TSTP Solution File: SYO240^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO240^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 00:50:59 EDT 2022
% Result : Timeout 299.17s 299.53s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO240^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n008.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 20:55:17 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'
% 0.12/0.34 Python 2.7.5
% 5.82/5.99 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 5.82/5.99 FOF formula (<kernel.Constant object at 0x257ff38>, <kernel.Type object at 0x257f128>) of role type named a_type
% 5.82/5.99 Using role type
% 5.82/5.99 Declaring a:Type
% 5.82/5.99 FOF formula (<kernel.Constant object at 0x257f248>, <kernel.Type object at 0x2583d88>) of role type named b_type
% 5.82/5.99 Using role type
% 5.82/5.99 Declaring b:Type
% 5.82/5.99 FOF formula (<kernel.Constant object at 0x257f050>, <kernel.DependentProduct object at 0x257f1b8>) of role type named cK
% 5.82/5.99 Using role type
% 5.82/5.99 Declaring cK:((a->(b->Prop))->(a->(b->Prop)))
% 5.82/5.99 FOF formula ((forall (Xu:(a->(b->Prop))) (Xv:(a->(b->Prop))), ((forall (Xx:a) (Xy:b), (((Xu Xx) Xy)->((Xv Xx) Xy)))->(forall (Xx:a) (Xy:b), ((((cK Xu) Xx) Xy)->(((cK Xv) Xx) Xy)))))->((ex (a->(b->Prop))) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))) of role conjecture named cTHM2B
% 5.82/5.99 Conjecture to prove = ((forall (Xu:(a->(b->Prop))) (Xv:(a->(b->Prop))), ((forall (Xx:a) (Xy:b), (((Xu Xx) Xy)->((Xv Xx) Xy)))->(forall (Xx:a) (Xy:b), ((((cK Xu) Xx) Xy)->(((cK Xv) Xx) Xy)))))->((ex (a->(b->Prop))) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))):Prop
% 5.82/5.99 Parameter a_DUMMY:a.
% 5.82/5.99 Parameter b_DUMMY:b.
% 5.82/5.99 We need to prove ['((forall (Xu:(a->(b->Prop))) (Xv:(a->(b->Prop))), ((forall (Xx:a) (Xy:b), (((Xu Xx) Xy)->((Xv Xx) Xy)))->(forall (Xx:a) (Xy:b), ((((cK Xu) Xx) Xy)->(((cK Xv) Xx) Xy)))))->((ex (a->(b->Prop))) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))))']
% 5.82/5.99 Parameter a:Type.
% 5.82/5.99 Parameter b:Type.
% 5.82/5.99 Parameter cK:((a->(b->Prop))->(a->(b->Prop))).
% 5.82/5.99 Trying to prove ((forall (Xu:(a->(b->Prop))) (Xv:(a->(b->Prop))), ((forall (Xx:a) (Xy:b), (((Xu Xx) Xy)->((Xv Xx) Xy)))->(forall (Xx:a) (Xy:b), ((((cK Xu) Xx) Xy)->(((cK Xv) Xx) Xy)))))->((ex (a->(b->Prop))) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))))
% 5.82/5.99 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))):(((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) (fun (x:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK x)) x)))
% 5.82/5.99 Found (eta_expansion_dep00 (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) as proof of (((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) b0)
% 5.82/5.99 Found ((eta_expansion_dep0 (fun (x1:(a->(b->Prop)))=> Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) as proof of (((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) b0)
% 5.82/5.99 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) as proof of (((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) b0)
% 5.82/5.99 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) as proof of (((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) b0)
% 5.82/5.99 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) as proof of (((eq ((a->(b->Prop))->Prop)) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu))) b0)
% 5.82/5.99 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.82/5.99 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 5.82/5.99 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 5.82/5.99 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 5.82/5.99 Found (fun (x0:(a->(b->Prop)))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 5.82/5.99 Found (fun (x0:(a->(b->Prop)))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(a->(b->Prop))), (((eq Prop) (f x)) (((eq (a->(b->Prop))) (cK x)) x)))
% 5.82/5.99 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.82/5.99 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 5.82/5.99 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 13.37/13.53 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 13.37/13.53 Found (fun (x0:(a->(b->Prop)))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (a->(b->Prop))) (cK x0)) x0))
% 13.37/13.53 Found (fun (x0:(a->(b->Prop)))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(a->(b->Prop))), (((eq Prop) (f x)) (((eq (a->(b->Prop))) (cK x)) x)))
% 13.37/13.53 Found eq_ref00:=(eq_ref0 (cK x0)):(((eq (a->(b->Prop))) (cK x0)) (cK x0))
% 13.37/13.53 Found (eq_ref0 (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 13.37/13.53 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->(b->Prop))) b0) (fun (x:a)=> (b0 x)))
% 13.37/13.53 Found (eta_expansion_dep00 b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 13.37/13.53 Found ((eta_expansion_dep0 (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 13.37/13.53 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 13.37/13.53 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 13.37/13.53 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 13.37/13.53 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 13.37/13.53 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 13.37/13.53 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 13.37/13.53 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 13.37/13.53 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 13.37/13.53 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 13.37/13.53 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 13.37/13.53 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 13.37/13.53 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 13.37/13.53 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 13.37/13.53 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 13.37/13.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 29.01/29.19 Found x10:(P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 29.01/29.19 Found x10:(P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 29.01/29.19 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 29.01/29.19 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 29.01/29.19 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 29.01/29.19 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 29.01/29.19 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 29.01/29.19 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 29.01/29.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 29.01/29.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 29.01/29.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 29.01/29.19 Found x10:(P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 29.01/29.19 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found x20:(P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 29.01/29.19 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 29.01/29.19 Found x20:(P (((cK x0) x1) y))
% 29.01/29.19 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P (((cK x0) x1) y))
% 29.01/29.19 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P0 (((cK x0) x1) y))
% 29.01/29.19 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.01/29.19 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 29.01/29.19 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.01/29.19 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 29.01/29.19 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 29.01/29.19 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.01/29.19 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 29.01/29.19 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 34.77/34.91 Found eta_expansion000:=(eta_expansion00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 34.77/34.91 Found (eta_expansion00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found ((eta_expansion0 Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 34.77/34.91 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 34.77/34.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 34.77/34.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 34.77/34.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 34.77/34.91 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 34.77/34.91 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 34.77/34.91 Found x20:(P (x0 x1))
% 34.77/34.91 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 34.77/34.91 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 34.77/34.91 Found x20:(P (x0 x1))
% 34.77/34.91 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 34.77/34.91 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 34.77/34.91 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 34.77/34.91 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 34.77/34.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 34.77/34.91 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 34.77/34.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 34.77/34.91 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 34.77/34.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 34.77/34.91 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 34.77/34.91 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 34.77/34.91 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 57.26/57.42 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 57.26/57.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 57.26/57.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 57.26/57.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 57.26/57.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 57.26/57.42 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 57.26/57.42 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 57.26/57.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 57.26/57.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x20:(P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 57.26/57.42 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 57.26/57.42 Found x30:(P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 57.26/57.42 Found x30:(P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 57.26/57.42 Found x30:(P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 57.26/57.42 Found x30:(P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 57.26/57.42 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 57.26/57.42 Found x20:(P ((x0 x1) y))
% 57.26/57.42 Found (fun (x20:(P ((x0 x1) y)))=> x20) as proof of (P ((x0 x1) y))
% 57.26/57.42 Found (fun (x20:(P ((x0 x1) y)))=> x20) as proof of (P0 ((x0 x1) y))
% 57.26/57.42 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 57.26/57.42 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 57.26/57.42 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 57.26/57.42 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found eta_expansion000:=(eta_expansion00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 69.47/69.66 Found (eta_expansion00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found ((eta_expansion0 Prop) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion b) Prop) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion b) Prop) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion b) Prop) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 69.47/69.66 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 69.47/69.66 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 69.47/69.66 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 69.47/69.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 69.47/69.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 69.47/69.66 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 69.47/69.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 69.47/69.66 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 69.47/69.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 69.47/69.66 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 69.47/69.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 69.47/69.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 69.47/69.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.12 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.12 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.12 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.12 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.12 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.12 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.13 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 70.97/71.13 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 70.97/71.13 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 70.97/71.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.97/71.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 82.18/82.38 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.18/82.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 82.18/82.38 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.18/82.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 82.18/82.38 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 82.18/82.38 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 82.18/82.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.18/82.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 82.18/82.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 82.18/82.38 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 82.18/82.38 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 82.18/82.38 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 82.18/82.38 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 82.18/82.38 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 82.18/82.38 Found x20:(P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 82.18/82.38 Found x20:(P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 82.18/82.38 Found x20:(P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 82.18/82.38 Found x20:(P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 82.18/82.38 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 82.18/82.38 Found x30:(P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 82.18/82.38 Found x30:(P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 82.18/82.38 Found x30:(P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 82.18/82.38 Found x30:(P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 82.18/82.38 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 112.98/113.17 Found x30:(P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 112.98/113.17 Found x30:(P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 112.98/113.17 Found x30:(P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 112.98/113.17 Found x30:(P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P ((x0 x1) x2))
% 112.98/113.17 Found (fun (x30:(P ((x0 x1) x2)))=> x30) as proof of (P0 ((x0 x1) x2))
% 112.98/113.17 Found eta_expansion000:=(eta_expansion00 (cK x0)):(((eq (a->(b->Prop))) (cK x0)) (fun (x:a)=> ((cK x0) x)))
% 112.98/113.17 Found (eta_expansion00 (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 112.98/113.17 Found ((eta_expansion0 (b->Prop)) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 112.98/113.17 Found (((eta_expansion a) (b->Prop)) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 112.98/113.17 Found (((eta_expansion a) (b->Prop)) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 112.98/113.17 Found (((eta_expansion a) (b->Prop)) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 112.98/113.17 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->(b->Prop))) b0) (fun (x:a)=> (b0 x)))
% 112.98/113.17 Found (eta_expansion_dep00 b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 112.98/113.17 Found ((eta_expansion_dep0 (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 112.98/113.17 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 112.98/113.17 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 112.98/113.17 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 112.98/113.17 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq ((a->(b->Prop))->Prop)) a0) (fun (x:(a->(b->Prop)))=> (a0 x)))
% 112.98/113.17 Found (eta_expansion_dep00 a0) as proof of (((eq ((a->(b->Prop))->Prop)) a0) b0)
% 112.98/113.17 Found ((eta_expansion_dep0 (fun (x1:(a->(b->Prop)))=> Prop)) a0) as proof of (((eq ((a->(b->Prop))->Prop)) a0) b0)
% 112.98/113.17 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) a0) as proof of (((eq ((a->(b->Prop))->Prop)) a0) b0)
% 112.98/113.17 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) a0) as proof of (((eq ((a->(b->Prop))->Prop)) a0) b0)
% 112.98/113.17 Found (((eta_expansion_dep (a->(b->Prop))) (fun (x1:(a->(b->Prop)))=> Prop)) a0) as proof of (((eq ((a->(b->Prop))->Prop)) a0) b0)
% 112.98/113.17 Found eq_ref00:=(eq_ref0 b0):(((eq ((a->(b->Prop))->Prop)) b0) b0)
% 112.98/113.17 Found (eq_ref0 b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found eq_ref00:=(eq_ref0 b0):(((eq ((a->(b->Prop))->Prop)) b0) b0)
% 112.98/113.17 Found (eq_ref0 b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found ((eq_ref ((a->(b->Prop))->Prop)) b0) as proof of (((eq ((a->(b->Prop))->Prop)) b0) (fun (Xu:(a->(b->Prop)))=> (((eq (a->(b->Prop))) (cK Xu)) Xu)))
% 112.98/113.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 112.98/113.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 112.98/113.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 112.98/113.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.36/114.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.36/114.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.36/114.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.36/114.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.36/114.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 114.36/114.55 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 114.36/114.55 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 114.36/114.55 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.98/116.16 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 115.98/116.16 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 115.98/116.16 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.98/116.16 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found x1:(P (cK x0))
% 115.98/116.16 Instantiate: b0:=(cK x0):(a->(b->Prop))
% 115.98/116.16 Found x1 as proof of (P0 b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 115.98/116.16 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 115.98/116.16 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 115.98/116.16 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 115.98/116.16 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 115.98/116.16 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.98/116.16 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 115.98/116.16 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.98/116.16 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 115.98/116.16 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 115.98/116.16 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 115.98/116.16 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.98/116.16 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 127.00/127.24 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 127.00/127.24 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 127.00/127.24 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 127.00/127.24 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 127.00/127.24 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.00/127.24 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 127.00/127.24 Found x1:(P (cK x0))
% 127.00/127.24 Instantiate: f:=(cK x0):(a->(b->Prop))
% 127.00/127.24 Found x1 as proof of (P0 f)
% 127.00/127.24 Found eq_ref00:=(eq_ref0 (f x2)):(((eq (b->Prop)) (f x2)) (f x2))
% 127.00/127.24 Found (eq_ref0 (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (forall (x:a), (((eq (b->Prop)) (f x)) (x0 x)))
% 127.00/127.24 Found x1:(P (cK x0))
% 127.00/127.24 Instantiate: f:=(cK x0):(a->(b->Prop))
% 127.00/127.24 Found x1 as proof of (P0 f)
% 127.00/127.24 Found eq_ref00:=(eq_ref0 (f x2)):(((eq (b->Prop)) (f x2)) (f x2))
% 127.00/127.24 Found (eq_ref0 (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (((eq (b->Prop)) (f x2)) (x0 x2))
% 127.00/127.24 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (forall (x:a), (((eq (b->Prop)) (f x)) (x0 x)))
% 127.00/127.24 Found x1:(P (cK x0))
% 127.00/127.24 Instantiate: f:=(cK x0):(a->(b->Prop))
% 127.00/127.24 Found x1 as proof of (P0 f)
% 127.00/127.24 Found eq_ref00:=(eq_ref0 ((f x2) y)):(((eq Prop) ((f x2) y)) ((f x2) y))
% 127.00/127.24 Found (eq_ref0 ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) ((x0 x2) y))
% 127.00/127.24 Found ((eq_ref Prop) ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) ((x0 x2) y))
% 127.00/127.24 Found ((eq_ref Prop) ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) ((x0 x2) y))
% 127.00/127.24 Found (fun (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (((eq Prop) ((f x2) y)) ((x0 x2) y))
% 127.00/127.24 Found (fun (x2:a) (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (forall (y:b), (((eq Prop) ((f x2) y)) ((x0 x2) y)))
% 127.00/127.24 Found (fun (x2:a) (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (forall (x:a) (y:b), (((eq Prop) ((f x) y)) ((x0 x) y)))
% 127.00/127.24 Found eta_expansion_dep000:=(eta_expansion_dep00 (cK x0)):(((eq (a->(b->Prop))) (cK x0)) (fun (x:a)=> ((cK x0) x)))
% 127.00/127.24 Found (eta_expansion_dep00 (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 127.00/127.24 Found ((eta_expansion_dep0 (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 127.00/127.24 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 127.00/127.24 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 127.00/127.24 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 127.00/127.24 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 127.00/127.24 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 127.00/127.24 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 127.00/127.24 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 127.00/127.24 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) x0)
% 127.00/127.24 Found x30:(P (((cK x0) x1) x2))
% 127.00/127.24 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 127.00/127.24 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 127.00/127.24 Found x30:(P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 143.64/143.91 Found x30:(P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 143.64/143.91 Found x30:(P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 143.64/143.91 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 143.64/143.91 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 143.64/143.91 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 143.64/143.91 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 143.64/143.91 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 143.64/143.91 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 143.64/143.91 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found x1:(P x0)
% 143.64/143.91 Instantiate: x0:=(cK b0):(a->(b->Prop))
% 143.64/143.91 Found x1 as proof of (P0 b0)
% 143.64/143.91 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 143.64/143.91 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 143.64/143.91 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 143.64/143.91 Found x1:(P x0)
% 143.64/143.91 Instantiate: b0:=x0:(a->(b->Prop))
% 143.64/143.91 Found x1 as proof of (P0 b0)
% 143.64/143.91 Found eta_expansion_dep000:=(eta_expansion_dep00 (cK x0)):(((eq (a->(b->Prop))) (cK x0)) (fun (x:a)=> ((cK x0) x)))
% 143.64/143.91 Found (eta_expansion_dep00 (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 143.64/143.91 Found ((eta_expansion_dep0 (fun (x3:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 143.64/143.91 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 143.64/143.91 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 143.64/143.91 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b0)
% 143.64/143.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 143.64/143.91 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 143.64/143.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 143.64/143.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 143.64/143.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 143.64/143.91 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 143.64/143.91 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 143.64/143.91 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 154.25/154.48 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 154.25/154.48 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 154.25/154.48 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 154.25/154.48 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 154.25/154.48 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 154.25/154.48 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 154.25/154.48 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 154.25/154.48 Found x10:(P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 154.25/154.48 Found x10:(P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 154.25/154.48 Found x10:(P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 154.25/154.48 Found x10:(P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 154.25/154.48 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 154.25/154.48 Found x20:(P ((cK x0) x1))
% 154.25/154.48 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 154.25/154.48 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 154.25/154.48 Found x20:(P ((cK x0) x1))
% 154.25/154.48 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 156.85/157.07 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 156.85/157.07 Found x20:(P ((cK x0) x1))
% 156.85/157.07 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 156.85/157.07 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 156.85/157.07 Found eta_expansion_dep000:=(eta_expansion_dep00 (cK x0)):(((eq (a->(b->Prop))) (cK x0)) (fun (x:a)=> ((cK x0) x)))
% 156.85/157.07 Found (eta_expansion_dep00 (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b00)
% 156.85/157.07 Found ((eta_expansion_dep0 (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b00)
% 156.85/157.07 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b00)
% 156.85/157.07 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b00)
% 156.85/157.07 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) (cK x0)) as proof of (((eq (a->(b->Prop))) (cK x0)) b00)
% 156.85/157.07 Found eq_ref00:=(eq_ref0 b00):(((eq (a->(b->Prop))) b00) b00)
% 156.85/157.07 Found (eq_ref0 b00) as proof of (((eq (a->(b->Prop))) b00) x0)
% 156.85/157.07 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) x0)
% 156.85/157.07 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) x0)
% 156.85/157.07 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) x0)
% 156.85/157.07 Found x20:(P ((cK x0) x1))
% 156.85/157.07 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 156.85/157.07 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 156.85/157.07 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 156.85/157.07 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.85/157.07 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found x1:(P x0)
% 156.85/157.07 Instantiate: f:=x0:(a->(b->Prop))
% 156.85/157.07 Found x1 as proof of (P0 f)
% 156.85/157.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq (b->Prop)) (f x2)) (f x2))
% 156.85/157.07 Found (eq_ref0 (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (forall (x:a), (((eq (b->Prop)) (f x)) ((cK x0) x)))
% 156.85/157.07 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 156.85/157.07 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 156.85/157.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.85/157.07 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 156.85/157.07 Found x1:(P x0)
% 156.85/157.07 Instantiate: f:=x0:(a->(b->Prop))
% 156.85/157.07 Found x1 as proof of (P0 f)
% 156.85/157.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq (b->Prop)) (f x2)) (f x2))
% 156.85/157.07 Found (eq_ref0 (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found ((eq_ref (b->Prop)) (f x2)) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (((eq (b->Prop)) (f x2)) ((cK x0) x2))
% 156.85/157.07 Found (fun (x2:a)=> ((eq_ref (b->Prop)) (f x2))) as proof of (forall (x:a), (((eq (b->Prop)) (f x)) ((cK x0) x)))
% 166.10/166.31 Found x10:(P x0)
% 166.10/166.31 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 166.10/166.31 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 166.10/166.31 Found x10:(P x0)
% 166.10/166.31 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 166.10/166.31 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 166.10/166.31 Found x2:(P ((cK x0) x1))
% 166.10/166.31 Instantiate: b0:=((cK x0) x1):(b->Prop)
% 166.10/166.31 Found x2 as proof of (P0 b0)
% 166.10/166.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 166.10/166.31 Found (eta_expansion_dep00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found x2:(P ((cK x0) x1))
% 166.10/166.31 Instantiate: b0:=((cK x0) x1):(b->Prop)
% 166.10/166.31 Found x2 as proof of (P0 b0)
% 166.10/166.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 166.10/166.31 Found (eta_expansion_dep00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x20:(P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 166.10/166.31 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 166.10/166.31 Found x1:(P x0)
% 166.10/166.31 Instantiate: f:=x0:(a->(b->Prop))
% 166.10/166.31 Found x1 as proof of (P0 f)
% 166.10/166.31 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 166.10/166.31 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 166.10/166.31 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 166.10/166.31 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 166.10/166.31 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 166.10/166.31 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 171.52/171.78 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 171.52/171.78 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 171.52/171.78 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 171.52/171.78 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 171.52/171.78 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 171.52/171.78 Found x20:(P (((cK x0) x1) y))
% 171.52/171.78 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P (((cK x0) x1) y))
% 171.52/171.78 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P0 (((cK x0) x1) y))
% 171.52/171.78 Found x10:(P b0)
% 171.52/171.78 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 171.52/171.78 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 171.52/171.78 Found x20:(P (((cK x0) x1) y))
% 171.52/171.78 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P (((cK x0) x1) y))
% 171.52/171.78 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P0 (((cK x0) x1) y))
% 171.52/171.78 Found x1:(P x0)
% 171.52/171.78 Instantiate: x0:=(cK a0):(a->(b->Prop))
% 171.52/171.78 Found x1 as proof of (P0 a0)
% 171.52/171.78 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->(b->Prop))) a0) (fun (x:a)=> (a0 x)))
% 171.52/171.78 Found (eta_expansion_dep00 a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found ((eta_expansion_dep0 (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found x1:(P x0)
% 171.52/171.78 Instantiate: x0:=(cK a0):(a->(b->Prop))
% 171.52/171.78 Found x1 as proof of (P0 (cK a0))
% 171.52/171.78 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->(b->Prop))) a0) (fun (x:a)=> (a0 x)))
% 171.52/171.78 Found (eta_expansion_dep00 a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found ((eta_expansion_dep0 (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) a0) as proof of (((eq (a->(b->Prop))) a0) x0)
% 171.52/171.78 Found x2:(P ((cK x0) x1))
% 171.52/171.78 Instantiate: f:=((cK x0) x1):(b->Prop)
% 171.52/171.78 Found x2 as proof of (P0 f)
% 171.52/171.78 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 171.52/171.78 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((x0 x1) x)))
% 171.52/171.78 Found x2:(P ((cK x0) x1))
% 171.52/171.78 Instantiate: f:=((cK x0) x1):(b->Prop)
% 171.52/171.78 Found x2 as proof of (P0 f)
% 171.52/171.78 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 171.52/171.78 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((x0 x1) x)))
% 171.52/171.78 Found x2:(P ((cK x0) x1))
% 171.52/171.78 Instantiate: f:=((cK x0) x1):(b->Prop)
% 171.52/171.78 Found x2 as proof of (P0 f)
% 171.52/171.78 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 171.52/171.78 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 171.52/171.78 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((x0 x1) x)))
% 171.52/171.78 Found x2:(P ((cK x0) x1))
% 171.52/171.78 Instantiate: f:=((cK x0) x1):(b->Prop)
% 171.52/171.78 Found x2 as proof of (P0 f)
% 171.52/171.78 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 171.52/171.78 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 179.41/179.67 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 179.41/179.67 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 179.41/179.67 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((x0 x1) x3))
% 179.41/179.67 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((x0 x1) x)))
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((f x2) y)):(((eq Prop) ((f x2) y)) ((f x2) y))
% 179.41/179.67 Found (eq_ref0 ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) (((cK x0) x2) y))
% 179.41/179.67 Found ((eq_ref Prop) ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) (((cK x0) x2) y))
% 179.41/179.67 Found ((eq_ref Prop) ((f x2) y)) as proof of (((eq Prop) ((f x2) y)) (((cK x0) x2) y))
% 179.41/179.67 Found (fun (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (((eq Prop) ((f x2) y)) (((cK x0) x2) y))
% 179.41/179.67 Found (fun (x2:a) (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (forall (y:b), (((eq Prop) ((f x2) y)) (((cK x0) x2) y)))
% 179.41/179.67 Found (fun (x2:a) (y:b)=> ((eq_ref Prop) ((f x2) y))) as proof of (forall (x:a) (y:b), (((eq Prop) ((f x) y)) (((cK x0) x) y)))
% 179.41/179.67 Found x2:(P (((cK x0) x1) y))
% 179.41/179.67 Instantiate: b0:=(((cK x0) x1) y):Prop
% 179.41/179.67 Found x2 as proof of (P0 b0)
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 179.41/179.67 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 179.41/179.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.41/179.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 179.41/179.67 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.41/179.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 179.41/179.67 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.41/179.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 179.41/179.67 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 179.41/179.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.41/179.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) x2))
% 179.41/179.67 Found eq_ref00:=(eq_ref0 ((x0 x1) x2)):(((eq Prop) ((x0 x1) x2)) ((x0 x1) x2))
% 179.41/179.67 Found (eq_ref0 ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 193.47/193.74 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 193.47/193.74 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 193.47/193.74 Found ((eq_ref Prop) ((x0 x1) x2)) as proof of (((eq Prop) ((x0 x1) x2)) b0)
% 193.47/193.74 Found x10:(P b0)
% 193.47/193.74 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 193.47/193.74 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 193.47/193.74 Found x10:(P b0)
% 193.47/193.74 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 193.47/193.74 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 193.47/193.74 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 193.47/193.74 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 193.47/193.74 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 193.47/193.74 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 193.47/193.74 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 193.47/193.74 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 193.47/193.74 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 193.47/193.74 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 193.47/193.74 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 193.47/193.74 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 193.47/193.74 Found x10:(P1 x0)
% 193.47/193.74 Found (fun (x10:(P1 x0))=> x10) as proof of (P1 x0)
% 193.47/193.74 Found (fun (x10:(P1 x0))=> x10) as proof of (P2 x0)
% 218.50/218.80 Found x10:(P1 x0)
% 218.50/218.80 Found (fun (x10:(P1 x0))=> x10) as proof of (P1 x0)
% 218.50/218.80 Found (fun (x10:(P1 x0))=> x10) as proof of (P2 x0)
% 218.50/218.80 Found x10:(P b0)
% 218.50/218.80 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 218.50/218.80 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 218.50/218.80 Found x10:(P x0)
% 218.50/218.80 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 218.50/218.80 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->Prop))) b0) b0)
% 218.50/218.80 Found (eq_ref0 b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b0) as proof of (((eq (a->(b->Prop))) b0) (cK x0))
% 218.50/218.80 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 218.50/218.80 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 218.50/218.80 Found x20:(P1 ((cK x0) x1))
% 218.50/218.80 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 218.50/218.80 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 218.50/218.80 Found x20:(P1 ((cK x0) x1))
% 218.50/218.80 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 218.50/218.80 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 218.50/218.80 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 218.50/218.80 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 218.50/218.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 218.50/218.80 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 218.50/218.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 218.50/218.80 Found x10:(P1 x0)
% 218.50/218.80 Found (fun (x10:(P1 x0))=> x10) as proof of (P1 x0)
% 218.50/218.80 Found (fun (x10:(P1 x0))=> x10) as proof of (P2 x0)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 b00):(((eq (a->(b->Prop))) b00) b00)
% 218.50/218.80 Found (eq_ref0 b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 x0):(((eq (a->(b->Prop))) x0) x0)
% 218.50/218.80 Found (eq_ref0 x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 218.50/218.80 Found ((eq_ref (a->(b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 218.50/218.80 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 218.50/218.80 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 218.50/218.80 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 218.50/218.80 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 218.50/218.80 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 220.88/221.22 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 220.88/221.22 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 220.88/221.22 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 220.88/221.22 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 220.88/221.22 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 220.88/221.22 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 220.88/221.22 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 220.88/221.22 Found x2:(P (x0 x1))
% 220.88/221.22 Instantiate: x0:=(cK b0):(a->(b->Prop))
% 220.88/221.22 Found x2 as proof of (P0 b0)
% 220.88/221.22 Found eta_expansion000:=(eta_expansion00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 220.88/221.22 Found (eta_expansion00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found ((eta_expansion0 (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found x2:(P (x0 x1))
% 220.88/221.22 Instantiate: x0:=(cK b0):(a->(b->Prop))
% 220.88/221.22 Found x2 as proof of (P0 b0)
% 220.88/221.22 Found eta_expansion000:=(eta_expansion00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 220.88/221.22 Found (eta_expansion00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found ((eta_expansion0 (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 220.88/221.22 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 220.88/221.22 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 220.88/221.22 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 223.28/223.57 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 223.28/223.57 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 223.28/223.57 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found x20:(P ((cK x0) x1))
% 223.28/223.57 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 223.28/223.57 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 223.28/223.57 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 223.28/223.57 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 223.28/223.57 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found x20:(P ((cK x0) x1))
% 223.28/223.57 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P ((cK x0) x1))
% 223.28/223.57 Found (fun (x20:(P ((cK x0) x1)))=> x20) as proof of (P0 ((cK x0) x1))
% 223.28/223.57 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 223.28/223.57 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (x0 x1))
% 223.28/223.57 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 223.28/223.57 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 223.28/223.57 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 223.28/223.57 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found eta_expansion000:=(eta_expansion00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 223.28/223.57 Found (eta_expansion00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found ((eta_expansion0 Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 223.28/223.57 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 223.28/223.57 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 223.28/223.57 Found eta_expansion_dep000:=(eta_expansion_dep00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 225.59/225.88 Found (eta_expansion_dep00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 225.59/225.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found eta_expansion000:=(eta_expansion00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 225.59/225.88 Found (eta_expansion00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found ((eta_expansion0 Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 225.59/225.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found eta_expansion000:=(eta_expansion00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 225.59/225.88 Found (eta_expansion00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found ((eta_expansion0 Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion b) Prop) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 225.59/225.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found eta_expansion_dep000:=(eta_expansion_dep00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 225.59/225.88 Found (eta_expansion_dep00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 225.59/225.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((cK x0) x1))
% 225.59/225.88 Found eta_expansion_dep000:=(eta_expansion_dep00 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (fun (x:b)=> ((x0 x1) x)))
% 225.59/225.88 Found (eta_expansion_dep00 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 225.59/225.88 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found x20:(P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 231.24/231.51 Found x20:(P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 231.24/231.51 Found x20:(P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 231.24/231.51 Found x20:(P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P1 ((cK x0) x1))
% 231.24/231.51 Found (fun (x20:(P1 ((cK x0) x1)))=> x20) as proof of (P2 ((cK x0) x1))
% 231.24/231.51 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 231.24/231.51 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found x2:(P0 b0)
% 231.24/231.51 Instantiate: b0:=((cK x0) x1):(b->Prop)
% 231.24/231.51 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((cK x0) x1))
% 231.24/231.51 Found (fun (P0:((b->Prop)->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((cK x0) x1)))
% 231.24/231.51 Found (fun (P0:((b->Prop)->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 231.24/231.51 Found eq_ref00:=(eq_ref0 (x0 x1)):(((eq (b->Prop)) (x0 x1)) (x0 x1))
% 231.24/231.51 Found (eq_ref0 (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found ((eq_ref (b->Prop)) (x0 x1)) as proof of (((eq (b->Prop)) (x0 x1)) b0)
% 231.24/231.51 Found x2:(P0 b0)
% 231.24/231.51 Instantiate: b0:=((cK x0) x1):(b->Prop)
% 231.24/231.51 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((cK x0) x1))
% 231.24/231.51 Found (fun (P0:((b->Prop)->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((cK x0) x1)))
% 231.24/231.51 Found (fun (P0:((b->Prop)->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 231.24/231.51 Found eta_expansion000:=(eta_expansion00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 231.24/231.51 Found (eta_expansion00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found ((eta_expansion0 (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion a) (b->Prop)) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 231.24/231.51 Found (eta_expansion_dep00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found ((eta_expansion_dep0 (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 231.24/231.51 Found eq_ref00:=(eq_ref0 b00):(((eq (a->(b->Prop))) b00) b00)
% 231.24/231.51 Found (eq_ref0 b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 231.24/231.51 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 231.24/231.51 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 231.24/231.51 Found ((eq_ref (a->(b->Prop))) b00) as proof of (((eq (a->(b->Prop))) b00) b0)
% 231.24/231.51 Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 231.24/231.51 Found (eta_expansion_dep00 x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 231.24/231.51 Found ((eta_expansion_dep0 (fun (x2:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 231.24/231.51 Found (((eta_expansion_dep a) (fun (x2:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b00)
% 255.10/255.41 Found x20:(P1 (((cK x0) x1) y))
% 255.10/255.41 Found (fun (x20:(P1 (((cK x0) x1) y)))=> x20) as proof of (P1 (((cK x0) x1) y))
% 255.10/255.41 Found (fun (x20:(P1 (((cK x0) x1) y)))=> x20) as proof of (P2 (((cK x0) x1) y))
% 255.10/255.41 Found x2:(P (x0 x1))
% 255.10/255.41 Instantiate: b0:=(x0 x1):(b->Prop)
% 255.10/255.41 Found x2 as proof of (P0 b0)
% 255.10/255.41 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 255.10/255.41 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found x2:(P (x0 x1))
% 255.10/255.41 Instantiate: b0:=(x0 x1):(b->Prop)
% 255.10/255.41 Found x2 as proof of (P0 b0)
% 255.10/255.41 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 255.10/255.41 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 255.10/255.41 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 255.10/255.41 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 255.10/255.41 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 255.10/255.41 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 255.10/255.41 Found eq_ref00:=(eq_ref0 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) ((cK x0) x1))
% 255.10/255.41 Found (eq_ref0 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found ((eq_ref (b->Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b00)
% 255.10/255.41 Found x20:(P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 255.10/255.41 Found x20:(P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 255.10/255.41 Found x20:(P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 255.10/255.41 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 255.10/255.41 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 255.10/255.41 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 255.10/255.41 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 255.10/255.41 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 255.10/255.41 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 255.10/255.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 255.10/255.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 256.27/256.59 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 256.27/256.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 256.27/256.59 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 256.27/256.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found x20:(P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 256.27/256.59 Found x20:(P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 256.27/256.59 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 256.27/256.59 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 256.27/256.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 256.27/256.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 256.27/256.59 Found x20:(P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 256.27/256.59 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 256.27/256.59 Found x20:(P (((cK x0) x1) y))
% 256.27/256.59 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P (((cK x0) x1) y))
% 256.27/256.59 Found (fun (x20:(P (((cK x0) x1) y)))=> x20) as proof of (P0 (((cK x0) x1) y))
% 256.27/256.59 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 256.27/256.59 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 256.27/256.59 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 256.27/256.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 256.27/256.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) y))
% 256.27/256.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 256.27/256.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 256.27/256.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 257.50/257.78 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 257.50/257.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 257.50/257.78 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 257.50/257.78 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 257.50/257.78 Found x2:(P ((x0 x1) y))
% 257.50/257.78 Instantiate: x0:=(cK b0):(a->(b->Prop))
% 257.50/257.78 Found x2 as proof of (P0 b0)
% 257.50/257.78 Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 257.50/257.78 Found (eta_expansion_dep00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 257.50/257.78 Found ((eta_expansion_dep0 (fun (x4:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 257.50/257.78 Found (((eta_expansion_dep a) (fun (x4:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 257.50/257.78 Found (((eta_expansion_dep a) (fun (x4:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 257.50/257.78 Found (((eta_expansion_dep a) (fun (x4:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 257.50/257.78 Found (eq_ref0 a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 257.50/257.78 Found (eq_ref0 a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found ((eq_ref a) a0) as proof of (((eq a) a0) x1)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 257.50/257.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 257.50/257.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 257.50/257.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 257.50/257.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 257.50/257.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 257.50/257.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 257.50/257.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 258.46/258.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 258.46/258.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 258.46/258.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 258.46/258.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found eq_ref00:=(eq_ref0 (((cK x0) x1) x2)):(((eq Prop) (((cK x0) x1) x2)) (((cK x0) x1) x2))
% 258.46/258.78 Found (eq_ref0 (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found ((eq_ref Prop) (((cK x0) x1) x2)) as proof of (((eq Prop) (((cK x0) x1) x2)) b0)
% 258.46/258.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.46/258.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 258.46/258.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((x0 x1) x2))
% 268.78/269.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 268.78/269.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 268.78/269.12 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 268.78/269.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 268.78/269.12 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 268.78/269.12 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found x2:(P0 b0)
% 268.78/269.12 Instantiate: b0:=(((cK x0) x1) y):Prop
% 268.78/269.12 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 (((cK x0) x1) y))
% 268.78/269.12 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 (((cK x0) x1) y)))
% 268.78/269.12 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 268.78/269.12 Found x10:(P x0)
% 268.78/269.12 Found (fun (x10:(P x0))=> x10) as proof of (P x0)
% 268.78/269.12 Found (fun (x10:(P x0))=> x10) as proof of (P0 x0)
% 268.78/269.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 268.78/269.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 268.78/269.12 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found eq_ref00:=(eq_ref0 ((x0 x1) y)):(((eq Prop) ((x0 x1) y)) ((x0 x1) y))
% 268.78/269.12 Found (eq_ref0 ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found ((eq_ref Prop) ((x0 x1) y)) as proof of (((eq Prop) ((x0 x1) y)) b0)
% 268.78/269.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 268.78/269.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((cK x0) x1) y))
% 268.78/269.12 Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (a->(b->Prop))) x0) (fun (x:a)=> (x0 x)))
% 268.78/269.12 Found (eta_expansion_dep00 x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 268.78/269.12 Found ((eta_expansion_dep0 (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 268.78/269.12 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 268.78/269.12 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 281.91/282.23 Found (((eta_expansion_dep a) (fun (x3:a)=> (b->Prop))) x0) as proof of (((eq (a->(b->Prop))) x0) b0)
% 281.91/282.23 Found x2:(P (x0 x1))
% 281.91/282.23 Instantiate: b0:=(x0 x1):(b->Prop)
% 281.91/282.23 Found x2 as proof of (P0 b0)
% 281.91/282.23 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 281.91/282.23 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found x2:(P (x0 x1))
% 281.91/282.23 Instantiate: b0:=(x0 x1):(b->Prop)
% 281.91/282.23 Found x2 as proof of (P0 b0)
% 281.91/282.23 Found eta_expansion_dep000:=(eta_expansion_dep00 ((cK x0) x1)):(((eq (b->Prop)) ((cK x0) x1)) (fun (x:b)=> (((cK x0) x1) x)))
% 281.91/282.23 Found (eta_expansion_dep00 ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) ((cK x0) x1)) as proof of (((eq (b->Prop)) ((cK x0) x1)) b0)
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x2:(P ((x0 x1) y))
% 281.91/282.23 Instantiate: b0:=((x0 x1) y):Prop
% 281.91/282.23 Found x2 as proof of (P0 b0)
% 281.91/282.23 Found eq_ref00:=(eq_ref0 (((cK x0) x1) y)):(((eq Prop) (((cK x0) x1) y)) (((cK x0) x1) y))
% 281.91/282.23 Found (eq_ref0 (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 281.91/282.23 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 281.91/282.23 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 281.91/282.23 Found ((eq_ref Prop) (((cK x0) x1) y)) as proof of (((eq Prop) (((cK x0) x1) y)) b0)
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 281.91/282.23 Found x20:(P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 281.91/282.23 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found x20:(P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P (x0 x1))
% 299.17/299.53 Found (fun (x20:(P (x0 x1)))=> x20) as proof of (P0 (x0 x1))
% 299.17/299.53 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 299.17/299.53 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq (b->Prop)) (b0 x1)) (b0 x1))
% 299.17/299.53 Found (eq_ref0 (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found ((eq_ref (b->Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found ((eq_ref (b->Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found ((eq_ref (b->Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 299.17/299.53 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) (x0 x1))
% 299.17/299.53 Found eta_expansion_dep000:=(eta_expansion_dep00 (b0 x1)):(((eq (b->Prop)) (b0 x1)) (fun (x:b)=> ((b0 x1) x)))
% 299.17/299.53 Found (eta_expansion_dep00 (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (b0 x1)) as proof of (((eq (b->Prop)) (b0 x1)) b00)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x2:(P (x0 x1))
% 299.17/299.53 Instantiate: f:=(x0 x1):(b->Prop)
% 299.17/299.53 Found x2 as proof of (P0 f)
% 299.17/299.53 Found x30:(P (((cK x0) x1) x2))
% 299.17/299.53 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 299.17/299.53 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P0 (((cK x0) x1) x2))
% 299.17/299.53 Found x30:(P (((cK x0) x1) x2))
% 299.17/299.53 Found (fun (x30:(P (((cK x0) x1) x2)))=> x30) as proof of (P (((cK x0) x1) x2))
% 299.17/299.53 Foun
%------------------------------------------------------------------------------