TSTP Solution File: SEU861^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU861^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n108.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 13:33:18 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 : SEU861^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n108.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 11:37:26 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 0x16ca488>, <kernel.Type object at 0x16ca3b0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1299518>, <kernel.DependentProduct object at 0x16ca1b8>) of role type named cB
% Using role type
% Declaring cB:(a->Prop)
% FOF formula (<kernel.Constant object at 0x16ca878>, <kernel.DependentProduct object at 0x16d32d8>) of role type named cC
% Using role type
% Declaring cC:(a->Prop)
% FOF formula (((and (forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P Z))))->(P cC)))) (forall (Xx:a), ((cB Xx)->(cC Xx))))->(forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))->(P cB)))) of role conjecture named cTHM531E_pme
% Conjecture to prove = (((and (forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P Z))))->(P cC)))) (forall (Xx:a), ((cB Xx)->(cC Xx))))->(forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))->(P cB)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(((and (forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P Z))))->(P cC)))) (forall (Xx:a), ((cB Xx)->(cC Xx))))->(forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))->(P cB))))']
% Parameter a:Type.
% Parameter cB:(a->Prop).
% Parameter cC:(a->Prop).
% Trying to prove (((and (forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P Z))))->(P cC)))) (forall (Xx:a), ((cB Xx)->(cC Xx))))->(forall (P:((a->Prop)->Prop)), (((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))->(P cB))))
% Found x4:(P cB)
% Found (fun (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of (P cB)
% Found (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect10 (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found ((and_rect1 (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found (fun (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x4:(P cB)
% Found (fun (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of (P cB)
% Found (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect10 (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found ((and_rect1 (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4)) as proof of (P cB)
% Found (fun (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x4:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:(P cB)) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x4))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cB x1))
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion_dep00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion_dep0 (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eq_ref00:=(eq_ref0 cB):(((eq (a->Prop)) cB) cB)
% Found (eq_ref0 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion_dep00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion_dep0 (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x4:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (cB x3))
% Found (fun (x3:a)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found x6:(P cB)
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (P cB)
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (P cB)
% Found (fun (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (P cB)
% Found (fun (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((P cB)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (P cB)) (fun (x6:(P cB)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b
% Found x50:=(x5 x40):(P cB)
% Found (x5 x40) as proof of (P cB)
% Found (fun (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of (P cB)
% Found (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of (((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (P cB)
% Found (fun (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))
% Found (fun (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))
% Found (fun (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found x41:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found eta_expansion_dep000:=(eta_expansion_dep00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion_dep00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion_dep0 (fun (x6:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (and_rect20 (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found ((and_rect2 (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (and_rect20 (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found ((and_rect2 (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found x30:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found x50:=(x5 x40):(P cB)
% Found (x5 x40) as proof of (P cB)
% Found (fun (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of (P cB)
% Found (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)) as proof of (((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40))) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (P cB)
% Found (fun (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))
% Found (fun (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))
% Found (fun (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x4:((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x5:(((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x5) x4)) (P cB)) (fun (x5:((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB))) (x6:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x5 x40)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found x41:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x30 (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41)) as proof of (P cB)
% Found ((x3 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41)) as proof of (P cB)
% Found ((x3 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x41)) as proof of (P cB)
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x10 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x1 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x1 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x30 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x3 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x3 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6) as proof of ((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (and_rect20 (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found ((and_rect2 (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6)) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (not ((ex a) (fun (Xt:a)=> (cB Xt))))
% Found (fun (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x6:((not ((ex a) (fun (Xt:a)=> (cB Xt))))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (fun (x6:(not ((ex a) (fun (Xt:a)=> (cB Xt))))) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x6))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found x40:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x30 (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40)) as proof of (P cB)
% Found ((x3 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40)) as proof of (P cB)
% Found (fun (x400:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x3 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40))) as proof of (P cB)
% Found (fun (x400:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x3 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x40))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found x50:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x30 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x3 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found ((x3 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50)) as proof of (P cB)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))) b)
% Found eq_ref00:=(eq_ref0 cB):(((eq (a->Prop)) cB) cB)
% Found (eq_ref0 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x410:=(x41 x40):(P cB)
% Found (x41 x40) as proof of (P cB)
% Found ((x4 x30) x40) as proof of (P cB)
% Found (fun (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of (P cB)
% Found (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of (((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (P cB)
% Found (fun (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))
% Found (fun (x3:((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))
% Found (fun (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found x31:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found x31:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x300 (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31)) as proof of (P cB)
% Found ((x30 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31)) as proof of (P cB)
% Found ((x30 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31)) as proof of (P cB)
% Found x31:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x300 (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31)) as proof of (P cB)
% Found ((x30 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31)) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x30 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31))) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x30 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x31))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found x30:False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x3000 (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x300 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x300 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of (P cB)
% Found (fun (x300:(forall (E0:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E0 Xt)))->False)->(P E0)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x300 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found (fun (x300:(forall (E0:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E0 Xt)))->False)->(P E0)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x300 cB) (fun (x5:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (E0:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E0 Xt)))->False)->(P E0)))->((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))) b)
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x7:False
% Found (fun (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of False
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found ((and_rect2 False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7)) as proof of False
% Found (fun (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of False
% Found (fun (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x6:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x7:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x7) x6)) False) (fun (x7:False) (x8:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x7))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x60:=(x6 x50):False
% Found (x6 x50) as proof of False
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of False
% Found (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of ((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found ((and_rect2 False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found (fun (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of False
% Found (fun (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (fun (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found x50:False
% Found (fun (x500:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x500:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found x60:=(x6 x50):False
% Found (x6 x50) as proof of False
% Found (fun (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of False
% Found (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)) as proof of ((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found ((and_rect2 False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50))) as proof of False
% Found (fun (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of False
% Found (fun (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (fun (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False))
% Found (fun (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x5:((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x50:((ex a) (fun (Xt:a)=> (cB Xt))))=> (((fun (P0:Type) (x6:((((ex a) (fun (Xt:a)=> (cB Xt)))->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x6) x5)) False) (fun (x6:(((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (x7:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x6 x50)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))
% Found x50:False
% Found (fun (x500:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of False
% Found (fun (x500:((ex a) (fun (Xt:a)=> (cB Xt))))=> x50) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (cB x5))
% Found (fun (x5:a)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found x30:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x40 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found eta_expansion000:=(eta_expansion00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion0 Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion a) Prop) cB) as proof of (((eq (a->Prop)) cB) b)
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b
% Found x410:=(x41 x40):(P cB)
% Found (x41 x40) as proof of (P cB)
% Found ((x4 x30) x40) as proof of (P cB)
% Found (fun (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of (P cB)
% Found (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB))
% Found (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)) as proof of (((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->(P cB)))
% Found (and_rect20 (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found ((and_rect2 (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40))) as proof of (P cB)
% Found (fun (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (P cB)
% Found (fun (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))
% Found (fun (x3:((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))
% Found (fun (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB))))
% Found (fun (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x3:((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x30:(forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))) (x40:(forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0))))=> (((fun (P0:Type) (x4:(((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x4) x3)) (P cB)) (fun (x4:((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx0:a) (Z0:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx0)))))->(P Z0)))->(P cB)))) (x5:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> ((x4 x30) x40)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y0:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y0)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y0 Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((forall (E:(a->Prop)), ((not ((ex a) (fun (Xt:a)=> (E Xt))))->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z0:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z0 Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z0)))->(P cB)))))
% Found x30:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x40 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found (fun (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of (P cB)
% Found (fun (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P cB)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(P cB)))) b)
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (((ex a) (fun (Xt:a)=> (cB Xt)))->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(((ex a) (fun (Xt:a)=> (cB Xt)))->False)))) b)
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found x51:False
% Found (fun (x7:(cB x6))=> x51) as proof of False
% Found (fun (x7:(cB x6))=> x51) as proof of ((cB x6)->False)
% Found x41:False
% Found (fun (x7:(cB x6))=> x41) as proof of False
% Found (fun (x7:(cB x6))=> x41) as proof of ((cB x6)->False)
% Found x51:False
% Found (fun (x7:(cB x6))=> x51) as proof of False
% Found (fun (x7:(cB x6))=> x51) as proof of ((cB x6)->False)
% Found x31:False
% Found (fun (x6:(cB x4))=> x31) as proof of False
% Found (fun (x6:(cB x4))=> x31) as proof of ((cB x4)->False)
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found x30:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x40 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found (fun (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of (P cB)
% Found (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found or_introl00:=(or_introl0 (((eq a) Xx_28) Xx)):((cB Xx_28)->((or (cB Xx_28)) (((eq a) Xx_28) Xx)))
% Found (or_introl0 (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx)) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))
% Found (fun (Xx_28:a)=> ((or_introl (cB Xx_28)) (((eq a) Xx_28) Xx))) as proof of (forall (Xx_28:a), ((cB Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found x51:False
% Found (fun (x7:(cB x6))=> x51) as proof of False
% Found (fun (x6:a) (x7:(cB x6))=> x51) as proof of ((cB x6)->False)
% Found (fun (x6:a) (x7:(cB x6))=> x51) as proof of (forall (x:a), ((cB x)->False))
% Found x31:False
% Found (fun (x6:(cB x4))=> x31) as proof of False
% Found (fun (x4:a) (x6:(cB x4))=> x31) as proof of ((cB x4)->False)
% Found (fun (x4:a) (x6:(cB x4))=> x31) as proof of (forall (x:a), ((cB x)->False))
% Found x41:False
% Found (fun (x7:(cB x6))=> x41) as proof of False
% Found (fun (x6:a) (x7:(cB x6))=> x41) as proof of ((cB x6)->False)
% Found (fun (x6:a) (x7:(cB x6))=> x41) as proof of (forall (x:a), ((cB x)->False))
% Found x51:False
% Found (fun (x7:(cB x6))=> x51) as proof of False
% Found (fun (x6:a) (x7:(cB x6))=> x51) as proof of ((cB x6)->False)
% Found (fun (x6:a) (x7:(cB x6))=> x51) as proof of (forall (x:a), ((cB x)->False))
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of (forall (x:a), ((cB x)->False))
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of (forall (x:a), ((cB x)->False))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (cB x4))
% Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) (cB x)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found x50:False
% Found (fun (x8:(cB x7))=> x50) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x50) as proof of (forall (x:a), ((cB x)->False))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt)))))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (not ((ex a) (fun (Xt:a)=> (cB Xt))))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(not ((ex a) (fun (Xt:a)=> (cB Xt))))))) b)
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found x30:False
% Found (fun (x8:(cB x7))=> x30) as proof of False
% Found (fun (x8:(cB x7))=> x30) as proof of ((cB x7)->False)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of (forall (x:a), ((cB x)->False))
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of (forall (x:a), ((cB x)->False))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found x30:False
% Found (fun (x8:(cB x7))=> x30) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x30) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x30) as proof of (forall (x:a), ((cB x)->False))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) b)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x30:False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of False
% Found (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30) as proof of (((ex a) (fun (Xt:a)=> (cB Xt)))->False)
% Found (x40 (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)) as proof of (P cB)
% Found (fun (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of (P cB)
% Found (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB))
% Found (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30))) as proof of ((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->(P cB)))
% Found (and_rect10 (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)))) as proof of (P cB)
% Found ((and_rect1 (P cB)) (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)))) as proof of (P cB)
% Found (((fun (P0:Type) (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->P0)))=> (((((and_rect (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))) P0) x4) x0)) (P cB)) (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)))) as proof of (P cB)
% Found (((fun (P0:Type) (x4:((forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))->((forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))->P0)))=> (((((and_rect (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z)))) P0) x4) x0)) (P cB)) (fun (x4:(forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E)))) (x5:(forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (P Y)) (forall (Xx_28:a), ((Z Xx_28)->((or (Y Xx_28)) (((eq a) Xx_28) Xx)))))->(P Z))))=> ((x4 cB) (fun (x6:((ex a) (fun (Xt:a)=> (cB Xt))))=> x30)))) as proof of (P cB)
% Found x10:=(x1 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 b))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 b))
% Found x30:=(x3 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 b))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 b))
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (b x6))):((b x6)->(b x6))
% Found (eq_ref00 (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))) as proof of (forall (x:a), ((b x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x30 (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))) as proof of False
% Found ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))))) as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x10 (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found ((x1 b) (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found ((x1 b) (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cB):(((eq (a->Prop)) cB) cB)
% Found (eq_ref0 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x3:(((ex a) (fun (Xt:a)=> (E Xt)))->False)
% Instantiate: b:=E:(a->Prop)
% Found x3 as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x300 x3) as proof of (P0 b)
% Found ((x30 b) x3) as proof of (P0 b)
% Found ((x30 b) x3) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cB):(((eq (a->Prop)) cB) cB)
% Found (eq_ref0 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x4:(((ex a) (fun (Xt:a)=> (E Xt)))->False)
% Instantiate: b:=E:(a->Prop)
% Found x4 as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x30 x4) as proof of (P0 b)
% Found ((x3 b) x4) as proof of (P0 b)
% Found ((x3 b) x4) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (b x6))):((b x6)->(b x6))
% Found (eq_ref00 (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))) as proof of ((b x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))) as proof of (forall (x:a), ((b x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x10 (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))) as proof of False
% Found ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6))))))) as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x30 (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found ((x3 b) (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found ((x3 b) (fun (x5:((ex a) (fun (Xt:a)=> (b Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((b x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (b Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (b x6)))))))) as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion_dep00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion_dep0 (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x5:(((ex a) (fun (Xt:a)=> (E Xt)))->False)
% Instantiate: b:=E:(a->Prop)
% Found x5 as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x10 x5) as proof of (P0 b)
% Found ((x1 b) x5) as proof of (P0 b)
% Found ((x1 b) x5) as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 cB):(((eq (a->Prop)) cB) (fun (x:a)=> (cB x)))
% Found (eta_expansion_dep00 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eta_expansion_dep0 (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x5:(((ex a) (fun (Xt:a)=> (E Xt)))->False)
% Instantiate: b:=E:(a->Prop)
% Found x5 as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x30 x5) as proof of (P0 b)
% Found ((x3 b) x5) as proof of (P0 b)
% Found ((x3 b) x5) as proof of (P0 b)
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False)))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False)))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and (forall (x60:a), ((cB x60)->False))) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->(forall (x60:a), ((cB x60)->False))))) b)
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found eq_ref00:=(eq_ref0 cB):(((eq (a->Prop)) cB) cB)
% Found (eq_ref0 cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found ((eq_ref (a->Prop)) cB) as proof of (((eq (a->Prop)) cB) b)
% Found x5:(((ex a) (fun (Xt:a)=> (E Xt)))->False)
% Instantiate: b:=E:(a->Prop)
% Found x5 as proof of (((ex a) (fun (Xt:a)=> (b Xt)))->False)
% Found (x30 x5) as proof of (P0 b)
% Found ((x3 b) x5) as proof of (P0 b)
% Found ((x3 b) x5) as proof of (P0 b)
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found x10:=(x1 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found x10:=(x1 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found (x1 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found x30:=(x3 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found x30:=(x3 E):((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P E))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found (x3 E) as proof of ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->(P0 f))
% Found x9:False
% Found (fun (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of False
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9) as proof of (False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found ((and_rect2 False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9)) as proof of False
% Found (fun (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of False
% Found (fun (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)
% Found (fun (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x8:((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))))=> (((fun (P0:Type) (x9:(False->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x9) x8)) False) (fun (x9:False) (x11:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> x9))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (f x6))):((f x6)->(f x6))
% Found (eq_ref00 (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of (forall (x:a), ((f x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x30 (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of (((ex a) (fun (Xt:a)=> (f Xt)))->False)
% Found (x10 (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x1 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x1 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found x70:False
% Found (fun (x700:(cB x6))=> x70) as proof of False
% Found (fun (x700:(cB x6))=> x70) as proof of ((cB x6)->False)
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (f x6))):((f x6)->(f x6))
% Found (eq_ref00 (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of (forall (x:a), ((f x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x30 (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of (((ex a) (fun (Xt:a)=> (f Xt)))->False)
% Found (x10 (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x1 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x1 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x3 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (f x6))):((f x6)->(f x6))
% Found (eq_ref00 (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of (forall (x:a), ((f x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x10 (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of (((ex a) (fun (Xt:a)=> (f Xt)))->False)
% Found (x30 (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x3 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x3 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found eq_ref000:=(eq_ref00 (fun (x7:Prop)=> (f x6))):((f x6)->(f x6))
% Found (eq_ref00 (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found ((eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of ((f x6)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))))
% Found (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))) as proof of (forall (x:a), ((f x)->((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))))
% Found (ex_ind00 (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found ((ex_ind0 ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))) as proof of ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))
% Found (x10 (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of False
% Found (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6))))))) as proof of (((ex a) (fun (Xt:a)=> (f Xt)))->False)
% Found (x30 (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x3 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found ((x3 f) (fun (x5:((ex a) (fun (Xt:a)=> (f Xt))))=> ((x1 (fun (x7:(a->Prop))=> False)) (((fun (P1:Prop) (x6:(forall (x:a), ((f x)->P1)))=> (((((ex_ind a) (fun (Xt:a)=> (f Xt))) P1) x6) x5)) ((and (forall (E:(a->Prop)), ((((ex a) (fun (Xt:a)=> (E Xt)))->False)->False))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False)))) (fun (x6:a)=> (((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and False) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->False))) (fun (x7:Prop)=> (f x6)))))))) as proof of (P0 f)
% Found x70:False
% Found (fun (x700:(cB x6))=> x70) as proof of False
% Found (fun (x700:(cB x6))=> x70) as proof of ((cB x6)->False)
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b
% Found x60:False
% Found (fun (x8:(cB x7))=> x60) as proof of False
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of ((cB x7)->False)
% Found (fun (x7:a) (x8:(cB x7))=> x60) as proof of (forall (x:a), ((cB x)->False))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x80:=(x8 x70):False
% Found (x8 x70) as proof of False
% Found (fun (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of False
% Found (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of (((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found (fun (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of False
% Found (fun (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of ((cB x6)->False)
% Found (fun (Z:(a->Prop)) (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False))
% Found (fun (Xx:a) (Z:(a->Prop)) (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of (forall (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of (forall (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))
% Found (fun (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)) (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))
% Found eq_ref00:=(eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))):(((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False))))
% Found (eq_ref0 (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) b)
% Found ((eq_ref Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) as proof of (((eq Prop) (forall (Y:(a->Prop)) (Xx:a) (Z:(a->Prop)), (((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))->((cB x6)->False)))) b)
% Found x80:=(x8 x70):False
% Found (x8 x70) as proof of False
% Found (fun (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of False
% Found (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of ((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False)
% Found (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)) as proof of (((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->False))
% Found (and_rect20 (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70))) as proof of False
% Found (fun (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of False
% Found (fun (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))) P0) x8) x7)) False) (fun (x8:((cB x6)->False)) (x9:(forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))=> (x8 x70)))) as proof of ((cB x6)->False)
% Found (fun (Z:(a->Prop)) (x7:((and ((cB x6)->False)) (forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx)))))) (x70:(cB x6))=> (((fun (P0:Type) (x8:(((cB x6)->False)->((forall (Xx_27:a), ((Z Xx_27)->((or (Y Xx_27)) (((eq a) Xx_27) Xx))))->P0)))=> (((((and_rect ((cB x6)->False)) (forall (Xx_27:a)
% EOF
%------------------------------------------------------------------------------