TSTP Solution File: SYO235^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO235^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n022.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 00:50:58 EDT 2022
% Result : Timeout 285.88s 286.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO235^5 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n022.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 20:35:57 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
% 2.25/2.46 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.25/2.46 FOF formula (<kernel.Constant object at 0xa47bd8>, <kernel.Sort object at 0x2b03ffdd45a8>) of role type named cB
% 2.25/2.46 Using role type
% 2.25/2.46 Declaring cB:Prop
% 2.25/2.46 FOF formula (<kernel.Constant object at 0xa47a28>, <kernel.Sort object at 0x2b03ffdd45a8>) of role type named cA
% 2.25/2.46 Using role type
% 2.25/2.46 Declaring cA:Prop
% 2.25/2.46 FOF formula (((or (forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))) ((iff cA) cB))->(((eq Prop) cA) cB)) of role conjecture named cTHM505
% 2.25/2.46 Conjecture to prove = (((or (forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))) ((iff cA) cB))->(((eq Prop) cA) cB)):Prop
% 2.25/2.46 We need to prove ['(((or (forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))) ((iff cA) cB))->(((eq Prop) cA) cB))']
% 2.25/2.46 Parameter cB:Prop.
% 2.25/2.46 Parameter cA:Prop.
% 2.25/2.46 Trying to prove (((or (forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))) ((iff cA) cB))->(((eq Prop) cA) cB))
% 2.25/2.46 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) cB))
% 2.25/2.46 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 2.25/2.46 Found x100:=(x10 x0):(P cB)
% 2.25/2.46 Found (x10 x0) as proof of (P cB)
% 2.25/2.46 Found ((x1 P) x0) as proof of (P cB)
% 2.25/2.46 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 2.25/2.46 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 2.25/2.46 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 2.25/2.46 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 2.25/2.46 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 2.25/2.46 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 2.25/2.46 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 2.25/2.46 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 2.25/2.46 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 2.25/2.46 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 2.25/2.46 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 2.25/2.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 2.25/2.46 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 2.25/2.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 2.25/2.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 2.25/2.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 2.25/2.46 Found x100:=(x10 x0):(P cB)
% 2.25/2.46 Found (x10 x0) as proof of (P cB)
% 2.25/2.46 Found ((x1 P) x0) as proof of (P cB)
% 2.25/2.46 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 2.25/2.46 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 5.66/5.85 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found x00:(P cA)
% 5.66/5.85 Found (fun (x00:(P cA))=> x00) as proof of (P cA)
% 5.66/5.85 Found (fun (x00:(P cA))=> x00) as proof of (P0 cA)
% 5.66/5.85 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 5.66/5.85 Found (eq_ref00 P) as proof of (P0 cA)
% 5.66/5.85 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 5.66/5.85 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 5.66/5.85 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 5.66/5.85 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.66/5.85 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 5.66/5.85 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.66/5.85 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found x10:(P cA)
% 5.66/5.85 Found (fun (x10:(P cA))=> x10) as proof of (P cA)
% 5.66/5.85 Found (fun (x10:(P cA))=> x10) as proof of (P0 cA)
% 5.66/5.85 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 5.66/5.85 Found (eq_ref00 P) as proof of (P0 cA)
% 5.66/5.85 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 5.66/5.85 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 5.66/5.85 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 5.66/5.85 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 5.66/5.85 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 5.66/5.85 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 5.66/5.85 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.66/5.85 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 5.66/5.85 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 5.66/5.85 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 5.66/5.85 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 5.66/5.85 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 5.66/5.85 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 5.66/5.85 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 5.66/5.85 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 5.66/5.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.66/5.85 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 5.66/5.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found x0:(((eq Prop) cA) cB)
% 10.53/10.68 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 10.53/10.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.53/10.68 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 10.53/10.68 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 10.53/10.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.53/10.68 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found x30:(P cA)
% 10.53/10.68 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 10.53/10.68 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 10.53/10.68 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 10.53/10.68 Found (eq_ref00 P) as proof of (P0 cA)
% 10.53/10.68 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 10.53/10.68 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 10.53/10.68 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 10.53/10.68 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.53/10.68 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 10.53/10.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 10.53/10.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.53/10.68 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 10.53/10.68 Found x100:=(x10 x0):(P cB)
% 10.53/10.68 Found (x10 x0) as proof of (P cB)
% 10.53/10.68 Found ((x1 P) x0) as proof of (P cB)
% 10.53/10.68 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 10.53/10.68 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 10.53/10.68 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 10.53/10.68 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 10.53/10.68 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 16.36/16.61 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 16.36/16.61 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 16.36/16.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 16.36/16.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found x100:=(x10 x0):(P cB)
% 16.36/16.61 Found (x10 x0) as proof of (P cB)
% 16.36/16.61 Found ((x1 P) x0) as proof of (P cB)
% 16.36/16.61 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 16.36/16.61 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 16.36/16.61 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 16.36/16.61 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 16.36/16.61 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 16.36/16.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 16.36/16.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 16.36/16.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 16.36/16.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.36/16.61 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 16.36/16.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.26/22.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 22.26/22.42 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.26/22.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.26/22.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 22.26/22.42 Found x0:(P cA)
% 22.26/22.42 Instantiate: b:=cA:Prop
% 22.26/22.42 Found x0 as proof of (P0 b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found x0:(P cA)
% 22.26/22.42 Instantiate: b:=cA:Prop
% 22.26/22.42 Found x0 as proof of (P0 b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 22.26/22.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 22.26/22.42 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 22.26/22.42 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 22.26/22.42 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 22.26/22.42 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 22.26/22.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.26/22.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 22.26/22.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 22.26/22.42 Found x0:(((eq Prop) cA) cB)
% 22.26/22.42 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 27.46/27.63 Found x1:(P cA)
% 27.46/27.63 Instantiate: b:=cA:Prop
% 27.46/27.63 Found x1 as proof of (P0 b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 27.46/27.63 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 27.46/27.63 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.46/27.63 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 27.46/27.63 Found (eq_ref00 P) as proof of (P0 cA)
% 27.46/27.63 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 27.46/27.63 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 27.46/27.63 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 27.46/27.63 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.46/27.63 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 27.46/27.63 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found x0:(P0 b)
% 27.46/27.63 Instantiate: b:=cA:Prop
% 27.46/27.63 Found (fun (x0:(P0 b))=> x0) as proof of (P0 cA)
% 27.46/27.63 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 cA))
% 27.46/27.63 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 27.46/27.63 Found x0:(P cB)
% 27.46/27.63 Instantiate: b:=cB:Prop
% 27.46/27.63 Found x0 as proof of (P0 b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 27.46/27.63 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found x00:(P cA)
% 27.46/27.63 Found (fun (x00:(P cA))=> x00) as proof of (P cA)
% 27.46/27.63 Found (fun (x00:(P cA))=> x00) as proof of (P0 cA)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 27.46/27.63 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.46/27.63 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found x1:(P cA)
% 27.46/27.63 Instantiate: b:=cA:Prop
% 27.46/27.63 Found x1 as proof of (P0 b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 27.46/27.63 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 27.46/27.63 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 27.46/27.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.46/27.63 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 27.46/27.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.16 Found x0:(P cA)
% 34.92/35.16 Instantiate: b:=cA:Prop
% 34.92/35.16 Found x0 as proof of (P0 b)
% 34.92/35.16 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 34.92/35.16 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 34.92/35.16 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 34.92/35.16 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 34.92/35.16 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 34.92/35.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.16 Found (eq_ref0 b) as proof of (P b)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (P b)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (P b)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (P b)
% 34.92/35.16 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 34.92/35.16 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.16 Found x0:(P cB)
% 34.92/35.16 Instantiate: b:=cB:Prop
% 34.92/35.16 Found x0 as proof of (P0 b)
% 34.92/35.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 34.92/35.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 34.92/35.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.16 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.17 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 34.92/35.17 Found (eq_ref00 P) as proof of (P0 cA)
% 34.92/35.17 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 34.92/35.17 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 34.92/35.17 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 34.92/35.17 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 34.92/35.17 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.17 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.17 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.17 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.17 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 34.92/35.17 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 34.92/35.17 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.17 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.92/35.17 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 34.92/35.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 41.75/41.93 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 41.75/41.93 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 41.75/41.93 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 41.75/41.93 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 41.75/41.93 Found x3:(P cA)
% 41.75/41.93 Instantiate: b:=cA:Prop
% 41.75/41.93 Found x3 as proof of (P0 b)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 41.75/41.93 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 41.75/41.93 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 41.75/41.93 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 41.75/41.93 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 41.75/41.93 Found x100:=(x10 x0):(P cB)
% 41.75/41.93 Found (x10 x0) as proof of (P b)
% 41.75/41.93 Found ((x1 P) x0) as proof of (P b)
% 41.75/41.93 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P b)
% 41.75/41.93 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P b))
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 41.75/41.93 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found x1:(P0 b)
% 41.75/41.93 Instantiate: b:=cA:Prop
% 41.75/41.93 Found (fun (x1:(P0 b))=> x1) as proof of (P0 cA)
% 41.75/41.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 cA))
% 41.75/41.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 41.75/41.93 Found x10:(P cA)
% 41.75/41.93 Found (fun (x10:(P cA))=> x10) as proof of (P cA)
% 41.75/41.93 Found (fun (x10:(P cA))=> x10) as proof of (P0 cA)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 41.75/41.93 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.75/41.93 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 41.75/41.93 Found x00:(P b)
% 41.75/41.93 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 41.75/41.93 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 41.75/41.93 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 41.75/41.93 Found (eq_ref00 P) as proof of (P0 b)
% 41.75/41.93 Found ((eq_ref0 b) P) as proof of (P0 b)
% 41.75/41.93 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 41.75/41.93 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 41.75/41.93 Found x1:(P cB)
% 41.75/41.93 Instantiate: b:=cB:Prop
% 41.75/41.93 Found x1 as proof of (P0 b)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 41.75/41.93 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.75/41.93 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 41.75/41.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 41.75/41.93 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 41.75/41.93 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 41.75/41.93 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.24/45.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.24/45.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 45.24/45.42 Found (eq_ref00 P) as proof of (P0 cB)
% 45.24/45.42 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 45.24/45.42 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 45.24/45.42 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.24/45.42 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found x1:(P0 b)
% 45.24/45.42 Instantiate: b:=cA:Prop
% 45.24/45.42 Found (fun (x1:(P0 b))=> x1) as proof of (P0 cA)
% 45.24/45.42 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 cA))
% 45.24/45.42 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 45.24/45.42 Found x0:(((eq Prop) cA) cB)
% 45.24/45.42 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 45.24/45.42 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 45.24/45.42 Found x0:(((eq Prop) cA) cB)
% 45.24/45.42 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 45.24/45.42 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 45.24/45.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.24/45.42 Found (eq_ref0 b) as proof of (P b)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (P b)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (P b)
% 45.24/45.42 Found ((eq_ref Prop) b) as proof of (P b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found x3:(P cA)
% 45.24/45.42 Instantiate: b:=cA:Prop
% 45.24/45.42 Found x3 as proof of (P0 b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 45.24/45.42 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 45.24/45.42 Found x100:=(x10 x0):(P cB)
% 45.24/45.42 Found (x10 x0) as proof of (P cB)
% 45.24/45.42 Found ((x1 P) x0) as proof of (P cB)
% 45.24/45.42 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 45.24/45.42 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 45.24/45.42 Found x1:(P cB)
% 45.24/45.42 Instantiate: b:=cB:Prop
% 45.24/45.42 Found x1 as proof of (P0 b)
% 45.24/45.42 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 45.24/45.42 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 45.24/45.42 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found x0:(P cA)
% 54.47/54.70 Instantiate: b:=cA:Prop
% 54.47/54.70 Found x0 as proof of (P0 b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 54.47/54.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 54.47/54.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.47/54.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 54.47/54.70 Found x1:(P cB)
% 54.47/54.70 Instantiate: b:=cB:Prop
% 54.47/54.70 Found x1 as proof of (P0 b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 54.47/54.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 54.47/54.70 Found x1:(P cA)
% 54.47/54.70 Instantiate: b:=cA:Prop
% 54.47/54.70 Found x1 as proof of (P0 b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 54.47/54.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found x00:(P cB)
% 54.47/54.70 Found (fun (x00:(P cB))=> x00) as proof of (P cB)
% 54.47/54.70 Found (fun (x00:(P cB))=> x00) as proof of (P0 cB)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.47/54.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 54.47/54.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 54.47/54.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 54.47/54.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 54.47/54.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 54.47/54.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 54.47/54.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 54.47/54.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 54.47/54.70 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 54.47/54.70 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 54.47/54.70 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 54.47/54.70 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 54.47/54.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.47/54.70 Found (eq_ref0 b) as proof of (P b)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (P b)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (P b)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (P b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 54.47/54.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.47/54.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 54.47/54.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 54.47/54.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 54.47/54.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 58.52/58.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 58.52/58.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 58.52/58.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 58.52/58.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 58.52/58.70 Found x1:(P cB)
% 58.52/58.70 Instantiate: b:=cB:Prop
% 58.52/58.70 Found x1 as proof of (P0 b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 58.52/58.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 58.52/58.70 Found (eq_ref00 P) as proof of (P0 cA)
% 58.52/58.70 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 58.52/58.70 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 58.52/58.70 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 58.52/58.70 Found x10:(P b)
% 58.52/58.70 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 58.52/58.70 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 58.52/58.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 58.52/58.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 58.52/58.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 58.52/58.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 58.52/58.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 58.52/58.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 58.52/58.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 58.52/58.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 58.52/58.70 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 58.52/58.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 58.52/58.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 58.52/58.70 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 58.52/58.70 Found (eq_ref00 P) as proof of (P0 b)
% 58.52/58.70 Found ((eq_ref0 b) P) as proof of (P0 b)
% 58.52/58.70 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 58.52/58.70 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 58.52/58.70 Found eq_substitution00000:=(eq_substitution0000 (fun (x3:Prop)=> x3)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 58.52/58.70 Found (eq_substitution0000 (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 58.52/58.70 Found ((eq_substitution000 cB) (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 58.52/58.70 Found (((eq_substitution00 cA) cB) (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 58.52/58.70 Found ((((eq_substitution0 Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 64.05/64.26 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 64.05/64.26 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 64.05/64.26 Found x100:=(x10 x0):(P cB)
% 64.05/64.26 Found (x10 x0) as proof of (P cB)
% 64.05/64.26 Found ((x1 P) x0) as proof of (P cB)
% 64.05/64.26 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 64.05/64.26 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 64.05/64.26 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 64.05/64.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found x30:(P cA)
% 64.05/64.26 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 64.05/64.26 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 64.05/64.26 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.05/64.26 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 64.05/64.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 64.05/64.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 64.05/64.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 64.05/64.26 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 64.05/64.26 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 64.05/64.26 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 64.05/64.26 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 64.05/64.26 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 64.05/64.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 64.05/64.26 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 64.05/64.26 Found x3:(P0 b)
% 64.05/64.26 Instantiate: b:=cA:Prop
% 64.05/64.26 Found (fun (x3:(P0 b))=> x3) as proof of (P0 cA)
% 64.05/64.26 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 cA))
% 64.05/64.26 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 64.05/64.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.05/64.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 64.05/64.26 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 64.05/64.26 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 64.05/64.26 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 64.05/64.26 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 64.05/64.26 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 67.11/67.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 67.11/67.36 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found x00:(P b)
% 67.11/67.36 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 67.11/67.36 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 67.11/67.36 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 67.11/67.36 Found (eq_ref00 P) as proof of (P0 cB)
% 67.11/67.36 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 67.11/67.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 67.11/67.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 67.11/67.36 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 67.11/67.36 Found (eq_ref00 P) as proof of (P0 cB)
% 67.11/67.36 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 67.11/67.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 67.11/67.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 67.11/67.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 67.11/67.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 67.11/67.36 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.11/67.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 67.11/67.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 67.11/67.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 70.24/70.52 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 70.24/70.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 70.24/70.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 70.24/70.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 70.24/70.52 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 70.24/70.52 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 70.24/70.52 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 70.24/70.52 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 70.24/70.52 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 70.24/70.52 Found x100:=(x10 x0):(P1 cB)
% 70.24/70.52 Found (x10 x0) as proof of (P1 cB)
% 70.24/70.52 Found ((x1 P1) x0) as proof of (P1 cB)
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 cB)
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 70.24/70.52 Found x100:=(x10 x0):(P1 cB)
% 70.24/70.52 Found (x10 x0) as proof of (P1 cB)
% 70.24/70.52 Found ((x1 P1) x0) as proof of (P1 cB)
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 cB)
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 70.24/70.52 Found x3:(P cB)
% 70.24/70.52 Instantiate: b:=cB:Prop
% 70.24/70.52 Found x3 as proof of (P0 b)
% 70.24/70.52 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 70.24/70.52 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 70.24/70.52 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 70.24/70.52 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 70.24/70.52 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x1) as proof of (((eq Prop) b) cB)
% 70.24/70.52 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x1) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found x10:(P b)
% 70.24/70.52 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 70.24/70.52 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 70.24/70.52 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 70.24/70.52 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 73.54/73.74 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 73.54/73.74 Found (eq_ref00 P) as proof of (P0 b)
% 73.54/73.74 Found ((eq_ref0 b) P) as proof of (P0 b)
% 73.54/73.74 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 73.54/73.74 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 73.54/73.74 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 73.54/73.74 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 73.54/73.74 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 73.54/73.74 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cA))
% 73.54/73.74 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 73.54/73.74 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 73.54/73.74 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 73.54/73.74 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 73.54/73.74 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 73.54/73.74 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 73.54/73.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 73.54/73.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 73.54/73.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 73.54/73.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 73.54/73.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 73.54/73.74 Found x100:=(x10 x0):(P cB)
% 73.54/73.74 Found (x10 x0) as proof of (P cB)
% 73.54/73.74 Found ((x1 P) x0) as proof of (P cB)
% 73.54/73.74 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 73.54/73.74 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 73.54/73.74 Found eq_substitution00000:=(eq_substitution0000 (fun (x3:Prop)=> x3)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 73.54/73.74 Found (eq_substitution0000 (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found ((eq_substitution000 cB) (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found (((eq_substitution00 cA) cB) (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found ((((eq_substitution0 Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x3:Prop)=> x3)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 73.54/73.74 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 73.54/73.74 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 73.54/73.74 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 73.54/73.74 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 73.54/73.74 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 73.54/73.74 Found x00:(P cA)
% 73.54/73.74 Found (fun (x00:(P cA))=> x00) as proof of (P cA)
% 73.54/73.74 Found (fun (x00:(P cA))=> x00) as proof of (P0 cA)
% 73.54/73.74 Found x10:(P cB)
% 73.54/73.74 Found (fun (x10:(P cB))=> x10) as proof of (P cB)
% 73.54/73.74 Found (fun (x10:(P cB))=> x10) as proof of (P0 cB)
% 73.54/73.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 73.54/73.74 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 73.54/73.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 80.32/80.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 80.32/80.54 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 80.32/80.54 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 80.32/80.54 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 80.32/80.54 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 80.32/80.54 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 80.32/80.54 Found (eq_ref00 P) as proof of (P0 cA)
% 80.32/80.54 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 80.32/80.54 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 80.32/80.54 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 80.32/80.54 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 80.32/80.54 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 80.32/80.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 80.32/80.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 80.32/80.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 80.32/80.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 80.32/80.54 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found x3:(P0 b)
% 80.32/80.54 Instantiate: b:=cA:Prop
% 80.32/80.54 Found (fun (x3:(P0 b))=> x3) as proof of (P0 cA)
% 80.32/80.54 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 cA))
% 80.32/80.54 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% 80.32/80.54 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 80.32/80.54 Found (eq_ref00 P) as proof of (P0 cA)
% 80.32/80.54 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 80.32/80.54 Found (eq_ref00 P) as proof of (P0 cA)
% 80.32/80.54 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 80.32/80.54 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found x3:(P0 b)
% 80.32/80.54 Instantiate: b:=cA:Prop
% 80.32/80.54 Found (fun (x3:(P0 b))=> x3) as proof of (P0 cA)
% 80.32/80.54 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 cA))
% 80.32/80.54 Found (fun (P0:(Prop->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% 80.32/80.54 Found x20:=(x2 x10):cA
% 80.32/80.54 Found (x2 x10) as proof of cA
% 80.32/80.54 Found (x2 x10) as proof of cA
% 80.32/80.54 Found x10:=(x1 x20):cB
% 80.32/80.54 Found (x1 x20) as proof of cB
% 80.32/80.54 Found (x1 x20) as proof of cB
% 80.32/80.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.32/80.54 Found (eq_ref0 b) as proof of (P b)
% 80.32/80.54 Found ((eq_ref Prop) b) as proof of (P b)
% 80.32/80.54 Found ((eq_ref Prop) b) as proof of (P b)
% 80.32/80.54 Found ((eq_ref Prop) b) as proof of (P b)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 80.32/80.54 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 80.32/80.54 Found (eq_ref00 P) as proof of (P0 cB)
% 80.32/80.54 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 80.32/80.54 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 80.32/80.54 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 80.32/80.54 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 80.32/80.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.32/80.54 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 84.94/85.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.94/85.16 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 84.94/85.16 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 84.94/85.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 84.94/85.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 84.94/85.16 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.94/85.16 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 84.94/85.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.94/85.16 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 84.94/85.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.94/85.16 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 84.94/85.16 Found x3:(P cB)
% 84.94/85.16 Instantiate: b:=cB:Prop
% 84.94/85.16 Found x3 as proof of (P0 b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 84.94/85.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found x3:(P cB)
% 84.94/85.16 Instantiate: b:=cB:Prop
% 84.94/85.16 Found x3 as proof of (P0 b)
% 84.94/85.16 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 84.94/85.16 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 84.94/85.16 Found x30:(P cA)
% 84.94/85.16 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 84.94/85.16 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 84.94/85.16 Found x30:(P cA)
% 84.94/85.16 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 84.94/85.16 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 84.94/85.16 Found x10:=(x1 x20):cB
% 84.94/85.16 Found (x1 x20) as proof of cB
% 84.94/85.16 Found (x1 x20) as proof of cB
% 84.94/85.16 Found x20:=(x2 x10):cA
% 84.94/85.16 Found (x2 x10) as proof of cA
% 84.94/85.16 Found (x2 x10) as proof of cA
% 84.94/85.16 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 84.94/85.16 Found (eq_ref00 P) as proof of (P0 cA)
% 84.94/85.16 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 84.94/85.16 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 84.94/85.16 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 84.94/85.16 Found x100:=(x10 x0):(P1 cB)
% 84.94/85.16 Found (x10 x0) as proof of (P1 cB)
% 84.94/85.16 Found ((x1 P1) x0) as proof of (P1 cB)
% 84.94/85.16 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P1) x0)) as proof of (P1 cB)
% 84.94/85.16 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P1) x0)) as proof of ((((eq Prop) cA) cB)->(P1 cB))
% 84.94/85.16 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 84.94/85.16 Found (eq_ref00 P) as proof of (P0 cA)
% 84.94/85.16 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 84.94/85.16 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 84.94/85.16 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 87.72/87.99 Found x100:=(x10 x0):(P1 cB)
% 87.72/87.99 Found (x10 x0) as proof of (P1 cB)
% 87.72/87.99 Found ((x1 P1) x0) as proof of (P1 cB)
% 87.72/87.99 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P1) x0)) as proof of (P1 cB)
% 87.72/87.99 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P1) x0)) as proof of ((((eq Prop) cA) cB)->(P1 cB))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found x3:(P cB)
% 87.72/87.99 Instantiate: b:=cB:Prop
% 87.72/87.99 Found x3 as proof of (P0 b)
% 87.72/87.99 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 87.72/87.99 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 87.72/87.99 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 87.72/87.99 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 87.72/87.99 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 87.72/87.99 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 87.72/87.99 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 87.72/87.99 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 87.72/87.99 Found x1:(((eq Prop) cA) cB)
% 87.72/87.99 Found (fun (x1:(((eq Prop) cA) cB))=> x1) as proof of (((eq Prop) b) cB)
% 87.72/87.99 Found (fun (x1:(((eq Prop) cA) cB))=> x1) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 87.72/87.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 87.72/87.99 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 87.72/87.99 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 87.72/87.99 Found x10:(P cB)
% 87.72/87.99 Found (fun (x10:(P cB))=> x10) as proof of (P cB)
% 87.72/87.99 Found (fun (x10:(P cB))=> x10) as proof of (P0 cB)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 94.61/94.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 94.61/94.82 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 94.61/94.82 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 94.61/94.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 94.61/94.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 94.61/94.82 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 94.61/94.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 94.61/94.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 94.61/94.82 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 94.61/94.82 Found x20:=(x2 x10):cA
% 94.61/94.82 Found (x2 x10) as proof of cA
% 94.61/94.82 Found (x2 x10) as proof of cA
% 94.61/94.82 Found x10:=(x1 x20):cB
% 94.61/94.82 Found (x1 x20) as proof of cB
% 94.61/94.82 Found (x1 x20) as proof of cB
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 94.61/94.82 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 94.61/94.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 94.61/94.82 Found x30:=(x3 x20):cA
% 94.61/94.82 Found (x3 x20) as proof of cA
% 94.61/94.82 Found (x3 x20) as proof of cA
% 94.61/94.82 Found x20:=(x2 x30):cB
% 94.61/94.82 Found (x2 x30) as proof of cB
% 94.61/94.82 Found (x2 x30) as proof of cB
% 94.61/94.82 Found x30:(P cA)
% 94.61/94.82 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 94.61/94.82 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 94.61/94.82 Found x30:(P cA)
% 94.61/94.82 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 94.61/94.82 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 94.61/94.82 Found x20:=(x2 x10):cA
% 94.61/94.82 Found (x2 x10) as proof of cA
% 94.61/94.82 Found (x2 x10) as proof of cA
% 94.61/94.82 Found x10:=(x1 x20):cB
% 94.61/94.82 Found (x1 x20) as proof of cB
% 94.61/94.82 Found (x1 x20) as proof of cB
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 94.61/94.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 94.61/94.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 94.61/94.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 94.61/94.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 94.61/94.82 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 94.61/94.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 94.61/94.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 94.61/94.82 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/103.59 Found (eq_ref0 b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 103.33/103.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/103.59 Found (eq_ref0 b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (P b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 103.33/103.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found x10:=(x1 x20):cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found x20:=(x2 x10):cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 103.33/103.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 103.33/103.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found x20:=(x2 x10):cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found x10:=(x1 x20):cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found x10:=(x1 x20):cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found (x1 x20) as proof of cB
% 103.33/103.59 Found x20:=(x2 x10):cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found (x2 x10) as proof of cA
% 103.33/103.59 Found x3:(P cB)
% 103.33/103.59 Instantiate: b:=cB:Prop
% 103.33/103.59 Found x3 as proof of (P0 b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 103.33/103.59 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found x3:(P cB)
% 103.33/103.59 Instantiate: b:=cB:Prop
% 103.33/103.59 Found x3 as proof of (P0 b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 103.33/103.59 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/103.59 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 103.33/103.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 103.33/103.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 103.33/103.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 103.33/103.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 103.33/103.59 Found x10:(P cA)
% 103.33/103.59 Found (fun (x10:(P cA))=> x10) as proof of (P cA)
% 103.33/103.59 Found (fun (x10:(P cA))=> x10) as proof of (P0 cA)
% 103.33/103.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.33/103.59 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 109.47/109.68 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 109.47/109.68 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 109.47/109.68 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 109.47/109.68 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 109.47/109.68 Found (eq_ref00 P) as proof of (P0 cA)
% 109.47/109.68 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 109.47/109.68 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 109.47/109.68 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 109.47/109.68 Found x1:(P cB)
% 109.47/109.68 Instantiate: b:=cB:Prop
% 109.47/109.68 Found x1 as proof of (P0 b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 109.47/109.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found x1:(P cB)
% 109.47/109.68 Instantiate: b:=cB:Prop
% 109.47/109.68 Found x1 as proof of (P0 b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 109.47/109.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.47/109.68 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 109.47/109.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 109.47/109.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.47/109.68 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 109.47/109.68 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 109.47/109.68 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.47/109.68 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 109.47/109.68 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 109.47/109.68 Found (eq_ref00 P) as proof of (P0 b)
% 109.47/109.68 Found ((eq_ref0 b) P) as proof of (P0 b)
% 109.47/109.68 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 109.47/109.68 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 109.47/109.68 Found x30:(P b)
% 109.47/109.68 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 109.47/109.68 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 109.47/109.68 Found x20:=(x2 x10):cA
% 109.47/109.68 Found (x2 x10) as proof of cA
% 109.47/109.68 Found (x2 x10) as proof of cA
% 109.47/109.68 Found x10:=(x1 x20):cB
% 109.47/109.68 Found (x1 x20) as proof of cB
% 109.47/109.68 Found (x1 x20) as proof of cB
% 109.47/109.68 Found x10:(P b)
% 109.47/109.68 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 109.47/109.68 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 116.10/116.35 Found x20:=(x2 x10):cA
% 116.10/116.35 Found (x2 x10) as proof of cA
% 116.10/116.35 Found (x2 x10) as proof of cA
% 116.10/116.35 Found x10:=(x1 x20):cB
% 116.10/116.35 Found (x1 x20) as proof of cB
% 116.10/116.35 Found (x1 x20) as proof of cB
% 116.10/116.35 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 116.10/116.35 Found (eq_ref00 P) as proof of (P0 cB)
% 116.10/116.35 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 116.10/116.35 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 116.10/116.35 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 116.10/116.35 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 116.10/116.35 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 116.10/116.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.10/116.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 116.10/116.35 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 116.10/116.35 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 116.10/116.35 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) cA))
% 116.10/116.35 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 116.10/116.35 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 116.10/116.35 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 116.10/116.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.10/116.35 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 116.10/116.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 116.10/116.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 116.10/116.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 116.10/116.35 Found x10:=(x1 x20):cB
% 116.10/116.35 Found (x1 x20) as proof of cB
% 116.10/116.35 Found (x1 x20) as proof of cB
% 116.10/116.35 Found x20:=(x2 x10):cA
% 116.10/116.35 Found (x2 x10) as proof of cA
% 116.10/116.35 Found (x2 x10) as proof of cA
% 116.10/116.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 116.10/116.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.10/116.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found x20:=(x2 x30):cB
% 116.10/116.35 Found (x2 x30) as proof of cB
% 116.10/116.35 Found (x2 x30) as proof of cB
% 116.10/116.35 Found x30:=(x3 x20):cA
% 116.10/116.35 Found (x3 x20) as proof of cA
% 116.10/116.35 Found (x3 x20) as proof of cA
% 116.10/116.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 116.10/116.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 116.10/116.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.10/116.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.10/116.35 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 116.10/116.35 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 116.10/116.35 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 116.10/116.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.10/116.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 116.10/116.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.89/123.15 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.89/123.15 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 122.89/123.15 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 122.89/123.15 Found x20:=(x2 x10):cA
% 122.89/123.15 Found (x2 x10) as proof of cA
% 122.89/123.15 Found (x2 x10) as proof of cA
% 122.89/123.15 Found x10:=(x1 x20):cB
% 122.89/123.15 Found (x1 x20) as proof of cB
% 122.89/123.15 Found (x1 x20) as proof of cB
% 122.89/123.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.89/123.15 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 122.89/123.15 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b0) cB)
% 122.89/123.15 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b0) cB))
% 122.89/123.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.89/123.15 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 122.89/123.15 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 122.89/123.15 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 122.89/123.15 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 122.89/123.15 Found (eq_ref00 P) as proof of (P0 cB)
% 122.89/123.15 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 122.89/123.15 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 122.89/123.15 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 122.89/123.15 Found x0:(((eq Prop) cA) cB)
% 122.89/123.15 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 122.89/123.15 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 122.89/123.15 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 122.89/123.15 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b0) b))
% 122.89/123.15 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b0) b))
% 128.67/128.94 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b0) b))
% 128.67/128.94 Found x1:(P0 cA)
% 128.67/128.94 Found (fun (x1:(P0 cA))=> x1) as proof of (P0 cA)
% 128.67/128.94 Found (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1) as proof of ((P0 cA)->(P0 cA))
% 128.67/128.94 Found (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1) as proof of (P cA)
% 128.67/128.94 Found (x00 (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1)) as proof of (P b)
% 128.67/128.94 Found ((x0 P) (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1)) as proof of (P b)
% 128.67/128.94 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x0 P) (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1))) as proof of (P b)
% 128.67/128.94 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x0 P) (fun (P0:(Prop->Prop)) (x1:(P0 cA))=> x1))) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P b))
% 128.67/128.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.67/128.94 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 128.67/128.94 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.67/128.94 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 128.67/128.94 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 128.67/128.94 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.67/128.94 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found x10:(P cB)
% 128.67/128.94 Found (fun (x10:(P cB))=> x10) as proof of (P cB)
% 128.67/128.94 Found (fun (x10:(P cB))=> x10) as proof of (P0 cB)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.67/128.94 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 128.67/128.94 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 128.67/128.94 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 128.67/128.94 Found (eq_ref00 P) as proof of (P0 b)
% 128.67/128.94 Found ((eq_ref0 b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 128.67/128.94 Found (eq_ref00 P) as proof of (P0 b)
% 128.67/128.94 Found ((eq_ref0 b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 128.67/128.94 Found (eq_ref00 P) as proof of (P0 b)
% 128.67/128.94 Found ((eq_ref0 b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 128.67/128.94 Found x30:(P b)
% 128.67/128.94 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 128.67/128.94 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 128.67/128.94 Found x30:(P b)
% 128.67/128.94 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 128.67/128.94 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 128.67/128.94 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 128.67/128.94 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 128.67/128.94 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 131.67/131.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 131.67/131.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.67/131.92 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 131.67/131.92 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 131.67/131.92 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 131.67/131.92 Found x10:=(x1 x20):cB
% 131.67/131.92 Found (x1 x20) as proof of cB
% 131.67/131.92 Found (x1 x20) as proof of cB
% 131.67/131.92 Found x20:=(x2 x10):cA
% 131.67/131.92 Found (x2 x10) as proof of cA
% 131.67/131.92 Found (x2 x10) as proof of cA
% 131.67/131.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 131.67/131.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 131.67/131.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 131.67/131.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 131.67/131.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 131.67/131.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.67/131.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 131.67/131.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 131.67/131.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.67/131.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 131.67/131.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.67/131.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.67/131.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 131.67/131.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 131.67/131.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 131.67/131.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found x30:(P cB)
% 137.30/137.57 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 137.30/137.57 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.30/137.57 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 137.30/137.57 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found x0:(((eq Prop) cA) cB)
% 137.30/137.57 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 137.30/137.57 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 137.30/137.57 Found x200:=(x20 x1):(P1 cB)
% 137.30/137.57 Found (x20 x1) as proof of (P1 cB)
% 137.30/137.57 Found ((x2 P1) x1) as proof of (P1 cB)
% 137.30/137.57 Found (fun (x2:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x2 P1) x1)) as proof of (P1 cB)
% 137.30/137.57 Found (fun (x2:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x2 P1) x1)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 137.30/137.57 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 137.30/137.57 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.30/137.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 137.30/137.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 137.30/137.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 137.30/137.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.30/137.57 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 137.30/137.57 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.30/137.57 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 137.30/137.57 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 137.30/137.57 Found x200:=(x20 x1):(P1 cB)
% 137.30/137.57 Found (x20 x1) as proof of (P1 b)
% 137.30/137.57 Found ((x2 P1) x1) as proof of (P1 b)
% 137.30/137.57 Found (fun (x2:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x2 P1) x1)) as proof of (P1 b)
% 137.30/137.57 Found (fun (x2:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x2 P1) x1)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 b))
% 137.30/137.57 Found x1:(((eq Prop) cA) cB)
% 137.30/137.57 Instantiate: b:=cB:Prop
% 137.30/137.57 Found x1 as proof of (((eq Prop) cA) b)
% 137.30/137.57 Found x0:(P cB)
% 137.30/137.57 Instantiate: b:=cB:Prop
% 137.30/137.57 Found x0 as proof of (P0 b)
% 137.30/137.57 Found ((eq_sym0100 x1) x0) as proof of (P cA)
% 137.30/137.57 Found ((eq_sym0100 x1) x0) as proof of (P cA)
% 137.30/137.57 Found (((fun (x2:(((eq Prop) cA) b))=> ((eq_sym010 x2) P)) x1) x0) as proof of (P cA)
% 137.30/137.57 Found (((fun (x2:(((eq Prop) cA) cB))=> (((eq_sym01 cB) x2) P)) x1) x0) as proof of (P cA)
% 137.30/137.57 Found (((fun (x2:(((eq Prop) cA) cB))=> ((((eq_sym0 cA) cB) x2) P)) x1) x0) as proof of (P cA)
% 137.30/137.57 Found (fun (x1:(((eq Prop) cA) cB))=> (((fun (x2:(((eq Prop) cA) cB))=> ((((eq_sym0 cA) cB) x2) P)) x1) x0)) as proof of (P cA)
% 137.30/137.57 Found (fun (x1:(((eq Prop) cA) cB))=> (((fun (x2:(((eq Prop) cA) cB))=> ((((eq_sym0 cA) cB) x2) P)) x1) x0)) as proof of ((((eq Prop) cA) cB)->(P cA))
% 137.30/137.57 Found x0:(P cB)
% 137.30/137.57 Instantiate: b:=cB:Prop
% 137.30/137.57 Found x0 as proof of (P0 b)
% 137.30/137.57 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 137.30/137.57 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found x0:(P cB)
% 142.62/142.89 Instantiate: b:=cB:Prop
% 142.62/142.89 Found x0 as proof of (P0 b)
% 142.62/142.89 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 142.62/142.89 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 142.62/142.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 142.62/142.89 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 142.62/142.89 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 142.62/142.89 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 142.62/142.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 142.62/142.89 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 142.62/142.89 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 142.62/142.89 Found (eq_ref00 P) as proof of (P0 cB)
% 142.62/142.89 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 142.62/142.89 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 142.62/142.89 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 142.62/142.89 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 142.62/142.89 Found (eq_ref00 P) as proof of (P0 cB)
% 142.62/142.89 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 142.62/142.89 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 142.62/142.89 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 142.62/142.89 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 142.62/142.89 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 142.62/142.89 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 142.62/142.89 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 142.62/142.89 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 147.78/148.02 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 147.78/148.02 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 147.78/148.02 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 147.78/148.02 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 147.78/148.02 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 147.78/148.02 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 147.78/148.02 Found x0:(((eq Prop) cA) cB)
% 147.78/148.02 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b0) cB)
% 147.78/148.02 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b0) cB))
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 147.78/148.02 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 147.78/148.02 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 147.78/148.02 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 147.78/148.02 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.78/148.02 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.78/148.02 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 147.78/148.02 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.78/148.02 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 147.78/148.02 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.78/148.02 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 147.78/148.02 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 147.78/148.02 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b0) b))
% 147.78/148.02 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b0) b))
% 147.78/148.02 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b0) b))
% 147.78/148.02 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 147.78/148.02 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 147.78/148.02 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 156.04/156.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 156.04/156.36 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 156.04/156.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 156.04/156.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 156.04/156.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.04/156.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 156.04/156.36 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 156.04/156.36 Found (eq_ref00 P) as proof of (P0 cB)
% 156.04/156.36 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 156.04/156.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 156.04/156.36 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 156.04/156.36 Found x10:(P b)
% 156.04/156.36 Found (fun (x10:(P b))=> x10) as proof of (P b)
% 156.04/156.36 Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 156.04/156.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.04/156.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found x10:=(x1 x20):cB
% 156.04/156.36 Found (x1 x20) as proof of cB
% 156.04/156.36 Found (x1 x20) as proof of cB
% 156.04/156.36 Found x20:=(x2 x10):cA
% 156.04/156.36 Found (x2 x10) as proof of cA
% 156.04/156.36 Found (x2 x10) as proof of cA
% 156.04/156.36 Found x30:(P cB)
% 156.04/156.36 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 156.04/156.36 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 156.04/156.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 156.04/156.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found x30:(P cB)
% 156.04/156.36 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 156.04/156.36 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 156.04/156.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 156.04/156.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 156.04/156.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.04/156.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 156.04/156.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 156.04/156.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 156.04/156.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 160.50/160.77 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 160.50/160.77 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.50/160.77 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 160.50/160.77 Found x10:=(x1 x20):cB
% 160.50/160.77 Found (x1 x20) as proof of cB
% 160.50/160.77 Found (x1 x20) as proof of cB
% 160.50/160.77 Found x20:=(x2 x10):cA
% 160.50/160.77 Found (x2 x10) as proof of cA
% 160.50/160.77 Found (x2 x10) as proof of cA
% 160.50/160.77 Found x200:=(x20 x1):(P1 cB)
% 160.50/160.77 Found (x20 x1) as proof of (P1 cB)
% 165.60/165.84 Found ((x2 P1) x1) as proof of (P1 cB)
% 165.60/165.84 Found (fun (x2:(((eq Prop) cA) cB))=> ((x2 P1) x1)) as proof of (P1 cB)
% 165.60/165.84 Found (fun (x2:(((eq Prop) cA) cB))=> ((x2 P1) x1)) as proof of ((((eq Prop) cA) cB)->(P1 cB))
% 165.60/165.84 Found x30:(P cA)
% 165.60/165.84 Found (fun (x30:(P cA))=> x30) as proof of (P cA)
% 165.60/165.84 Found (fun (x30:(P cA))=> x30) as proof of (P0 cA)
% 165.60/165.84 Found eq_ref000:=(eq_ref00 P):((P cA)->(P cA))
% 165.60/165.84 Found (eq_ref00 P) as proof of (P0 cA)
% 165.60/165.84 Found ((eq_ref0 cA) P) as proof of (P0 cA)
% 165.60/165.84 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 165.60/165.84 Found (((eq_ref Prop) cA) P) as proof of (P0 cA)
% 165.60/165.84 Found x200:=(x20 x1):(P1 cB)
% 165.60/165.84 Found (x20 x1) as proof of (P1 b)
% 165.60/165.84 Found ((x2 P1) x1) as proof of (P1 b)
% 165.60/165.84 Found (fun (x2:(((eq Prop) cA) cB))=> ((x2 P1) x1)) as proof of (P1 b)
% 165.60/165.84 Found (fun (x2:(((eq Prop) cA) cB))=> ((x2 P1) x1)) as proof of ((((eq Prop) cA) cB)->(P1 b))
% 165.60/165.84 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 165.60/165.84 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.60/165.84 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.60/165.84 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 165.60/165.84 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 165.60/165.84 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 165.60/165.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.60/165.84 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 165.60/165.84 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.60/165.84 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 165.60/165.84 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 165.60/165.84 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) cB)
% 165.60/165.84 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) cB))
% 165.60/165.84 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 165.60/165.84 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 165.60/165.84 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 165.60/165.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.57/169.86 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 169.57/169.86 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 169.57/169.86 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 169.57/169.86 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 169.57/169.86 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 169.57/169.86 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 169.57/169.86 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 169.57/169.86 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cA) b))
% 169.57/169.86 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 169.57/169.86 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 169.57/169.86 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.57/169.86 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.57/169.86 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 169.57/169.86 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 169.57/169.86 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 169.57/169.86 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 169.57/169.86 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 169.57/169.86 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 169.57/169.86 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 169.57/169.86 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 181.88/182.18 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 181.88/182.18 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 181.88/182.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.88/182.18 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 181.88/182.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 181.88/182.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 181.88/182.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 181.88/182.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 181.88/182.18 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 181.88/182.18 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 181.88/182.18 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 181.88/182.18 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 181.88/182.18 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 181.88/182.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 181.88/182.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 181.88/182.18 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 181.88/182.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 181.88/182.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x20:=(x2 x10):cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found (x2 x10) as proof of cA
% 181.88/182.18 Found x10:=(x1 x20):cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found (x1 x20) as proof of cB
% 181.88/182.18 Found x100:=(x10 x0):(P cB)
% 181.88/182.18 Found (x10 x0) as proof of (P cB)
% 181.88/182.18 Found ((x1 P) x0) as proof of (P cB)
% 181.88/182.18 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 181.88/182.18 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 181.88/182.18 Found x100:=(x10 x0):(P cB)
% 181.88/182.18 Found (x10 x0) as proof of (P cB)
% 181.88/182.18 Found ((x1 P) x0) as proof of (P cB)
% 181.88/182.18 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 181.88/182.18 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 186.78/187.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.08 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 186.78/187.08 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 186.78/187.08 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.08 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found x20:=(x2 x10):cA
% 186.78/187.08 Found (x2 x10) as proof of cA
% 186.78/187.08 Found (x2 x10) as proof of cA
% 186.78/187.08 Found x10:=(x1 x20):cB
% 186.78/187.08 Found (x1 x20) as proof of cB
% 186.78/187.08 Found (x1 x20) as proof of cB
% 186.78/187.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.08 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 186.78/187.08 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.08 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 186.78/187.09 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.09 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 186.78/187.09 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 186.78/187.09 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 186.78/187.09 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 186.78/187.09 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 186.78/187.09 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 186.78/187.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.78/187.09 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 186.78/187.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 186.78/187.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 186.78/187.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 186.78/187.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 186.78/187.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 190.29/190.58 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 190.29/190.58 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 190.29/190.58 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b))
% 190.29/190.58 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 190.29/190.58 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.29/190.58 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.29/190.58 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 190.29/190.58 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 190.29/190.58 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.29/190.58 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 190.29/190.58 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 190.29/190.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 190.29/190.58 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 190.29/190.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 190.29/190.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 190.29/190.58 Found x0:(((eq Prop) cA) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 190.29/190.58 Found x0:(((eq Prop) cA) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 190.29/190.58 Found x0:(((eq Prop) cA) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 190.29/190.58 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 195.05/195.35 Found x20:=(x2 x10):cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found x10:=(x1 x20):cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found x0:(((eq Prop) cA) cB)
% 195.05/195.35 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) cB)
% 195.05/195.35 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cB))
% 195.05/195.35 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 195.05/195.35 Found (eq_ref00 P) as proof of (P0 cB)
% 195.05/195.35 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 195.05/195.35 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 195.05/195.35 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 195.05/195.35 Found x10:=(x1 x20):cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found x20:=(x2 x10):cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found x30:(P cB)
% 195.05/195.35 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 195.05/195.35 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 195.05/195.35 Found x10:=(x1 x20):cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found x30:=(x3 x20):cA
% 195.05/195.35 Found (x3 x20) as proof of cA
% 195.05/195.35 Found (x3 x20) as proof of cA
% 195.05/195.35 Found x20:=(x2 x10):cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.05/195.35 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 195.05/195.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found x20:=(x2 x30):cB
% 195.05/195.35 Found (x2 x30) as proof of cB
% 195.05/195.35 Found (x2 x30) as proof of cB
% 195.05/195.35 Found x20:=(x2 x30):cB
% 195.05/195.35 Found (x2 x30) as proof of cB
% 195.05/195.35 Found (x2 x30) as proof of cB
% 195.05/195.35 Found x10:=(x1 x20):cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found (x1 x20) as proof of cB
% 195.05/195.35 Found x20:=(x2 x10):cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found (x2 x10) as proof of cA
% 195.05/195.35 Found x30:=(x3 x20):cA
% 195.05/195.35 Found (x3 x20) as proof of cA
% 195.05/195.35 Found (x3 x20) as proof of cA
% 195.05/195.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.05/195.35 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 195.05/195.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 195.05/195.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 195.05/195.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 195.05/195.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 195.05/195.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 195.05/195.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.05/195.35 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 195.05/195.35 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 195.05/195.35 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 195.05/195.35 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 200.73/200.99 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 200.73/200.99 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 200.73/200.99 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.73/200.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.73/200.99 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 200.73/200.99 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.73/200.99 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.73/200.99 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 200.73/200.99 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 200.73/200.99 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 200.73/200.99 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 200.73/200.99 Found x100:=(x10 x0):(P cB)
% 200.73/200.99 Found (x10 x0) as proof of (P cB)
% 200.73/200.99 Found ((x1 P) x0) as proof of (P cB)
% 200.73/200.99 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of (P cB)
% 200.73/200.99 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P cB))
% 200.73/200.99 Found x20:=(x2 x10):cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found x10:=(x1 x20):cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found x20:=(x2 x10):cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found x10:=(x1 x20):cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found x20:=(x2 x10):cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found x20:=(x2 x10):cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found x10:=(x1 x20):cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found x10:=(x1 x20):cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found x10:=(x1 x20):cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found (x1 x20) as proof of cB
% 200.73/200.99 Found x20:=(x2 x10):cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found (x2 x10) as proof of cA
% 200.73/200.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 200.73/200.99 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 200.73/200.99 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 200.73/200.99 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 200.73/200.99 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 200.73/200.99 Found (eq_sym01 cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 200.73/200.99 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 200.73/200.99 Found ((eq_sym0 cA) cB) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x30:=(x3 x20):cA
% 209.03/209.36 Found (x3 x20) as proof of cA
% 209.03/209.36 Found (x3 x20) as proof of cA
% 209.03/209.36 Found x30:=(x3 x20):cA
% 209.03/209.36 Found (x3 x20) as proof of cA
% 209.03/209.36 Found (x3 x20) as proof of cA
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x100:=(x10 x0):(P cB)
% 209.03/209.36 Found (x10 x0) as proof of (P cB)
% 209.03/209.36 Found ((x1 P) x0) as proof of (P cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 209.03/209.36 Found x100:=(x10 x0):(P cB)
% 209.03/209.36 Found (x10 x0) as proof of (P cB)
% 209.03/209.36 Found ((x1 P) x0) as proof of (P cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x100:=(x10 x0):(P0 cB)
% 209.03/209.36 Found (x10 x0) as proof of (P0 cB)
% 209.03/209.36 Found ((x1 P0) x0) as proof of (P0 cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P0) x0)) as proof of (P0 cB)
% 209.03/209.36 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P0) x0)) as proof of ((((eq Prop) cA) cB)->(P0 cB))
% 209.03/209.36 Found x10:=(x1 x20):cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found (x1 x20) as proof of cB
% 209.03/209.36 Found x20:=(x2 x10):cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found (x2 x10) as proof of cA
% 209.03/209.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 209.03/209.36 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 209.03/209.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 209.03/209.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 209.03/209.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 209.03/209.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 209.03/209.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 209.03/209.36 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) b) cB)->(((eq Prop) cB) b))
% 209.03/209.36 Found eq_sym010 as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 209.03/209.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 209.03/209.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 209.03/209.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 209.03/209.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 209.03/209.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 209.03/209.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 209.03/209.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 209.03/209.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 209.03/209.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 209.03/209.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 216.54/216.82 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 216.54/216.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 216.54/216.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 216.54/216.82 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 216.54/216.82 Found (eq_ref00 P) as proof of (P0 b)
% 216.54/216.82 Found ((eq_ref0 b) P) as proof of (P0 b)
% 216.54/216.82 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.54/216.82 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.54/216.82 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 216.54/216.82 Found (eq_ref00 P) as proof of (P0 b)
% 216.54/216.82 Found ((eq_ref0 b) P) as proof of (P0 b)
% 216.54/216.82 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.54/216.82 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 216.54/216.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 216.54/216.82 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 216.54/216.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 216.54/216.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 216.54/216.82 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 216.54/216.82 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 216.54/216.82 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) cA))
% 216.54/216.82 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 216.54/216.82 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b))
% 216.54/216.82 Found x30:(P cB)
% 216.54/216.82 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 216.54/216.82 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 216.54/216.82 Found x30:(P b)
% 216.54/216.82 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 216.54/216.82 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 216.54/216.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.54/216.82 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 216.54/216.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 216.54/216.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 216.54/216.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 216.54/216.82 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 216.54/216.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 216.54/216.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 216.54/216.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 223.03/223.36 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 223.03/223.36 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b0))
% 223.03/223.36 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 223.03/223.36 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 223.03/223.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 223.03/223.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 223.03/223.36 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 223.03/223.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 223.03/223.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 223.03/223.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 223.03/223.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 223.03/223.36 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 223.03/223.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 223.03/223.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 223.03/223.36 Found x20:=(x2 x30):cB
% 223.03/223.36 Found (x2 x30) as proof of cB
% 223.03/223.36 Found (x2 x30) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x30:=(x3 x20):cA
% 223.03/223.36 Found (x3 x20) as proof of cA
% 223.03/223.36 Found (x3 x20) as proof of cA
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x10:=(x1 x20):cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found (x1 x20) as proof of cB
% 223.03/223.36 Found x20:=(x2 x10):cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found (x2 x10) as proof of cA
% 223.03/223.36 Found x20:=(x2 x30):cB
% 223.03/223.36 Found (x2 x30) as proof of cB
% 223.03/223.36 Found (x2 x30) as proof of cB
% 223.03/223.36 Found x30:=(x3 x20):cA
% 229.11/229.47 Found (x3 x20) as proof of cA
% 229.11/229.47 Found (x3 x20) as proof of cA
% 229.11/229.47 Found x100:=(x10 x0):(P cB)
% 229.11/229.47 Found (x10 x0) as proof of (P cB)
% 229.11/229.47 Found ((x1 P) x0) as proof of (P cB)
% 229.11/229.47 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of (P cB)
% 229.11/229.47 Found (fun (x1:(((eq Prop) cA) cB))=> ((x1 P) x0)) as proof of ((((eq Prop) cA) cB)->(P cB))
% 229.11/229.47 Found x20:=(x2 x30):cB
% 229.11/229.47 Found (x2 x30) as proof of cB
% 229.11/229.47 Found (x2 x30) as proof of cB
% 229.11/229.47 Found x30:=(x3 x20):cA
% 229.11/229.47 Found (x3 x20) as proof of cA
% 229.11/229.47 Found (x3 x20) as proof of cA
% 229.11/229.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.11/229.47 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 229.11/229.47 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 229.11/229.47 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.11/229.47 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 229.11/229.47 Found x10:=(x1 x20):cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found x20:=(x2 x10):cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found x10:=(x1 x20):cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found x10:=(x1 x20):cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found (x1 x20) as proof of cB
% 229.11/229.47 Found x20:=(x2 x10):cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found x20:=(x2 x10):cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 229.11/229.47 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 229.11/229.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 229.11/229.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 229.11/229.47 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 229.11/229.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 229.11/229.47 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 229.11/229.47 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 229.11/229.47 Found eq_sym010:=(eq_sym01 cB):((((eq Prop) cA) cB)->(((eq Prop) cB) cA))
% 229.11/229.47 Found (eq_sym01 cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 229.11/229.47 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 229.11/229.47 Found ((eq_sym0 cA) cB) as proof of ((((eq Prop) cA) cB)->(((eq Prop) cB) b0))
% 229.11/229.47 Found x20:=(x2 x10):cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 229.11/229.47 Found x20:=(x2 x10):cA
% 229.11/229.47 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.19/239.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 239.19/239.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 239.19/239.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 239.19/239.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 239.19/239.49 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 239.19/239.49 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 239.19/239.49 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 239.19/239.49 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 239.19/239.49 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x30:=(x3 x20):cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x30:=(x3 x20):cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x30:=(x3 x20):cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found (x3 x20) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found x10:=(x1 x20):cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found (x1 x20) as proof of cB
% 239.19/239.49 Found x20:=(x2 x10):cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found (x2 x10) as proof of cA
% 239.19/239.49 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 239.19/239.49 Found (eq_ref00 P) as proof of (P0 cB)
% 239.19/239.49 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 239.19/239.49 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 239.19/239.49 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 239.19/239.49 Found eq_ref000:=(eq_ref00 P):((P cB)->(P cB))
% 239.19/239.49 Found (eq_ref00 P) as proof of (P0 cB)
% 239.19/239.49 Found ((eq_ref0 cB) P) as proof of (P0 cB)
% 239.19/239.49 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 239.19/239.49 Found (((eq_ref Prop) cB) P) as proof of (P0 cB)
% 239.19/239.49 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 239.19/239.49 Found (eq_ref00 P) as proof of (P0 b)
% 239.19/239.49 Found ((eq_ref0 b) P) as proof of (P0 b)
% 239.19/239.49 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 239.19/239.49 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 239.19/239.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.19/239.49 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 239.19/239.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 239.19/239.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 239.19/239.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 239.19/239.49 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 239.19/239.49 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 239.19/239.49 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 239.19/239.49 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 239.19/239.49 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 239.19/239.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.19/239.49 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 249.27/249.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 249.27/249.59 Found x30:(P cB)
% 249.27/249.59 Found (fun (x30:(P cB))=> x30) as proof of (P cB)
% 249.27/249.59 Found (fun (x30:(P cB))=> x30) as proof of (P0 cB)
% 249.27/249.59 Found x30:(P b)
% 249.27/249.59 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 249.27/249.59 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 249.27/249.59 Found x30:(P b)
% 249.27/249.59 Found (fun (x30:(P b))=> x30) as proof of (P b)
% 249.27/249.59 Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% 249.27/249.59 Found x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))
% 249.27/249.59 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of (((eq Prop) b) b0)
% 249.27/249.59 Found (fun (x0:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> x0) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) b) b0))
% 249.27/249.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 249.27/249.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 249.27/249.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 249.27/249.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 249.27/249.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 249.27/249.59 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 249.27/249.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 249.27/249.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 249.27/249.59 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 249.27/249.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 249.27/249.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x10:=(x1 x20):cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x10:=(x1 x20):cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x10:=(x1 x20):cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 249.27/249.59 Found x10:=(x1 x20):cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found (x1 x20) as proof of cB
% 249.27/249.59 Found x20:=(x2 x10):cA
% 249.27/249.59 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x0:(((eq Prop) cA) cB)
% 263.36/263.70 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b0) cB)
% 263.36/263.70 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b0) cB))
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x30:=(x3 x20):cA
% 263.36/263.70 Found (x3 x20) as proof of cA
% 263.36/263.70 Found (x3 x20) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x30):cB
% 263.36/263.70 Found (x2 x30) as proof of cB
% 263.36/263.70 Found (x2 x30) as proof of cB
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found x20:=(x2 x10):cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found (x2 x10) as proof of cA
% 263.36/263.70 Found x10:=(x1 x20):cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found (x1 x20) as proof of cB
% 263.36/263.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 263.36/263.70 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 263.36/263.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 263.36/263.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 263.36/263.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 263.36/263.70 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 263.36/263.70 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 263.36/263.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 263.36/263.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 263.36/263.70 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 263.36/263.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 263.36/263.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 267.58/267.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 267.58/267.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 267.58/267.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 267.58/267.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.58/267.92 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x30:=(x3 x20):cA
% 267.58/267.92 Found (x3 x20) as proof of cA
% 267.58/267.92 Found (x3 x20) as proof of cA
% 267.58/267.92 Found x30:=(x3 x20):cA
% 267.58/267.92 Found (x3 x20) as proof of cA
% 267.58/267.92 Found (x3 x20) as proof of cA
% 267.58/267.92 Found x20:=(x2 x30):cB
% 267.58/267.92 Found (x2 x30) as proof of cB
% 267.58/267.92 Found (x2 x30) as proof of cB
% 267.58/267.92 Found x20:=(x2 x30):cB
% 267.58/267.92 Found (x2 x30) as proof of cB
% 267.58/267.92 Found (x2 x30) as proof of cB
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.58/267.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 267.58/267.92 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 267.58/267.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 267.58/267.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 267.58/267.92 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x100:=(x10 x0):(P1 cB)
% 267.58/267.92 Found (x10 x0) as proof of (P1 cB)
% 267.58/267.92 Found ((x1 P1) x0) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 267.58/267.92 Found x100:=(x10 x0):(P1 cB)
% 267.58/267.92 Found (x10 x0) as proof of (P1 cB)
% 267.58/267.92 Found ((x1 P1) x0) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 267.58/267.92 Found x100:=(x10 x0):(P1 cB)
% 267.58/267.92 Found (x10 x0) as proof of (P1 cB)
% 267.58/267.92 Found ((x1 P1) x0) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 cB)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 cB))
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x20:=(x2 x10):cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found (x2 x10) as proof of cA
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x10:=(x1 x20):cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found (x1 x20) as proof of cB
% 267.58/267.92 Found x100:=(x10 x0):(P1 cB)
% 267.58/267.92 Found (x10 x0) as proof of (P1 b)
% 267.58/267.92 Found ((x1 P1) x0) as proof of (P1 b)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 b)
% 267.58/267.92 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 b))
% 267.58/267.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.58/267.92 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 267.58/267.92 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 275.29/275.64 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found x100:=(x10 x0):(P1 cB)
% 275.29/275.64 Found (x10 x0) as proof of (P1 b)
% 275.29/275.64 Found ((x1 P1) x0) as proof of (P1 b)
% 275.29/275.64 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 b)
% 275.29/275.64 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 b))
% 275.29/275.64 Found x100:=(x10 x0):(P1 cB)
% 275.29/275.64 Found (x10 x0) as proof of (P1 b)
% 275.29/275.64 Found ((x1 P1) x0) as proof of (P1 b)
% 275.29/275.64 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of (P1 b)
% 275.29/275.64 Found (fun (x1:(forall (Q:(Prop->Prop)), ((Q cA)->(Q cB))))=> ((x1 P1) x0)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(P1 b))
% 275.29/275.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 275.29/275.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 275.29/275.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 275.29/275.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 275.29/275.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 275.29/275.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x10:=(x1 x20):cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found x10:=(x1 x20):cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 275.29/275.64 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 275.29/275.64 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 275.29/275.64 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 275.29/275.64 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 275.29/275.64 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 275.29/275.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 275.29/275.64 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x10:=(x1 x20):cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x10:=(x1 x20):cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found (x1 x20) as proof of cB
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 275.29/275.64 Found x20:=(x2 x10):cA
% 275.29/275.64 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x30:=(x3 x20):cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found x0:(((eq Prop) cA) cB)
% 285.88/286.29 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) b0)
% 285.88/286.29 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) b0))
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x0:(((eq Prop) cA) cB)
% 285.88/286.29 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of (((eq Prop) b) b0)
% 285.88/286.29 Found (fun (x0:(((eq Prop) cA) cB))=> x0) as proof of ((((eq Prop) cA) cB)->(((eq Prop) b) b0))
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 285.88/286.29 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b0)
% 285.88/286.29 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 285.88/286.29 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 285.88/286.29 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b0)
% 285.88/286.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 285.88/286.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cA)
% 285.88/286.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 285.88/286.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 285.88/286.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cA)
% 285.88/286.29 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 285.88/286.29 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 285.88/286.29 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 285.88/286.29 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b)
% 285.88/286.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 285.88/286.29 Found (eq_ref0 b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cB)
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x30:=(x3 x20):cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found x30:=(x3 x20):cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found (x3 x20) as proof of cA
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found x20:=(x2 x10):cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found (x2 x10) as proof of cA
% 285.88/286.29 Found x10:=(x1 x20):cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 285.88/286.29 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found eq_substitution00000:=(eq_substitution0000 (fun (x2:Prop)=> x2)):((((eq Prop) cA) cB)->(((eq Prop) cA) cB))
% 293.27/293.61 Found (eq_substitution0000 (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found ((eq_substitution000 cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found (((eq_substitution00 cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found ((((eq_substitution0 Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found (((((eq_substitution Prop) Prop) cA) cB) (fun (x2:Prop)=> x2)) as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cA) b))
% 293.27/293.61 Found x0:(P cA)
% 293.27/293.61 Instantiate: b:=cA:Prop
% 293.27/293.61 Found x0 as proof of (P0 b)
% 293.27/293.61 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 293.27/293.61 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 293.27/293.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 293.27/293.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 293.27/293.61 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x20:=(x2 x10):cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found (x2 x10) as proof of cA
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found x10:=(x1 x20):cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found (x1 x20) as proof of cB
% 293.27/293.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.27/293.61 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 293.27/293.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 293.27/293.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 293.27/293.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 293.27/293.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 293.27/293.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) cB)
% 293.27/293.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 293.27/293.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 293.27/293.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) cB)
% 293.27/293.61 Found eq_ref00:=(eq_ref0 cA):(((eq Prop) cA) cA)
% 296.76/297.20 Found (eq_ref0 cA) as proof of (((eq Prop) cA) b0)
% 296.76/297.20 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 296.76/297.20 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 296.76/297.20 Found ((eq_ref Prop) cA) as proof of (((eq Prop) cA) b0)
% 296.76/297.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 296.76/297.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 296.76/297.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 296.76/297.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 296.76/297.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 296.76/297.20 Found x10:=(x1 x20):cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found x20:=(x2 x10):cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found x10:=(x1 x20):cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found x20:=(x2 x10):cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found x20:=(x2 x10):cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found (x2 x10) as proof of cA
% 296.76/297.20 Found x10:=(x1 x20):cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found (x1 x20) as proof of cB
% 296.76/297.20 Found eq_sym010:=(eq_sym01 b):((((eq Prop) cA) b)->(((eq Prop) b) cA))
% 296.76/297.21 Found eq_sym010 as proof of ((forall (Q:(Prop->Prop)), ((Q cA)->(Q cB)))->(((eq Prop) cB) b0))
% 296.76/297.21 Found x3:(P cA)
% 296.76/297.21 Instantiate: b:=cA:Prop
% 296.76/297.21 Found x3 as proof of (P0 b)
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x20:=(x2 x30):cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found x30:=(x3 x20):cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x30:=(x3 x20):cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found x20:=(x2 x30):cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found x3:(P cA)
% 296.76/297.21 Instantiate: b:=cA:Prop
% 296.76/297.21 Found x3 as proof of (P0 b)
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x20:=(x2 x30):cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found x20:=(x2 x30):cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found x30:=(x3 x20):cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x30:=(x3 x20):cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x10:=(x1 x20):cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found (x1 x20) as proof of cB
% 296.76/297.21 Found x20:=(x2 x10):cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found (x2 x10) as proof of cA
% 296.76/297.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 296.76/297.21 Found (eq_ref0 b) as proof of (((eq Prop) b) cA)
% 296.76/297.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 296.76/297.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 296.76/297.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) cA)
% 296.76/297.21 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 296.76/297.21 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found x20:=(x2 x30):cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found (x2 x30) as proof of cB
% 296.76/297.21 Found x30:=(x3 x20):cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found (x3 x20) as proof of cA
% 296.76/297.21 Found eq_ref00:=(eq_ref0 cB):(((eq Prop) cB) cB)
% 296.76/297.21 Found (eq_ref0 cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found ((eq_ref Prop) cB) as proof of (((eq Prop) cB) b)
% 296.76/297.21 Found eq_re
%------------------------------------------------------------------------------