TSTP Solution File: SYO340^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO340^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 00:51:12 EDT 2022
% Result : Timeout 300.03s 300.59s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO340^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n015.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 : Sat Mar 12 05:15:19 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.39/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x20dae18>, <kernel.DependentProduct object at 0x20d5488>) of role type named cG
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring cG:(fofType->fofType)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2adf3c755ea8>, <kernel.Single object at 0x20da200>) of role type named cK
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring cK:fofType
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x20dacb0>, <kernel.DependentProduct object at 0x20d5488>) of role type named cR
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring cR:(fofType->(fofType->Prop))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x20da200>, <kernel.DependentProduct object at 0x20d5d88>) of role type named cF
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring cF:(fofType->(fofType->fofType))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x20da200>, <kernel.DependentProduct object at 0x20d5b48>) of role type named cP
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring cP:(fofType->Prop)
% 0.39/0.62 FOF formula (forall (X:fofType) (Y:fofType) (Q:(fofType->(fofType->Prop))), ((iff ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((and ((and ((or (cP ((cF X) (cG X)))) ((Q ((cF X) (cG X))) (cG Y)))) ((or ((cP ((cF X) (cG X)))->False)) ((Q1 ((cF X) (cG X))) Y)))) (forall (Y0:fofType), ((and ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) ((cR (cG Y0)) cK))) ((Q1 X) (cG Y0)))))))))) of role conjecture named cTHM74B_1
% 0.39/0.62 Conjecture to prove = (forall (X:fofType) (Y:fofType) (Q:(fofType->(fofType->Prop))), ((iff ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((and ((and ((or (cP ((cF X) (cG X)))) ((Q ((cF X) (cG X))) (cG Y)))) ((or ((cP ((cF X) (cG X)))->False)) ((Q1 ((cF X) (cG X))) Y)))) (forall (Y0:fofType), ((and ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) ((cR (cG Y0)) cK))) ((Q1 X) (cG Y0)))))))))):Prop
% 0.39/0.62 We need to prove ['(forall (X:fofType) (Y:fofType) (Q:(fofType->(fofType->Prop))), ((iff ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((and ((and ((or (cP ((cF X) (cG X)))) ((Q ((cF X) (cG X))) (cG Y)))) ((or ((cP ((cF X) (cG X)))->False)) ((Q1 ((cF X) (cG X))) Y)))) (forall (Y0:fofType), ((and ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) ((cR (cG Y0)) cK))) ((Q1 X) (cG Y0))))))))))']
% 49.59/49.78 Parameter fofType:Type.
% 49.59/49.78 Parameter cG:(fofType->fofType).
% 49.59/49.78 Parameter cK:fofType.
% 49.59/49.78 Parameter cR:(fofType->(fofType->Prop)).
% 49.59/49.78 Parameter cF:(fofType->(fofType->fofType)).
% 49.59/49.78 Parameter cP:(fofType->Prop).
% 49.59/49.78 Trying to prove (forall (X:fofType) (Y:fofType) (Q:(fofType->(fofType->Prop))), ((iff ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((and ((and ((or (cP ((cF X) (cG X)))) ((Q ((cF X) (cG X))) (cG Y)))) ((or ((cP ((cF X) (cG X)))->False)) ((Q1 ((cF X) (cG X))) Y)))) (forall (Y0:fofType), ((and ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) ((cR (cG Y0)) cK))) ((Q1 X) (cG Y0))))))))))
% 49.59/49.78 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 49.59/49.78 Found classic0:=(classic ((x2 ((cF X) (cG X))) Y)):((or ((x2 ((cF X) (cG X))) Y)) (not ((x2 ((cF X) (cG X))) Y)))
% 49.59/49.78 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 49.59/49.78 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (or_comm_i00 (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found classic0:=(classic ((x2 ((cF X) (cG X))) Y)):((or ((x2 ((cF X) (cG X))) Y)) (not ((x2 ((cF X) (cG X))) Y)))
% 85.28/85.48 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (or_comm_i00 (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 85.28/85.48 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 85.28/85.48 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 85.28/85.48 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 103.41/103.62 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 103.41/103.62 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 103.41/103.62 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 103.41/103.62 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 103.41/103.62 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 103.41/103.62 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 103.41/103.62 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 103.41/103.62 Found x00:((x0 X) Y0)
% 103.41/103.62 Found x00 as proof of False
% 103.41/103.62 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 103.41/103.62 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 103.41/103.62 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 103.41/103.62 Found ((or_introl1 ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 103.41/103.62 Found (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 103.41/103.62 Found (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 103.41/103.62 Found (or_introl00 (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 103.41/103.62 Found ((or_introl0 ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 103.41/103.62 Found (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 103.41/103.62 Found (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 103.41/103.62 Found x00:((x0 X) Y0)
% 103.41/103.62 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 103.41/103.62 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 103.41/103.62 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 103.41/103.62 Found ((or_introl1 (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 103.41/103.62 Found (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 103.41/103.62 Found (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 103.41/103.62 Found (or_introl00 (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 103.41/103.62 Found ((or_introl0 ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 103.41/103.62 Found (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 113.60/113.82 Found (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 113.60/113.82 Found ((conj20 (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 113.60/113.82 Found (((conj2 ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 113.60/113.82 Found ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 113.60/113.82 Found (fun (Y0:fofType)=> ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 113.60/113.82 Found (fun (Y0:fofType)=> ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))))) as proof of (forall (Y0:fofType), ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))))
% 113.60/113.83 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 113.60/113.83 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 113.60/113.83 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 113.60/113.83 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 113.60/113.83 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 135.12/135.42 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 135.12/135.42 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 135.12/135.42 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 135.12/135.42 Found False_rect00:=(False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))):((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.12/135.42 Found (False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.12/135.42 Found ((fun (P:Type)=> ((False_rect P) x70)) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.12/135.43 Found ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.12/135.43 Found (fun (x7:((cP ((cF X) (cG X)))->False))=> ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.12/135.43 Found (fun (x7:((cP ((cF X) (cG X)))->False))=> ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of (((cP ((cF X) (cG X)))->False)->((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))
% 135.64/135.89 Found False_rect00:=(False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))):((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.64/135.89 Found (False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.64/135.89 Found ((fun (P:Type)=> ((False_rect P) x60)) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 135.64/135.89 Found ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 137.81/138.07 Found (fun (x7:(cP ((cF X) (cG X))))=> ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 137.81/138.07 Found (fun (x7:(cP ((cF X) (cG X))))=> ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((cP ((cF X) (cG X)))->((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))
% 137.81/138.07 Found classic0:=(classic ((x4 ((cF X) (cG X))) Y)):((or ((x4 ((cF X) (cG X))) Y)) (not ((x4 ((cF X) (cG X))) Y)))
% 137.81/138.07 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 137.81/138.07 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (or_comm_i00 (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 157.92/158.15 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 157.92/158.15 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found classic0:=(classic ((x2 ((cF X) (cG X))) Y)):((or ((x2 ((cF X) (cG X))) Y)) (not ((x2 ((cF X) (cG X))) Y)))
% 157.92/158.15 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (or_comm_i00 (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 157.92/158.15 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 157.92/158.15 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 157.92/158.15 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 157.92/158.15 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 187.69/187.96 Found x00:((x0 X) Y0)
% 187.69/187.96 Found x00 as proof of False
% 187.69/187.96 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 187.69/187.96 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 187.69/187.96 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 187.69/187.96 Found ((or_introl1 (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 187.69/187.96 Found (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 187.69/187.96 Found (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 187.69/187.96 Found (or_introl00 (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 187.69/187.96 Found ((or_introl0 ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 187.69/187.96 Found (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 187.69/187.96 Found (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 187.69/187.96 Found x00:((x0 X) Y0)
% 187.69/187.96 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 187.69/187.96 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 187.69/187.96 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 187.69/187.96 Found ((or_introl1 ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 187.69/187.96 Found (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 187.69/187.96 Found (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 187.69/187.96 Found (or_introl00 (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 187.69/187.96 Found ((or_introl0 ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 187.69/187.96 Found (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 187.69/187.96 Found (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))) as proof of ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))
% 187.69/187.96 Found ((conj20 (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 187.69/187.96 Found (((conj2 ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 227.18/227.51 Found ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00)))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 227.18/227.51 Found (fun (Y0:fofType)=> ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))))) as proof of ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))))
% 227.18/227.51 Found (fun (Y0:fofType)=> ((((conj ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))) (((or_introl ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x0 X) Y0))=> x00)))) (((or_introl ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0))) (((or_introl (((x0 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x0 X) Y0))=> x00))))) as proof of (forall (Y0:fofType), ((and ((or ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))) ((or ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x0 X) (cG Y0)))))
% 227.18/227.51 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 227.18/227.51 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 227.18/227.51 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 227.18/227.51 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 227.18/227.51 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 227.18/227.51 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 227.18/227.51 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 227.18/227.51 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 227.18/227.51 Found x7:(cP ((cF X) (cG X)))
% 227.18/227.51 Found (fun (x7:(cP ((cF X) (cG X))))=> x7) as proof of (cP ((cF X) (cG X)))
% 227.18/227.51 Found (fun (x7:(cP ((cF X) (cG X))))=> x7) as proof of ((cP ((cF X) (cG X)))->(cP ((cF X) (cG X))))
% 227.18/227.51 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 227.18/227.51 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 227.18/227.51 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found classic0:=(classic ((x4 ((cF X) (cG X))) Y)):((or ((x4 ((cF X) (cG X))) Y)) (not ((x4 ((cF X) (cG X))) Y)))
% 258.06/258.38 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x4 ((cF X) (cG X))) Y)) as proof of ((or ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (or_comm_i00 (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 258.06/258.38 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x4 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x4 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x4 ((cF X) (cG X))) Y))
% 258.06/258.38 Found classic0:=(classic ((x2 ((cF X) (cG X))) Y)):((or ((x2 ((cF X) (cG X))) Y)) (not ((x2 ((cF X) (cG X))) Y)))
% 258.06/258.38 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (or_comm_i00 (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 258.06/258.38 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 258.06/258.38 Found classic0:=(classic ((x0 ((cF X) (cG X))) Y)):((or ((x0 ((cF X) (cG X))) Y)) (not ((x0 ((cF X) (cG X))) Y)))
% 258.06/258.38 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (classic ((x0 ((cF X) (cG X))) Y)) as proof of ((or ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 258.06/258.38 Found (or_comm_i00 (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 258.06/258.38 Found (((or_comm_i ((x0 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False)) (classic ((x0 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x0 ((cF X) (cG X))) Y))
% 269.55/269.87 Found False_rect00:=(False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))):((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 269.55/269.87 Found (False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 269.55/269.87 Found ((fun (P:Type)=> ((False_rect P) x70)) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 269.55/269.87 Found ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 270.45/270.78 Found (fun (x7:((cP ((cF X) (cG X)))->False))=> ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 270.45/270.78 Found (fun (x7:((cP ((cF X) (cG X)))->False))=> ((fun (P:Type)=> ((False_rect P) (x7 x6))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of (((cP ((cF X) (cG X)))->False)->((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))
% 270.45/270.78 Found False_rect00:=(False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))):((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 270.45/270.78 Found (False_rect0 ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 270.45/270.78 Found ((fun (P:Type)=> ((False_rect P) x60)) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 270.45/270.78 Found ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 275.75/276.07 Found (fun (x7:(cP ((cF X) (cG X))))=> ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0))))))))))
% 275.75/276.07 Found (fun (x7:(cP ((cF X) (cG X))))=> ((fun (P:Type)=> ((False_rect P) (x6 x7))) ((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))) as proof of ((cP ((cF X) (cG X)))->((ex (fofType->(fofType->Prop))) (fun (Q1:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->Prop))) (fun (Q2:(fofType->(fofType->Prop)))=> ((and ((and ((Q1 ((cF X) (cG X))) Y)) (forall (Y0:fofType), ((and ((and ((or ((or (((Q1 X) Y0)->False)) (cP X))) ((Q X) (cG Y0)))) ((or ((or (((Q1 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0))))) ((or ((or ((or (((Q1 X) Y0)->False)) ((cP X)->False))) ((cR (cG Y0)) cK))) ((Q2 X) Y0)))))) (forall (Y0:fofType), ((and ((or ((or (((Q2 X) Y0)->False)) (cP X))) ((Q2 X) (cG Y0)))) ((or ((or (((Q2 X) Y0)->False)) ((cP X)->False))) ((Q1 X) (cG Y0)))))))))))
% 275.75/276.07 Found classic0:=(classic ((x2 ((cF X) (cG X))) Y)):((or ((x2 ((cF X) (cG X))) Y)) (not ((x2 ((cF X) (cG X))) Y)))
% 275.75/276.07 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 275.75/276.07 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 275.75/276.07 Found (classic ((x2 ((cF X) (cG X))) Y)) as proof of ((or ((x2 ((cF X) (cG X))) Y)) ((cP ((cF X) (cG X)))->False))
% 275.75/276.07 Found (or_comm_i00 (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 275.75/276.07 Found ((or_comm_i0 ((cP ((cF X) (cG X)))->False)) (classic ((x2 ((cF X) (cG X))) Y))) as proof of ((or ((cP ((cF X) (cG X)))->False)) ((x2 ((cF X) (cG X))) Y))
% 275.75/276.07 Found (((or_comm
%------------------------------------------------------------------------------