TSTP Solution File: SEU881^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU881^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n114.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:19 EDT 2014
% Result : Timeout 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU881^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n114.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:40:01 CDT 2014
% % CPUTime : 300.06
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x254f878>, <kernel.Type object at 0x254fc68>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x29273b0>, <kernel.DependentProduct object at 0x254fcb0>) of role type named cA
% Using role type
% Declaring cA:(((a->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x254fb90>, <kernel.DependentProduct object at 0x254f950>) of role type named cO
% Using role type
% Declaring cO:((a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x254f680>, <kernel.DependentProduct object at 0x254f5a8>) of role type named cT
% Using role type
% Declaring cT:(a->Prop)
% FOF formula (((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (((eq (((a->Prop)->Prop)->Prop)) cA) (fun (V:((a->Prop)->Prop))=> ((ex a) (fun (Xx:a)=> ((and (cT Xx)) (((eq ((a->Prop)->Prop)) V) (fun (U:(a->Prop))=> ((and (cO U)) (U Xx))))))))))->((ex (a->((a->Prop)->Prop))) (fun (Xf:(a->((a->Prop)->Prop)))=> ((ex (((a->Prop)->Prop)->a)) (fun (Xg:(((a->Prop)->Prop)->a))=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Xx:a), ((cT Xx)->(cA (Xf Xx)))))) (forall (W:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((W Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->(cO (fun (Xx:a)=> (W (Xf Xx)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx))))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cT (Xg Xx)))))) (forall (W:(a->Prop)), ((cO W)->((and (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W (Xg Xy)))))))))))))) (((eq (((a->Prop)->Prop)->((a->Prop)->Prop))) (fun (Xx:((a->Prop)->Prop))=> (Xf (Xg Xx)))) (fun (Xy:((a->Prop)->Prop))=> Xy)))) (((eq (a->a)) (fun (Xx:a)=> (Xg (Xf Xx)))) (fun (Xx:a)=> Xx)))))))) of role conjecture named cDOMTHM6_pme
% Conjecture to prove = (((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (((eq (((a->Prop)->Prop)->Prop)) cA) (fun (V:((a->Prop)->Prop))=> ((ex a) (fun (Xx:a)=> ((and (cT Xx)) (((eq ((a->Prop)->Prop)) V) (fun (U:(a->Prop))=> ((and (cO U)) (U Xx))))))))))->((ex (a->((a->Prop)->Prop))) (fun (Xf:(a->((a->Prop)->Prop)))=> ((ex (((a->Prop)->Prop)->a)) (fun (Xg:(((a->Prop)->Prop)->a))=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Xx:a), ((cT Xx)->(cA (Xf Xx)))))) (forall (W:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((W Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->(cO (fun (Xx:a)=> (W (Xf Xx)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx))))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cT (Xg Xx)))))) (forall (W:(a->Prop)), ((cO W)->((and (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W (Xg Xy)))))))))))))) (((eq (((a->Prop)->Prop)->((a->Prop)->Prop))) (fun (Xx:((a->Prop)->Prop))=> (Xf (Xg Xx)))) (fun (Xy:((a->Prop)->Prop))=> Xy)))) (((eq (a->a)) (fun (Xx:a)=> (Xg (Xf Xx)))) (fun (Xx:a)=> Xx)))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (((eq (((a->Prop)->Prop)->Prop)) cA) (fun (V:((a->Prop)->Prop))=> ((ex a) (fun (Xx:a)=> ((and (cT Xx)) (((eq ((a->Prop)->Prop)) V) (fun (U:(a->Prop))=> ((and (cO U)) (U Xx))))))))))->((ex (a->((a->Prop)->Prop))) (fun (Xf:(a->((a->Prop)->Prop)))=> ((ex (((a->Prop)->Prop)->a)) (fun (Xg:(((a->Prop)->Prop)->a))=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Xx:a), ((cT Xx)->(cA (Xf Xx)))))) (forall (W:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((W Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->(cO (fun (Xx:a)=> (W (Xf Xx)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx))))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cT (Xg Xx)))))) (forall (W:(a->Prop)), ((cO W)->((and (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W (Xg Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W (Xg Xy)))))))))))))) (((eq (((a->Prop)->Prop)->((a->Prop)->Prop))) (fun (Xx:((a->Prop)->Prop))=> (Xf (Xg Xx)))) (fun (Xy:((a->Prop)->Prop))=> Xy)))) (((eq (a->a)) (fun (Xx:a)=> (Xg (Xf Xx)))) (fun (Xx:a)=> Xx))))))))']
% Parameter a:Type.
% Parameter cA:(((a->Prop)->Prop)->Prop).
% Parameter cO:((a->Prop)->Prop).
% Parameter cT:(a->Prop).
% Trying to prove (((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (((eq (((a->Prop)->Prop)->Prop)) cA) (fun (V:((a->Prop)->Prop))=> ((ex a) (fun (Xx:a)=> ((and (cT Xx)) (((eq ((a->Prop)->Prop)) V) (fun (U:(a->Prop))=> ((and (cO U)) (U Xx))))))))))->((ex (a->((a->Prop)->Prop))) (fun (Xf:(a->((a->Prop)->Prop)))=> ((ex (((a->Prop)->Prop)->a)) (fun (Xg:(((a->Prop)->Prop)->a))=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx)))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(cO Xx)))->(cO (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))))) (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (cO Y)) (cO Z))->(cO (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))))) (forall (Xx:a), ((cT Xx)->(forall (Xy:a), ((cT Xy)->((forall (Y:(a->Prop)), ((cO Y)->((iff (Y Xx)) (Y Xy))))->(((eq a) Xx) Xy)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Xx:a), ((cT Xx)->(cA (Xf Xx)))))) (forall (W:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((W Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((W Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->(cO (fun (Xx:a)=> (W (Xf Xx)))))))) (forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), (False->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), (False->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:((((a->Prop)->Prop)->Prop)->Prop)), ((forall (Xx:(((a->Prop)->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Xx Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((ex (((a->Prop)->Prop)->Prop)) (fun (S:(((a->Prop)->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:(((a->Prop)->Prop)->Prop)) (Z:(((a->Prop)->Prop)->Prop)), (((and ((and ((and (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), ((Y Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:((a->Prop)->Prop)), ((Z Xx)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:((a->Prop)->Prop)), (((and (Y Xx)) (Z Xx))->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy:(a->Prop))=> False))) (forall (Xx0:((a->Prop)->Prop)), ((X Xx0)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx0 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:((a->Prop)->Prop)), (((and (cA Xy)) (forall (Xx0:(a->Prop)), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:((a->Prop)->Prop)), ((cA Xx)->(forall (Xy:((a->Prop)->Prop)), ((cA Xy)->((forall (Y:(((a->Prop)->Prop)->Prop)), (((and (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:((a->Prop)->Prop)), ((Y Xx0)->((ex ((a->Prop)->Prop)) (fun (Xe:((a->Prop)->Prop))=> ((and ((and (forall (X:(((a->Prop)->Prop)->Prop)), (((and (X (fun (Xy0:(a->Prop))=> False))) (forall (Xx1:((a->Prop)->Prop)), ((X Xx1)->(forall (Xt:(a->Prop)), ((Xe Xt)->(X (fun (Xz:(a->Prop))=> ((or (Xx1 Xz)) (((eq (a->Prop)) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:((a->Prop)->Prop)), (((and (cA Xy0)) (forall (Xx1:(a->Prop)), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq ((a->Prop)->Prop)) Xx) Xy)))))))) (forall (Y:(a->Prop)), ((cO Y)->(forall (Xx:a), ((Y Xx)->(cT Xx))))))) (cO cT))) (cO (fun (Xx:a)=> False)))) (forall (K:((a->Prop)->Prop)), ((forall
% EOF
%------------------------------------------------------------------------------