TSTP Solution File: SEV006^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV006^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n093.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 13:33:32 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 : SEV006^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.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 07:24:36 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 0x170c128>, <kernel.Type object at 0x170cab8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))) ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))->False))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (((eq a) ((MEET Xx) Xy)) Xy)) (((eq a) ((JOIN Xx) Xy)) Xx))) (((eq a) ((MEET Xx) Xa)) Xa))) (((eq a) ((JOIN Xx) Xa)) Xx))) (((eq a) ((MEET Xx) Xb)) Xb))) (((eq a) ((JOIN Xx) Xb)) Xx))) (((eq a) ((MEET Xx) Xc)) Xc))) (((eq a) ((JOIN Xx) Xc)) Xx))) (((eq a) ((MEET Xa) Xb)) Xy))) (((eq a) ((JOIN Xa) Xb)) Xx))) (((eq a) ((MEET Xa) Xc)) Xa))) (((eq a) ((JOIN Xa) Xc)) Xc))) (((eq a) ((MEET Xa) Xy)) Xy))) (((eq a) ((JOIN Xa) Xy)) Xa))) (((eq a) ((MEET Xb) Xc)) Xy))) (((eq a) ((JOIN Xb) Xc)) Xx))) (((eq a) ((MEET Xb) Xy)) Xy))) (((eq a) ((JOIN Xb) Xy)) Xb))) (((eq a) ((MEET Xc) Xy)) Xy))) (((eq a) ((JOIN Xc) Xy)) Xc)))))))))))))) of role conjecture named cPENTAGON_THM2D_pme
% Conjecture to prove = (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))) ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))->False))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (((eq a) ((MEET Xx) Xy)) Xy)) (((eq a) ((JOIN Xx) Xy)) Xx))) (((eq a) ((MEET Xx) Xa)) Xa))) (((eq a) ((JOIN Xx) Xa)) Xx))) (((eq a) ((MEET Xx) Xb)) Xb))) (((eq a) ((JOIN Xx) Xb)) Xx))) (((eq a) ((MEET Xx) Xc)) Xc))) (((eq a) ((JOIN Xx) Xc)) Xx))) (((eq a) ((MEET Xa) Xb)) Xy))) (((eq a) ((JOIN Xa) Xb)) Xx))) (((eq a) ((MEET Xa) Xc)) Xa))) (((eq a) ((JOIN Xa) Xc)) Xc))) (((eq a) ((MEET Xa) Xy)) Xy))) (((eq a) ((JOIN Xa) Xy)) Xa))) (((eq a) ((MEET Xb) Xc)) Xy))) (((eq a) ((JOIN Xb) Xc)) Xx))) (((eq a) ((MEET Xb) Xy)) Xy))) (((eq a) ((JOIN Xb) Xy)) Xb))) (((eq a) ((MEET Xc) Xy)) Xy))) (((eq a) ((JOIN Xc) Xy)) Xc)))))))))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))) ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))->False))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (((eq a) ((MEET Xx) Xy)) Xy)) (((eq a) ((JOIN Xx) Xy)) Xx))) (((eq a) ((MEET Xx) Xa)) Xa))) (((eq a) ((JOIN Xx) Xa)) Xx))) (((eq a) ((MEET Xx) Xb)) Xb))) (((eq a) ((JOIN Xx) Xb)) Xx))) (((eq a) ((MEET Xx) Xc)) Xc))) (((eq a) ((JOIN Xx) Xc)) Xx))) (((eq a) ((MEET Xa) Xb)) Xy))) (((eq a) ((JOIN Xa) Xb)) Xx))) (((eq a) ((MEET Xa) Xc)) Xa))) (((eq a) ((JOIN Xa) Xc)) Xc))) (((eq a) ((MEET Xa) Xy)) Xy))) (((eq a) ((JOIN Xa) Xy)) Xa))) (((eq a) ((MEET Xb) Xc)) Xy))) (((eq a) ((JOIN Xb) Xc)) Xx))) (((eq a) ((MEET Xb) Xy)) Xy))) (((eq a) ((JOIN Xb) Xy)) Xb))) (((eq a) ((MEET Xc) Xy)) Xy))) (((eq a) ((JOIN Xc) Xy)) Xc))))))))))))))']
% Parameter a:Type.
% Trying to prove (forall (JOIN:(a->(a->a))) (MEET:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), (((eq a) ((JOIN Xx) Xx)) Xx))) (forall (Xx:a), (((eq a) ((MEET Xx) Xx)) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN ((JOIN Xx) Xy)) Xz)) ((JOIN Xx) ((JOIN Xy) Xz)))))) (forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((MEET ((MEET Xx) Xy)) Xz)) ((MEET Xx) ((MEET Xy) Xz)))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN Xx) Xy)) ((JOIN Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET Xx) Xy)) ((MEET Xy) Xx))))) (forall (Xx:a) (Xy:a), (((eq a) ((JOIN ((MEET Xx) Xy)) Xy)) Xy)))) (forall (Xx:a) (Xy:a), (((eq a) ((MEET ((JOIN Xx) Xy)) Xy)) Xy)))) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))) ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((JOIN Xx) ((MEET Xy) ((JOIN Xx) Xz)))) ((MEET ((JOIN Xx) Xy)) ((JOIN Xx) Xz))))->False))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (((eq a) ((MEET Xx) Xy)) Xy)) (((eq a) ((JOIN Xx) Xy)) Xx))) (((eq a) ((MEET Xx) Xa)) Xa))) (((eq a) ((JOIN Xx) Xa)) Xx))) (((eq a) ((MEET Xx) Xb)) Xb))) (((eq a) ((JOIN Xx) Xb)) Xx))) (((eq a) ((MEET Xx) Xc)) Xc))) (((eq a) ((JOIN Xx) Xc)) Xx))) (((eq a) ((MEET Xa) Xb)) Xy))) (((eq a) ((JOIN Xa) Xb)) Xx))) (((eq a) ((MEET Xa) Xc)) Xa))) (((eq a) ((JOIN Xa) Xc)) Xc))) (((eq a) ((MEET Xa) Xy)) Xy))) (((eq a) ((JOIN Xa) Xy)) Xa))) (((eq a) ((MEET Xb) Xc)) Xy))) (((eq a) ((JOIN Xb) Xc)) Xx))) (((eq a) ((MEET Xb) Xy)) Xy))) (((eq a) ((JOIN Xb) Xy)) Xb))) (((eq a) ((MEET Xc) Xy)) Xy))) (((eq a) ((JOIN Xc) Xy)) Xc))))))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x) Xy))))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eq_ref0 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x) Xy))))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x) Xy))))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x) Xy))))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eta_expansion00 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eta_expansion0 Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found ((eq_ref0 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy))))))))))))) (ex a)) as proof of (P (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) Xx)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) Xx)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) Xx)))) (not (((eq a) Xc) Xy)))) (not (((eq a) Xx) Xy)))))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eq_ref0 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eq_ref0 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) x)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) x)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) x)))) (not (((eq a) x4) x))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eta_expansion00 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eta_expansion0 Prop) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((((eta_expansion a) Prop) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eq_ref0 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found eq_ref000:=(eq_ref00 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))))
% Found (eq_ref00 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eq_ref0 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found (((eq_ref (a->Prop)) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy))))))))))) (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex a)):(((ex a) (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))->((ex a) (fun (x:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) x)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) x)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) x)))) (not (((eq a) x4) x))))))))))))
% Found (eta_expansion000 (ex a)) as proof of (P (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (((eq a) Xc) x4)))) (not (((eq a) Xc) Xy)))) (not (((eq a) x4) Xy)))))))))))
% Found ((eta_expansion00 (fun (Xy:a)=> ((ex a) (fun (Xa:a)=> ((ex a) (fun (Xb:a)=> ((ex a) (fun (Xc:a)=> ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq a) Xa) Xb))) (not (((eq a) Xa) Xc)))) (not (((eq a) Xa) x4)))) (not (((eq a) Xa) Xy)))) (not (((eq a) Xb) Xc)))) (not (((eq a) Xb) x4)))) (not (((eq a) Xb) Xy)))) (not (
% EOF
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