%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU880^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n099.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  : SEU880^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.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 11:39:46 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 0x1d4f6c8>, <kernel.Type object at 0x1d4fef0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1f23560>, <kernel.Type object at 0x1d4f9e0>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4f5a8>) of role type named f
% Using role type
% Declaring f:((a->Prop)->(b->Prop))
% FOF formula (<kernel.Constant object at 0x1d4fef0>, <kernel.DependentProduct object at 0x1d4fc20>) of role type named cA
% Using role type
% Declaring cA:((a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1d4ff38>, <kernel.DependentProduct object at 0x1d4f5a8>) of role type named cB
% Using role type
% Declaring cB:((b->Prop)->Prop)
% FOF formula ((iff ((and (forall (Xx:(a->Prop)), ((cA Xx)->(cB (f Xx))))) (forall (Xe:(b->Prop)), (((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx:(b->Prop)), ((X Xx)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx:b), ((Xe Xx)->((ex (b->Prop)) (fun (S:(b->Prop))=> ((and (cB S)) (S Xx)))))))->((and (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->(cA Xx)))) (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->((ex (a->Prop)) (fun (Xe0:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe0 Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe0)))) (forall (Xx0:a), ((Xe0 Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe0 Xx0)->(Xy Xx0))))->((and (cA Xy)) (forall (Xx0:b), ((Xe Xx0)->((f Xy) Xx0)))))))))))))))) ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:((a->Prop)->Prop)), (((and (forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:(a->Prop)), ((Y Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))))) (forall (Xx:(a->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:(a->Prop)), ((cA Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:(a->Prop)), (False->(cA Xx))))) (forall (Xx:(a->Prop)), (False->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:(((a->Prop)->Prop)->Prop)), ((forall (Xx:((a->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:(a->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:(a->Prop)), ((Xx Xx0)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx1:(a->Prop)), ((X Xx1)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx1 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:a), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx1:a), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:(a->Prop)), (((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:(a->Prop)), (((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:((a->Prop)->Prop)) (Z:((a->Prop)->Prop)), (((and ((and ((and (forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:(a->Prop)), ((Y Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:(a->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:(a->Prop)), ((Z Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:(a->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:(a->Prop)), (((and (Y Xx)) (Z Xx))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:(a->Prop)), ((cA Xx)->(forall (Xy:(a->Prop)), ((cA Xy)->((forall (Y:((a->Prop)->Prop)), (((and (forall (Xx0:(a->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:(a->Prop)), ((Y Xx0)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy0:a)=> False))) (forall (Xx1:(a->Prop)), ((X Xx1)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx1 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:a), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:(a->Prop)), (((and (cA Xy0)) (forall (Xx1:a), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq (a->Prop)) Xx) Xy)))))))) (forall (Y:((b->Prop)->Prop)), (((and (forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((Y Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx))))))) (forall (Xx:(b->Prop)), ((cB Xx)->(cB Xx))))) (forall (Xx:(b->Prop)), ((cB Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(cB Xy)))))))))) (forall (Xx:(b->Prop)), (False->(cB Xx))))) (forall (Xx:(b->Prop)), (False->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:(((b->Prop)->Prop)->Prop)), ((forall (Xx:((b->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:(b->Prop)), ((Xx Xx0)->(cB Xx0)))) (forall (Xx0:(b->Prop)), ((Xx Xx0)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx1:(b->Prop)), ((X Xx1)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx1 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:b), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx1:b), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cB Xx)))) (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:((b->Prop)->Prop)) (Z:((b->Prop)->Prop)), (((and ((and ((and (forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((Y Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:(b->Prop)), ((Z Xx)->(cB Xx))))) (forall (Xx:(b->Prop)), ((Z Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:(b->Prop)), (((and (Y Xx)) (Z Xx))->(cB Xx)))) (forall (Xx:(b->Prop)), (((and (Y Xx)) (Z Xx))->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:(b->Prop)), ((cB Xx)->(forall (Xy:(b->Prop)), ((cB Xy)->((forall (Y:((b->Prop)->Prop)), (((and (forall (Xx0:(b->Prop)), ((Y Xx0)->(cB Xx0)))) (forall (Xx0:(b->Prop)), ((Y Xx0)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy0:b)=> False))) (forall (Xx1:(b->Prop)), ((X Xx1)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx1 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:b), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:(b->Prop)), (((and (cB Xy0)) (forall (Xx1:b), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq (b->Prop)) Xx) Xy)))))))) (forall (Xx:(a->Prop)), ((cA Xx)->(cB (f Xx)))))) (forall (W:((b->Prop)->Prop)), (((and (forall (Xx:(b->Prop)), ((W Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((W Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->((and (forall (Xx:(a->Prop)), ((W (f Xx))->(cA Xx)))) (forall (Xx:(a->Prop)), ((W (f Xx))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(W (f Xy)))))))))))))) of role conjecture named cDOMTHM5_pme
% Conjecture to prove = ((iff ((and (forall (Xx:(a->Prop)), ((cA Xx)->(cB (f Xx))))) (forall (Xe:(b->Prop)), (((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx:(b->Prop)), ((X Xx)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx:b), ((Xe Xx)->((ex (b->Prop)) (fun (S:(b->Prop))=> ((and (cB S)) (S Xx)))))))->((and (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->(cA Xx)))) (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->((ex (a->Prop)) (fun (Xe0:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe0 Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe0)))) (forall (Xx0:a), ((Xe0 Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe0 Xx0)->(Xy Xx0))))->((and (cA Xy)) (forall (Xx0:b), ((Xe Xx0)->((f 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% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
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(Y:((b->Prop)->Prop)), (((and (forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((Y Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx))))))) (forall (Xx:(b->Prop)), ((cB Xx)->(cB Xx))))) (forall (Xx:(b->Prop)), ((cB Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(cB Xy)))))))))) (forall (Xx:(b->Prop)), (False->(cB Xx))))) (forall (Xx:(b->Prop)), (False->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:(((b->Prop)->Prop)->Prop)), ((forall (Xx:((b->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:(b->Prop)), ((Xx Xx0)->(cB Xx0)))) (forall (Xx0:(b->Prop)), ((Xx Xx0)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx1:(b->Prop)), ((X Xx1)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx1 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:b), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx1:b), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cB Xx)))) (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:((b->Prop)->Prop)) (Z:((b->Prop)->Prop)), (((and ((and ((and (forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((Y Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:(b->Prop)), ((Z Xx)->(cB Xx))))) (forall (Xx:(b->Prop)), ((Z Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:(b->Prop)), (((and (Y Xx)) (Z Xx))->(cB Xx)))) (forall (Xx:(b->Prop)), (((and (Y Xx)) (Z Xx))->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:(b->Prop)), ((cB Xx)->(forall (Xy:(b->Prop)), ((cB Xy)->((forall (Y:((b->Prop)->Prop)), (((and (forall (Xx0:(b->Prop)), ((Y Xx0)->(cB Xx0)))) (forall (Xx0:(b->Prop)), ((Y Xx0)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy0:b)=> False))) (forall (Xx1:(b->Prop)), ((X Xx1)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx1 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:b), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:(b->Prop)), (((and (cB Xy0)) (forall (Xx1:b), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq (b->Prop)) Xx) Xy)))))))) (forall (Xx:(a->Prop)), ((cA Xx)->(cB (f Xx)))))) (forall (W:((b->Prop)->Prop)), (((and (forall (Xx:(b->Prop)), ((W Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((W Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(W Xy)))))))))->((and (forall (Xx:(a->Prop)), ((W (f Xx))->(cA Xx)))) (forall (Xx:(a->Prop)), ((W (f Xx))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(W (f Xy))))))))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter f:((a->Prop)->(b->Prop)).
% Parameter cA:((a->Prop)->Prop).
% Parameter cB:((b->Prop)->Prop).
% Trying to prove ((iff ((and (forall (Xx:(a->Prop)), ((cA Xx)->(cB (f Xx))))) (forall (Xe:(b->Prop)), (((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx:(b->Prop)), ((X Xx)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx:b), ((Xe Xx)->((ex (b->Prop)) (fun (S:(b->Prop))=> ((and (cB S)) (S Xx)))))))->((and (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->(cA Xx)))) (forall (Xx:(a->Prop)), (((and (cA Xx)) (forall (Xx0:b), ((Xe Xx0)->((f Xx) Xx0))))->((ex (a->Prop)) (fun (Xe0:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe0 Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe0)))) (forall (Xx0:a), ((Xe0 Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe0 Xx0)->(Xy Xx0))))->((and (cA Xy)) (forall (Xx0:b), ((Xe Xx0)->((f Xy) Xx0)))))))))))))))) ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Y:((a->Prop)->Prop)), (((and (forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:(a->Prop)), ((Y Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))))) (forall (Xx:(a->Prop)), ((cA Xx)->(cA Xx))))) (forall (Xx:(a->Prop)), ((cA Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(cA Xy)))))))))) (forall (Xx:(a->Prop)), (False->(cA Xx))))) (forall (Xx:(a->Prop)), (False->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:(((a->Prop)->Prop)->Prop)), ((forall (Xx:((a->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:(a->Prop)), ((Xx Xx0)->(cA Xx0)))) (forall (Xx0:(a->Prop)), ((Xx Xx0)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx1:(a->Prop)), ((X Xx1)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx1 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:a), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx1:a), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:(a->Prop)), (((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cA Xx)))) (forall (Xx:(a->Prop)), (((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->((ex ((a->Prop)->Prop)) (fun (S:((a->Prop)->Prop))=> ((and (K S)) (S Xy)))))))))))))))) (forall (Y:((a->Prop)->Prop)) (Z:((a->Prop)->Prop)), (((and ((and ((and (forall (Xx:(a->Prop)), ((Y Xx)->(cA Xx)))) (forall (Xx:(a->Prop)), ((Y Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))) (forall (Xx:(a->Prop)), ((Z Xx)->(cA Xx))))) (forall (Xx:(a->Prop)), ((Z Xx)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->(Z Xy)))))))))->((and (forall (Xx:(a->Prop)), (((and (Y Xx)) (Z Xx))->(cA Xx)))) (forall (Xx:(a->Prop)), (((and (Y Xx)) (Z Xx))->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy:a)=> False))) (forall (Xx0:(a->Prop)), ((X Xx0)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx0 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:a), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(a->Prop)), (((and (cA Xy)) (forall (Xx0:a), ((Xe Xx0)->(Xy Xx0))))->((and (Y Xy)) (Z Xy)))))))))))))) (forall (Xx:(a->Prop)), ((cA Xx)->(forall (Xy:(a->Prop)), ((cA Xy)->((forall (Y:((a->Prop)->Prop)), (((and (forall (Xx0:(a->Prop)), ((Y Xx0)->(cA Xx0)))) (forall (Xx0:(a->Prop)), ((Y Xx0)->((ex (a->Prop)) (fun (Xe:(a->Prop))=> ((and ((and (forall (X:((a->Prop)->Prop)), (((and (X (fun (Xy0:a)=> False))) (forall (Xx1:(a->Prop)), ((X Xx1)->(forall (Xt:a), ((Xe Xt)->(X (fun (Xz:a)=> ((or (Xx1 Xz)) (((eq a) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:a), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy0:(a->Prop)), (((and (cA Xy0)) (forall (Xx1:a), ((Xe Xx1)->(Xy0 Xx1))))->(Y Xy0)))))))))->((iff (Y Xx)) (Y Xy))))->(((eq (a->Prop)) Xx) Xy)))))))) (forall (Y:((b->Prop)->Prop)), (((and (forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx)))) (forall (Xx:(b->Prop)), ((Y Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(Y Xy)))))))))->(forall (Xx:(b->Prop)), ((Y Xx)->(cB Xx))))))) (forall (Xx:(b->Prop)), ((cB Xx)->(cB Xx))))) (forall (Xx:(b->Prop)), ((cB Xx)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->(cB Xy)))))))))) (forall (Xx:(b->Prop)), (False->(cB Xx))))) (forall (Xx:(b->Prop)), (False->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), ((Xe Xx0)->(Xy Xx0))))->False))))))))) (forall (K:(((b->Prop)->Prop)->Prop)), ((forall (Xx:((b->Prop)->Prop)), ((K Xx)->((and (forall (Xx0:(b->Prop)), ((Xx Xx0)->(cB Xx0)))) (forall (Xx0:(b->Prop)), ((Xx Xx0)->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx1:(b->Prop)), ((X Xx1)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx1 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx1:b), ((Xe Xx1)->(Xx0 Xx1))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx1:b), ((Xe Xx1)->(Xy Xx1))))->(Xx Xy)))))))))))->((and (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->(cB Xx)))) (forall (Xx:(b->Prop)), (((ex ((b->Prop)->Prop)) (fun (S:((b->Prop)->Prop))=> ((and (K S)) (S Xx))))->((ex (b->Prop)) (fun (Xe:(b->Prop))=> ((and ((and (forall (X:((b->Prop)->Prop)), (((and (X (fun (Xy:b)=> False))) (forall (Xx0:(b->Prop)), ((X Xx0)->(forall (Xt:b), ((Xe Xt)->(X (fun (Xz:b)=> ((or (Xx0 Xz)) (((eq b) Xt) Xz)))))))))->(X Xe)))) (forall (Xx0:b), ((Xe Xx0)->(Xx Xx0))))) (forall (Xy:(b->Prop)), (((and (cB Xy)) (forall (Xx0:b), 
% EOF
%------------------------------------------------------------------------------