TSTP Solution File: SET632^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET632^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n179.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 13:30:54 EDT 2014
% Result : Timeout 300.09s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET632^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 10:27:46 CDT 2014
% % CPUTime : 300.09
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1057248>, <kernel.Type object at 0x12b67a0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((X Xx)->(Z Xx))))) (((ex a) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))->False))->(((eq (a->Prop)) X) (fun (Xx:a)=> False)))) of role conjecture named cBOOL_PROP_114_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((X Xx)->(Z Xx))))) (((ex a) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))->False))->(((eq (a->Prop)) X) (fun (Xx:a)=> False)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((X Xx)->(Z Xx))))) (((ex a) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))->False))->(((eq (a->Prop)) X) (fun (Xx:a)=> False))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((X Xx)->(Z Xx))))) (((ex a) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))->False))->(((eq (a->Prop)) X) (fun (Xx:a)=> False))))
% Found eq_ref00:=(eq_ref0 X):(((eq (a->Prop)) X) X)
% Found (eq_ref0 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq (a->Prop)) X) X)
% Found (eq_ref0 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found ((eq_ref (a->Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found eta_expansion000:=(eta_expansion00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion0 Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion_dep00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x00:(P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P0 (fun (Xx:a)=> False))
% Found x00:(P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found x20:(P X)
% Found (fun (x20:(P X))=> x20) as proof of (P X)
% Found (fun (x20:(P X))=> x20) as proof of (P0 X)
% Found x10:(P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P0 (X x0))
% Found x10:(P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P0 (X x0))
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eta_expansion000:=(eta_expansion00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion0 Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x00:(P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P0 (fun (Xx:a)=> False))
% Found x00:(P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x00:(P (fun (Xx:a)=> False)))=> x00) as proof of (P0 (fun (Xx:a)=> False))
% Found x10:(P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P0 (X x0))
% Found x10:(P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P (X x0))
% Found (fun (x10:(P (X x0)))=> x10) as proof of (P0 (X x0))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found eta_expansion000:=(eta_expansion00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion0 Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion a) Prop) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found x30:(P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P0 (X x2))
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found x30:(P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P0 (X x2))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x10:(P False)
% Found (fun (x10:(P False))=> x10) as proof of (P False)
% Found (fun (x10:(P False))=> x10) as proof of (P0 False)
% Found x10:(P False)
% Found (fun (x10:(P False))=> x10) as proof of (P False)
% Found (fun (x10:(P False))=> x10) as proof of (P0 False)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found x30:(P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P0 (X x2))
% Found x30:(P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P (X x2))
% Found (fun (x30:(P (X x2)))=> x30) as proof of (P0 (X x2))
% Found x30:(P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P0 (X x0))
% Found x30:(P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P0 (X x0))
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found x20:(P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x20:(P (fun (Xx:a)=> False)))=> x20) as proof of (P0 (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x10:(P False)
% Found (fun (x10:(P False))=> x10) as proof of (P False)
% Found (fun (x10:(P False))=> x10) as proof of (P0 False)
% Found x10:(P False)
% Found (fun (x10:(P False))=> x10) as proof of (P False)
% Found (fun (x10:(P False))=> x10) as proof of (P0 False)
% Found x30:(P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P0 (X x0))
% Found x30:(P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P (X x0))
% Found (fun (x30:(P (X x0)))=> x30) as proof of (P0 (X x0))
% Found x0:(P X)
% Instantiate: b:=X:(a->Prop)
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x0:(P X)
% Instantiate: f:=X:(a->Prop)
% Found x0 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) False))
% Found x0:(P X)
% Instantiate: f:=X:(a->Prop)
% Found x0 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) False))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 (X x4)):(((eq Prop) (X x4)) (X x4))
% Found (eq_ref0 (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x4)):(((eq Prop) (X x4)) (X x4))
% Found (eq_ref0 (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x0:(P X)
% Instantiate: b:=X:(a->Prop)
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eta_expansion_dep000:=(eta_expansion_dep00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion_dep00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (x:a)=> False))
% Found (eta_expansion_dep00 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eta_expansion_dep0 (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found (((eta_expansion_dep a) (fun (x5:a)=> Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x0:(P X)
% Instantiate: f:=X:(a->Prop)
% Found x0 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) False))
% Found x0:(P X)
% Instantiate: f:=X:(a->Prop)
% Found x0 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) False)
% Found (fun (x1:a)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:a), (((eq Prop) (f x)) False))
% Found eq_ref00:=(eq_ref0 (X x4)):(((eq Prop) (X x4)) (X x4))
% Found (eq_ref0 (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x4)):(((eq Prop) (X x4)) (X x4))
% Found (eq_ref0 (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found ((eq_ref Prop) (X x4)) as proof of (((eq Prop) (X x4)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x50:(P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P0 (X x4))
% Found x50:(P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P0 (X x4))
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found eta_expansion_dep000:=(eta_expansion_dep00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion_dep00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x0))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found x30:(P False)
% Found (fun (x30:(P False))=> x30) as proof of (P False)
% Found (fun (x30:(P False))=> x30) as proof of (P0 False)
% Found x30:(P False)
% Found (fun (x30:(P False))=> x30) as proof of (P False)
% Found (fun (x30:(P False))=> x30) as proof of (P0 False)
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found x40:(P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P (fun (Xx:a)=> False))
% Found (fun (x40:(P (fun (Xx:a)=> False)))=> x40) as proof of (P0 (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found eq_ref00:=(eq_ref0 False):(((eq Prop) False) False)
% Found (eq_ref0 False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found ((eq_ref Prop) False) as proof of (((eq Prop) False) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (X x2))
% Found x2:(P X)
% Instantiate: b:=X:(a->Prop)
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x00:(P X)
% Found (fun (x00:(P X))=> x00) as proof of (P X)
% Found (fun (x00:(P X))=> x00) as proof of (P0 X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 X):(((eq (a->Prop)) X) (fun (x:a)=> (X x)))
% Found (eta_expansion_dep00 X) as proof of (((eq (a->Prop)) X) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) X) as proof of (((eq (a->Prop)) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> False))
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> False)):(((eq (a->Prop)) (fun (Xx:a)=> False)) (fun (Xx:a)=> False))
% Found (eq_ref0 (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> False)) as proof of (((eq (a->Prop)) (fun (Xx:a)=> False)) b)
% Found x0:(P0 b)
% Instantiate: b:=X:(a->Prop)
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 X)
% Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 X))
% Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x50:(P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P0 (X x4))
% Found x50:(P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P (X x4))
% Found (fun (x50:(P (X x4)))=> x50) as proof of (P0 (X x4))
% Found x50:(P (X x0))
% Found (fun (x50:(P (X x0)))=> x50) as proof of (P (X x0))
% Found (fun (x50:(P (X x0)))=> x50) as proof of (P0 (X x0))
% Found x50:(P (X x0))
% Found (fun (x50:(P (X x0)))=> x50) as proof of (P (X x0))
% Found (fun (x50:(P (X x0)))=> x50) as proof of (P0 (X x0))
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found eq_ref00:=(eq_ref0 (X x0)):(((eq Prop) (X x0)) (X x0))
% Found (eq_ref0 (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found ((eq_ref Prop) (X x0)) as proof of (((eq Prop) (X x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x50:(P (X x2))
% Found (fun (x50:(P (X x2)))=> x50) as proof of (P (X x2))
% Found (fun (x50:(P (X x2)))=> x50) as proof of (P0 (X x2))
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x50:(P (X x2))
% Found (fun (x50:(P (X x2)))=> x50) as proof of (P (X x2))
% Found (fun (x50:(P (X x2)))=> x50) as proof of (P0 (X x2))
% Found eq_ref00:=(eq_ref0 (X x2)):(((eq Prop) (X x2)) (X x2))
% Found (eq_ref0 (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found ((eq_ref Prop) (X x2)) as proof of (((eq Prop) (X x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) False)
% Found x2:(P X)
% Instantiate: f:=X:(a->Prop)
% Found x2 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0
% EOF
%------------------------------------------------------------------------------