TSTP Solution File: SEV032^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV032^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n112.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 13:33:37 EDT 2014
% Result : Timeout 300.09s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV032^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.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 07:37:36 CDT 2014
% % CPUTime : 300.09
% 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 0x212e6c8>, <kernel.Type object at 0x212efc8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (T:((a->Prop)->Prop)) (U:((a->Prop)->Prop)), (((and ((and ((and ((and (not (((eq ((a->Prop)->Prop)) T) U))) (forall (Xp:(a->Prop)), ((T Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (T Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (T Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))) (forall (Xp:(a->Prop)), ((U Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (U Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (U Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))))) of role conjecture named cTHM266_LEMMA_pme
% Conjecture to prove = (forall (T:((a->Prop)->Prop)) (U:((a->Prop)->Prop)), (((and ((and ((and ((and (not (((eq ((a->Prop)->Prop)) T) U))) (forall (Xp:(a->Prop)), ((T Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (T Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (T Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))) (forall (Xp:(a->Prop)), ((U Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (U Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (U Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (T:((a->Prop)->Prop)) (U:((a->Prop)->Prop)), (((and ((and ((and ((and (not (((eq ((a->Prop)->Prop)) T) U))) (forall (Xp:(a->Prop)), ((T Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (T Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (T Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))) (forall (Xp:(a->Prop)), ((U Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (U Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (U Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))))']
% Parameter a:Type.
% Trying to prove (forall (T:((a->Prop)->Prop)) (U:((a->Prop)->Prop)), (((and ((and ((and ((and (not (((eq ((a->Prop)->Prop)) T) U))) (forall (Xp:(a->Prop)), ((T Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (T Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (T Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))) (forall (Xp:(a->Prop)), ((U Xp)->((ex a) (fun (Xz:a)=> (Xp Xz))))))) (forall (Xx:a), ((ex (a->Prop)) (fun (Xp:(a->Prop))=> ((and ((and (U Xp)) (Xp Xx))) (forall (Xq:(a->Prop)), (((and (U Xq)) (Xq Xx))->(((eq (a->Prop)) Xq) Xp))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq x)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq x)->False)) ((Xq Xy)->False))))))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq x)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq x)->False)) ((Xq Xy)->False))))))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq x)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq x)->False)) ((Xq Xy)->False))))))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq x)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq x)->False)) ((Xq Xy)->False))))))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found ((eta_expansion_dep0 (fun (x7:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion_dep a) (fun (x7:a)=> Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq x)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs x))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq x)->False)) ((Xq Xy)->False))))))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((or ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (T Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((U Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False)))))) ((and ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((and ((and (U Xs)) (Xs Xx))) (Xs Xy))))) (forall (Xq:(a->Prop)), ((T Xq)->((or ((Xq Xx)->False)) ((Xq Xy)->False))))))))))
% Found eq_ref00:=(eq_ref0 a0):(((eq (a->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (a->Prop)) a0) b)
% Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) b)
% Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) b)
% Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:a)=> ((or ((and ((ex (a->Prop
% EOF
%------------------------------------------------------------------------------