=(x3 (fun (x6:fofType)=> (P x0))):((P x0)->(P x0))
% 275.03/275.33 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 275.03/275.33 Found (x3 (fun (x6:fofType)=> (P x0))) as proof of (P0 x0)
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 275.03/275.33 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 275.03/275.33 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found eq_ref000:=(eq_ref00 P0):((P0 (not (((eq fofType) x1) U)))->(P0 (not (((eq fofType) x1) U))))
% 276.93/277.22 Found (eq_ref00 P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found ((eq_ref0 (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (((eq_ref Prop) (not (((eq fofType) x1) U))) P0) as proof of (P1 (not (((eq fofType) x1) U)))
% 276.93/277.22 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 276.93/277.22 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 276.93/277.22 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 276.93/277.22 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 276.93/277.22 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 276.93/277.22 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 276.93/277.22 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 276.93/277.22 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.93/277.22 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 276.93/277.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 276.93/277.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 276.93/277.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 276.93/277.22 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 276.93/277.22 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 276.93/277.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.93/277.22 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 277.89/278.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 277.89/278.24 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 277.89/278.24 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 277.89/278.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 277.89/278.24 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 277.89/278.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 277.89/278.24 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 277.89/278.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 277.89/278.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 277.89/278.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 277.89/278.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 279.92/280.25 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 279.92/280.25 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 279.92/280.25 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found x1:(((eq fofType) x0) U)
% 279.92/280.25 Instantiate: x0:=x2:fofType;b:=U:fofType
% 279.92/280.25 Found x1 as proof of (((eq fofType) x2) b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found x3:(((eq fofType) x2) U)
% 279.92/280.25 Instantiate: x2:=x0:fofType;b:=U:fofType
% 279.92/280.25 Found x3 as proof of (((eq fofType) x0) b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 279.92/280.25 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 279.92/280.25 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 279.92/280.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.92/280.25 Found (eq_ref0 b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 279.92/280.25 Found ((eq_ref Prop) b) as proof of (P0 b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 280.84/281.15 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.84/281.15 Found (eq_ref0 b) as proof of (P0 b)
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (P0 b)
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (P0 b)
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (P0 b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 280.84/281.15 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 280.84/281.15 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.84/281.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 280.84/281.15 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.84/281.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 280.84/281.15 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 280.84/281.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.84/281.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 280.84/281.15 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 282.73/283.04 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.73/283.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 282.73/283.04 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 282.73/283.04 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 282.73/283.04 Found x3:(((eq fofType) x0) U)
% 282.73/283.04 Instantiate: x0:=x1:fofType;b:=U:fofType
% 282.73/283.04 Found x3 as proof of (((eq fofType) x1) b)
% 282.73/283.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 282.73/283.04 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 282.73/283.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 282.73/283.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 282.73/283.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 282.73/283.04 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 282.73/283.04 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 282.73/283.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.73/283.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 282.73/283.04 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 290.29/290.62 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.29/290.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 290.29/290.62 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.29/290.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found eq_ref00:=(eq_ref0 (not (((eq fofType) x1) U))):(((eq Prop) (not (((eq fofType) x1) U))) (not (((eq fofType) x1) U)))
% 290.29/290.62 Found (eq_ref0 (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found ((eq_ref Prop) (not (((eq fofType) x1) U))) as proof of (((eq Prop) (not (((eq fofType) x1) U))) b)
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.29/290.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (((eq fofType) x0) x1)))
% 290.29/290.62 Found x3:(((eq fofType) x2) U)
% 290.29/290.62 Instantiate: x2:=x0:fofType;b:=U:fofType
% 290.29/290.62 Found x3 as proof of (((eq fofType) x0) b)
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.29/290.62 Found (eq_ref0 b) as proof of (((eq fofType) b) x4)
% 290.29/290.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 290.29/290.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 290.29/290.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x4)
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 290.29/290.62 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 290.29/290.62 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 290.29/290.62 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 290.29/290.62 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 290.29/290.62 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 290.29/290.62 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 290.29/290.62 Found x1 as proof of (P1 f)
% 290.29/290.62 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 294.65/295.02 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 294.65/295.02 Found x1 as proof of (P1 f)
% 294.65/295.02 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 294.65/295.02 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 294.65/295.02 Found x1 as proof of (P1 f)
% 294.65/295.02 Found x1:(P0 (fun (Y:fofType)=> (not (((eq fofType) x0) Y))))
% 294.65/295.02 Instantiate: f:=(fun (Y:fofType)=> (not (((eq fofType) x0) Y))):(fofType->Prop)
% 294.65/295.02 Found x1 as proof of (P1 f)
% 294.65/295.02 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 294.65/295.02 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 294.65/295.02 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))):(((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) (fun (x:fofType)=> (not (((eq fofType) x) U))))
% 294.65/295.02 Found (eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> (not (((eq fofType) Z) U)))) b0)
% 294.65/295.02 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 294.65/295.02 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 294.65/295.02 Found x6:(P x0)
% 294.65/295.02 Instantiate: b:=x0:fofType
% 294.65/295.02 Found x6 as proof of (P0 b)
% 294.65/295.02 Found x5:(((eq fofType) x4) U)
% 294.65/295.02 Instantiate: b:=U:fofType;x4:=x2:fofType
% 294.65/295.02 Found x5 as proof of (((eq fofType) x2) b)
% 294.65/295.02 Found x5:(((eq fofType) x4) U)
% 294.65/295.02 Found x5 as proof of (((eq fofType) x4) b)
% 294.65/295.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))->(P0 (fun (x:fofType)=> (not (((eq fofType) x) U)))))
% 294.65/295.02 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Z:fofType)=> (not (((eq fofType) Z) U))))
% 294.65/295.02 Found ((eta_expansion_dep00 (fun (Z:fofType)=> (not (((eq
%------------------------------------------------------------------------------