cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET630^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n117.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 13:30:53 EDT 2014

% Result   : Theorem 1.98s
% Output   : Proof 1.98s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET630^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n117.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 10:27:16 CDT 2014
% % CPUTime  : 1.98 
% 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 0x27bd4d0>, <kernel.Type object at 0x27dccf8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False)) of role conjecture named cBOOL_PROP_112_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False)):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False))
% Found x80:=(x8 x4):False
% Found (x8 x4) as proof of False
% Found (fun (x8:((X x0)->False))=> (x8 x4)) as proof of False
% Found (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)) as proof of (((X x0)->False)->False)
% Found (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)) as proof of ((Y x0)->(((X x0)->False)->False))
% Found (and_rect20 (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))) as proof of False
% Found ((and_rect2 False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))) as proof of False
% Found (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))) as proof of False
% Found (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))) as proof of False
% Found (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))) as proof of (((and (Y x0)) ((X x0)->False))->False)
% Found x80:=(x8 x5):False
% Found (x8 x5) as proof of False
% Found (fun (x8:((Y x0)->False))=> (x8 x5)) as proof of False
% Found (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)) as proof of (((Y x0)->False)->False)
% Found (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)) as proof of ((X x0)->(((Y x0)->False)->False))
% Found (and_rect20 (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found ((and_rect2 False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)))) as proof of False
% Found (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)))) as proof of (((and (X x0)) ((Y x0)->False))->False)
% Found ((or_ind00 (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))) as proof of False
% Found (((or_ind0 False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))) as proof of False
% Found ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))) as proof of False
% Found (fun (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))) as proof of False
% Found (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))) as proof of ((Y x0)->False)
% Found (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))) as proof of ((X x0)->((Y x0)->False))
% Found (and_rect10 (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))) as proof of False
% Found (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))) as proof of False
% Found (fun (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))) as proof of False
% Found (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))) as proof of (((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->False)
% Found (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))) as proof of (((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->False))
% Found (and_rect00 (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))) as proof of False
% Found ((and_rect0 False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))) as proof of False
% Found (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))) as proof of False
% Found (fun (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))) as proof of False
% Found (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))) as proof of (((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))->False)
% Found (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))) as proof of (forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->False))
% Found (ex_ind00 (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))))) as proof of False
% Found ((ex_ind0 False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))))) as proof of False
% Found (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))))) as proof of False
% Found (fun (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))))) as proof of False
% Found (fun (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))))) as proof of (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False)
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))))) as proof of (forall (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4)))))))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))))->False))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))))))
% Time elapsed = 1.661187s
% node=175 cost=801.000000 depth=33
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((or ((and (X x)) ((Y x)->False))) ((and (Y x)) ((X x)->False))))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))))=> (((fun (P:Type) (x2:(((and (X x0)) (Y x0))->(((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False)))) P) x2) x1)) False) (fun (x2:((and (X x0)) (Y x0))) (x3:((or ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and (Y x0)) ((X x0)->False))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and (Y x0)) ((X x0)->False))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and (Y x0)) ((X x0)->False)))=> (((fun (P:Type) (x7:((Y x0)->(((X x0)->False)->P)))=> (((((and_rect (Y x0)) ((X x0)->False)) P) x7) x6)) False) (fun (x7:(Y x0)) (x8:((X x0)->False))=> (x8 x4))))))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------