TSTP Solution File: SYO341^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO341^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n025.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 289.07s 289.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO341^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.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 05:25:01 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
% 0.45/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x2b72a595e5f0>, <kernel.DependentProduct object at 0x2b72a595eb48>) of role type named cG
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring cG:(fofType->fofType)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x13e5ea8>, <kernel.Single object at 0x2b72a595eb90>) of role type named cK
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring cK:fofType
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x13e5ea8>, <kernel.DependentProduct object at 0x2b72a595eb48>) of role type named cR
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring cR:(fofType->(fofType->Prop))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x2b72a595eea8>, <kernel.DependentProduct object at 0x2b72a595ecb0>) of role type named cF
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring cF:(fofType->(fofType->fofType))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x2b72a595e170>, <kernel.DependentProduct object at 0x2b72a595ecf8>) of role type named cP
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring cP:(fofType->Prop)
% 0.45/0.61 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 Y)))) ((Q ((cF X) (cG Y))) (cG Y)))) ((or ((cP ((cF X) (cG Y)))->False)) ((Q1 ((cF X) (cG Y))) 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 cTHM74A
% 0.45/0.61 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 Y)))) ((Q ((cF X) (cG Y))) (cG Y)))) ((or ((cP ((cF X) (cG Y)))->False)) ((Q1 ((cF X) (cG Y))) 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
% 0.45/0.61 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 Y)))) ((Q ((cF X) (cG Y))) (cG Y)))) ((or ((cP ((cF X) (cG Y)))->False)) ((Q1 ((cF X) (cG Y))) 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))))))))))']
% 47.22/47.40 Parameter fofType:Type.
% 47.22/47.40 Parameter cG:(fofType->fofType).
% 47.22/47.40 Parameter cK:fofType.
% 47.22/47.40 Parameter cR:(fofType->(fofType->Prop)).
% 47.22/47.40 Parameter cF:(fofType->(fofType->fofType)).
% 47.22/47.40 Parameter cP:(fofType->Prop).
% 47.22/47.40 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 Y)))) ((Q ((cF X) (cG Y))) (cG Y)))) ((or ((cP ((cF X) (cG Y)))->False)) ((Q1 ((cF X) (cG Y))) 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))))))))))
% 47.22/47.40 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 47.22/47.40 Found classic0:=(classic ((x2 ((cF X) (cG Y))) Y)):((or ((x2 ((cF X) (cG Y))) Y)) (not ((x2 ((cF X) (cG Y))) Y)))
% 47.22/47.40 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 47.22/47.40 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (or_comm_i00 (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found classic0:=(classic ((x2 ((cF X) (cG Y))) Y)):((or ((x2 ((cF X) (cG Y))) Y)) (not ((x2 ((cF X) (cG Y))) Y)))
% 79.84/80.08 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (or_comm_i00 (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 79.84/80.08 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 79.84/80.08 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 98.79/99.02 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 98.79/99.02 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 98.79/99.02 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 98.79/99.02 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 98.79/99.02 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 98.79/99.02 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 98.79/99.02 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 98.79/99.02 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 98.79/99.02 Found x00:((x0 X) Y0)
% 98.79/99.02 Found x00 as proof of False
% 98.79/99.02 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 98.79/99.02 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 98.79/99.02 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 98.79/99.02 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))
% 98.79/99.02 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))
% 98.79/99.02 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))
% 98.79/99.02 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)))
% 98.79/99.02 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)))
% 98.79/99.02 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)))
% 98.79/99.02 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)))
% 98.79/99.02 Found x00:((x0 X) Y0)
% 98.79/99.02 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 98.79/99.02 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 98.79/99.02 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 98.79/99.02 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))
% 98.79/99.02 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))
% 98.79/99.02 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))
% 98.79/99.02 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)))
% 98.79/99.02 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)))
% 98.79/99.02 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)))
% 108.40/108.64 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)))
% 108.40/108.64 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))))
% 108.40/108.64 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))))
% 108.40/108.64 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))))
% 108.40/108.64 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))))
% 108.40/108.64 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)))))
% 108.40/108.64 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 108.40/108.64 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 108.40/108.64 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 108.40/108.64 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 108.40/108.64 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 128.78/129.07 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 128.78/129.07 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 128.78/129.07 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 128.78/129.07 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))))))))))
% 128.78/129.07 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))))))))))
% 128.78/129.07 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))))))))))
% 128.78/129.07 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))))))))))
% 128.78/129.07 Found (fun (x7:((cP ((cF X) (cG Y)))->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))))))))))
% 128.78/129.07 Found (fun (x7:((cP ((cF X) (cG Y)))->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 Y)))->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)))))))))))
% 129.17/129.49 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))))))))))
% 129.17/129.49 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))))))))))
% 129.17/129.49 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))))))))))
% 129.17/129.49 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))))))))))
% 131.25/131.50 Found (fun (x7:(cP ((cF X) (cG Y))))=> ((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))))))))))
% 131.25/131.50 Found (fun (x7:(cP ((cF X) (cG Y))))=> ((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 Y)))->((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)))))))))))
% 131.25/131.50 Found classic0:=(classic ((x4 ((cF X) (cG Y))) Y)):((or ((x4 ((cF X) (cG Y))) Y)) (not ((x4 ((cF X) (cG Y))) Y)))
% 131.25/131.50 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 131.25/131.50 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (or_comm_i00 (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found classic0:=(classic ((x2 ((cF X) (cG Y))) Y)):((or ((x2 ((cF X) (cG Y))) Y)) (not ((x2 ((cF X) (cG Y))) Y)))
% 150.45/150.75 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (or_comm_i00 (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 150.45/150.75 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 150.45/150.75 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 177.83/178.18 Found x00:((x0 X) Y0)
% 177.83/178.18 Found x00 as proof of False
% 177.83/178.18 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 177.83/178.18 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 177.83/178.18 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 177.83/178.18 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))
% 177.83/178.18 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))
% 177.83/178.18 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))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 Found x00:((x0 X) Y0)
% 177.83/178.18 Found (fun (x00:((x0 X) Y0))=> x00) as proof of False
% 177.83/178.18 Found (fun (x00:((x0 X) Y0))=> x00) as proof of (((x0 X) Y0)->False)
% 177.83/178.18 Found (or_introl10 (fun (x00:((x0 X) Y0))=> x00)) as proof of ((or (((x0 X) Y0)->False)) ((cR (cG Y0)) cK))
% 177.83/178.18 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))
% 177.83/178.18 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))
% 177.83/178.18 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))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 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)))
% 177.83/178.18 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))))
% 177.83/178.18 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))))
% 213.92/214.30 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))))
% 213.92/214.30 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))))
% 213.92/214.30 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)))))
% 213.92/214.30 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 213.92/214.30 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 213.92/214.30 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 213.92/214.30 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 213.92/214.30 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 213.92/214.30 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 213.92/214.30 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 213.92/214.30 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 213.92/214.30 Found x7:(cP ((cF X) (cG Y)))
% 213.92/214.30 Found (fun (x7:(cP ((cF X) (cG Y))))=> x7) as proof of (cP ((cF X) (cG Y)))
% 213.92/214.30 Found (fun (x7:(cP ((cF X) (cG Y))))=> x7) as proof of ((cP ((cF X) (cG Y)))->(cP ((cF X) (cG Y))))
% 213.92/214.30 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 213.92/214.30 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found classic0:=(classic ((x4 ((cF X) (cG Y))) Y)):((or ((x4 ((cF X) (cG Y))) Y)) (not ((x4 ((cF X) (cG Y))) Y)))
% 244.28/244.60 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x4 ((cF X) (cG Y))) Y)) as proof of ((or ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (or_comm_i00 (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x4 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x4 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x4 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found classic0:=(classic ((x2 ((cF X) (cG Y))) Y)):((or ((x2 ((cF X) (cG Y))) Y)) (not ((x2 ((cF X) (cG Y))) Y)))
% 244.28/244.60 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (or_comm_i00 (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 244.28/244.60 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 244.28/244.60 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 244.28/244.60 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 255.79/256.13 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))))))))))
% 255.79/256.13 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))))))))))
% 255.79/256.13 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))))))))))
% 255.79/256.13 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))))))))))
% 256.70/257.02 Found (fun (x7:((cP ((cF X) (cG Y)))->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))))))))))
% 256.70/257.02 Found (fun (x7:((cP ((cF X) (cG Y)))->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 Y)))->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)))))))))))
% 256.70/257.02 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))))))))))
% 256.70/257.03 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))))))))))
% 256.70/257.03 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))))))))))
% 256.70/257.03 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))))))))))
% 262.08/262.47 Found (fun (x7:(cP ((cF X) (cG Y))))=> ((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))))))))))
% 262.08/262.47 Found (fun (x7:(cP ((cF X) (cG Y))))=> ((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 Y)))->((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)))))))))))
% 262.08/262.47 Found classic0:=(classic ((x2 ((cF X) (cG Y))) Y)):((or ((x2 ((cF X) (cG Y))) Y)) (not ((x2 ((cF X) (cG Y))) Y)))
% 262.08/262.47 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 262.08/262.47 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 262.08/262.47 Found (classic ((x2 ((cF X) (cG Y))) Y)) as proof of ((or ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 262.08/262.47 Found (or_comm_i00 (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 262.08/262.47 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found (((or_comm_i ((x2 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x2 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x2 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found classic0:=(classic ((x0 ((cF X) (cG Y))) Y)):((or ((x0 ((cF X) (cG Y))) Y)) (not ((x0 ((cF X) (cG Y))) Y)))
% 289.07/289.43 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 289.07/289.43 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 289.07/289.43 Found (classic ((x0 ((cF X) (cG Y))) Y)) as proof of ((or ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False))
% 289.07/289.43 Found (or_comm_i00 (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found ((or_comm_i0 ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found (((or_comm_i ((x0 ((cF X) (cG Y))) Y)) ((cP ((cF X) (cG Y)))->False)) (classic ((x0 ((cF X) (cG Y))) Y))) as proof of ((or ((cP ((cF X) (cG Y)))->False)) ((x0 ((cF X) (cG Y))) Y))
% 289.07/289.43 Found x00:((x2 X) Y0)
% 289.07/289.43 Found x00 as proof of False
% 289.07/289.43 Found (fun (x00:((x2 X) Y0))=> x00) as proof of False
% 289.07/289.43 Found (fun (x00:((x2 X) Y0))=> x00) as proof of (((x2 X) Y0)->False)
% 289.07/289.43 Found (or_introl10 (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))
% 289.07/289.43 Found ((or_introl1 ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))
% 289.07/289.43 Found (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))
% 289.07/289.43 Found (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))
% 289.07/289.43 Found (or_introl00 (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00))) as proof of ((or ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0)))
% 289.07/289.43 Found ((or_introl0 ((x2 X) (cG Y0))) (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00))) as proof of ((or ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0)))
% 289.07/289.43 Found (((or_introl ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0))) (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00))) as proof of ((or ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0)))
% 289.07/289.43 Found (((or_introl ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0))) (((or_introl (((x2 X) Y0)->False)) ((cR (cG Y0)) cK)) (fun (x00:((x2 X) Y0))=> x00))) as proof of ((or ((or (((x2 X) Y0)->False)) ((cR (cG Y0)) cK))) ((x2 X) (cG Y0)))
% 289.07/289.43 Found x00:((x2 X) Y0)
% 289.07/289.43 Found (fun (x00:((x2 X) Y0))=> x00) as proof of False
% 289.07/289.43 Found (fun (x00:((x2 X) Y0))=> x00) as proof of (((x2 X) Y0)->False)
% 289.07/289.43 Found (or_introl10 (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 289.07/289.43 Found ((or_introl1 (((cR (cG Y0)) cK)->False)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 289.07/289.43 Found (((or_introl (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 289.07/289.43 Found (((or_introl (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x2 X) Y0))=> x00)) as proof of ((or (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False))
% 289.07/289.43 Found (or_introl00 (((or_introl (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False)) (fun (x00:((x2 X) Y0))=> x00))) as proof of ((or ((or (((x2 X) Y0)->False)) (((cR (cG Y0)) cK)->False))) ((Q X) (cG Y0)))
% 289.07/289.43 Found ((or_introl0 ((Q X) (cG Y0))) (((or_
%------------------------------------------------------------------------------