%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV315^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n118.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 13:34:02 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV315^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n118.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 08:49:06 CDT 2014
% % CPUTime  : 300.01 
% 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 0x19e2950>, <kernel.Type object at 0x1bc3ef0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x19e27a0>, <kernel.Type object at 0x1bc3bd8>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x19e2950>, <kernel.Type object at 0x1bc3cb0>) of role type named c_type
% Using role type
% Declaring c:Type
% FOF formula (<kernel.Constant object at 0x18ac290>, <kernel.DependentProduct object at 0x1bc3a28>) of role type named cF
% Using role type
% Declaring cF:((a->(b->(c->Prop)))->(a->(b->(c->Prop))))
% FOF formula (<kernel.Constant object at 0x19e2950>, <kernel.DependentProduct object at 0x1bc3998>) of role type named cCL
% Using role type
% Declaring cCL:((a->(b->(c->Prop)))->Prop)
% FOF formula (((and ((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))) (forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa:a) (Xb:b) (Xc:c), ((((R Xa) Xb) Xc)->(((S Xa) Xb) Xc))))->(forall (Xa:a) (Xb:b) (Xc:c), (((((cF R) Xa) Xb) Xc)->((((cF S) Xa) Xb) Xc))))))->((ex (a->(b->(c->Prop)))) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))))))) of role conjecture named cFP_THM3_pme
% Conjecture to prove = (((and ((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))) (forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa:a) (Xb:b) (Xc:c), ((((R Xa) Xb) Xc)->(((S Xa) Xb) Xc))))->(forall (Xa:a) (Xb:b) (Xc:c), (((((cF R) Xa) Xb) Xc)->((((cF S) Xa) Xb) Xc))))))->((ex (a->(b->(c->Prop)))) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))))))):Prop
% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
% Parameter c_DUMMY:c.
% We need to prove ['(((and ((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))) (forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa:a) (Xb:b) (Xc:c), ((((R Xa) Xb) Xc)->(((S Xa) Xb) Xc))))->(forall (Xa:a) (Xb:b) (Xc:c), (((((cF R) Xa) Xb) Xc)->((((cF S) Xa) Xb) Xc))))))->((ex (a->(b->(c->Prop)))) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter c:Type.
% Parameter cF:((a->(b->(c->Prop)))->(a->(b->(c->Prop)))).
% Parameter cCL:((a->(b->(c->Prop)))->Prop).
% Trying to prove (((and ((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))) (forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa:a) (Xb:b) (Xc:c), ((((R Xa) Xb) Xc)->(((S Xa) Xb) Xc))))->(forall (Xa:a) (Xb:b) (Xc:c), (((((cF R) Xa) Xb) Xc)->((((cF S) Xa) Xb) Xc))))))->((ex (a->(b->(c->Prop)))) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))))
% Found eq_ref000:=(eq_ref00 ((x0 Xa) Xb)):((((x0 Xa) Xb) Xc)->(((x0 Xa) Xb) Xc))
% Found (eq_ref00 ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eq_ref000:=(eq_ref00 ((x2 Xa) Xb)):((((x2 Xa) Xb) Xc)->(((x2 Xa) Xb) Xc))
% Found (eq_ref00 ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x00000:=(x0000 x00):(((Y Xa) Xb) Xc)
% Found (x0000 x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x000 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x000 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((x000 Y) x00)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found eq_ref000:=(eq_ref00 ((x0 Xa) Xb)):((((x0 Xa) Xb) Xc)->(((x0 Xa) Xb) Xc))
% Found (eq_ref00 ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eq_ref00:=(eq_ref0 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))):(((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))))))
% Found (eq_ref0 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found ((eq_ref ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found ((eq_ref ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found ((eq_ref ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eq_ref000:=(eq_ref00 ((x4 Xa) Xb)):((((x4 Xa) Xb) Xc)->(((x4 Xa) Xb) Xc))
% Found (eq_ref00 ((x4 Xa) Xb)) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x4 Xa) Xb)) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x4 Xa) Xb)) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x4 Xa) Xb)) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x4 Xa) Xb))) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x4 Xa) Xb))) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x4 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x4 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x0100:=(x010 x00):(((Y Xa) Xb) Xc)
% Found (x010 x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x01 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x01 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))):(((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) (fun (x:(a->(b->(c->Prop))))=> ((and ((and (cCL x)) (((eq (a->(b->(c->Prop)))) (cF x)) x))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))))))
% Found (eta_expansion_dep00 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found ((eta_expansion_dep0 (fun (x3:(a->(b->(c->Prop))))=> Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion_dep (a->(b->(c->Prop)))) (fun (x3:(a->(b->(c->Prop))))=> Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion_dep (a->(b->(c->Prop)))) (fun (x3:(a->(b->(c->Prop))))=> Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion_dep (a->(b->(c->Prop)))) (fun (x3:(a->(b->(c->Prop))))=> Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found eq_ref000:=(eq_ref00 ((x0 Xa) Xb)):((((x0 Xa) Xb) Xc)->(((x0 Xa) Xb) Xc))
% Found (eq_ref00 ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x0 Xa) Xb)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x0 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eq_ref000:=(eq_ref00 ((x2 Xa) Xb)):((((x2 Xa) Xb) Xc)->(((x2 Xa) Xb) Xc))
% Found (eq_ref00 ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found ((eq_ref0 Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (((eq_ref c) Xc) ((x2 Xa) Xb)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c)=> (((eq_ref c) Xc) ((x2 Xa) Xb))) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x4 Xa) Xb) Xc)
% Instantiate: x4:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x4 Xa) Xb) Xc)
% Instantiate: x4:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x4 Xa) Xb) Xc)
% Instantiate: x4:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x4 Xa) Xb) Xc)
% Instantiate: x4:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x000:(((x0 Xa) Xb) Xc)
% Instantiate: x0:=Y:(a->(b->(c->Prop)))
% Found x000 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> x000) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found x01:(((x2 Xa) Xb) Xc)
% Instantiate: x2:=Y:(a->(b->(c->Prop)))
% Found x01 as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> x01) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found eta_expansion000:=(eta_expansion00 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))):(((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) (fun (x:(a->(b->(c->Prop))))=> ((and ((and (cCL x)) (((eq (a->(b->(c->Prop)))) (cF x)) x))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))))))
% Found (eta_expansion00 (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found ((eta_expansion0 Prop) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion (a->(b->(c->Prop)))) Prop) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion (a->(b->(c->Prop)))) Prop) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found (((eta_expansion (a->(b->(c->Prop)))) Prop) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) as proof of (((eq ((a->(b->(c->Prop)))->Prop)) (fun (X:(a->(b->(c->Prop))))=> ((and ((and (cCL X)) (((eq (a->(b->(c->Prop)))) (cF X)) X))) (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((X Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))))) b0)
% Found x0000000:=(x000000 x00):(((Y Xa) Xb) Xc)
% Found (x000000 x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x00000 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x0000 Y0) x001) x1)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x001:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x000 Y0) x001) x2)) Y0) x001) x1)) Y) x00)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found x0100:=(x010 x00):(((Y Xa) Xb) Xc)
% Found (x010 x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x01 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x01 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x4 Xa) Xb) Xc))=> ((x01 Y) x00)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x4 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found x010000:=(x01000 x00):(((Y Xa) Xb) Xc)
% Found (x01000 x00) as proof of (((Y Xa) Xb) Xc)
% Found ((x0100 Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x010 Y0) x000) x3)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (forall (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (forall (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x01:(((x2 Xa) Xb) Xc))=> (((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> ((((fun (Y0:(a->(b->(c->Prop)))) (x000:((and (cCL Y0)) (((eq (a->(b->(c->Prop)))) (cF Y0)) Y0)))=> (((x01 Y0) x000) x4)) Y0) x000) x3)) Y) x00)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x2 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))
% Found x3 as proof of (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa0:a) (Xb0:b) (Xc0:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa0) Xb0) Xc0)))))))
% Found x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))
% Found x4 as proof of (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))
% Found x1:((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))
% Found x1 as proof of ((and (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa0:a) (Xb0:b) (Xc0:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa0) Xb0) Xc0)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))
% Found x2:(forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa:a) (Xb:b) (Xc:c), ((((R Xa) Xb) Xc)->(((S Xa) Xb) Xc))))->(forall (Xa:a) (Xb:b) (Xc:c), (((((cF R) Xa) Xb) Xc)->((((cF S) Xa) Xb) Xc)))))
% Found x2 as proof of (forall (R:(a->(b->(c->Prop)))) (S:(a->(b->(c->Prop)))), (((and ((and (cCL R)) (cCL S))) (forall (Xa0:a) (Xb0:b) (Xc0:c), ((((R Xa0) Xb0) Xc0)->(((S Xa0) Xb0) Xc0))))->(forall (Xa0:a) (Xb0:b) (Xc0:c), (((((cF R) Xa0) Xb0) Xc0)->((((cF S) Xa0) Xb0) Xc0)))))
% Found x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))
% Found x00 as proof of ((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))
% Found (((((x0000 x00) x1) x4) x2) x3) as proof of (((Y Xa) Xb) Xc)
% Found ((((((x000 Y) x00) x1) x4) x2) x3) as proof of (((Y Xa) Xb) Xc)
% Found ((((((x000 Y) x00) x1) x4) x2) x3) as proof of (((Y Xa) Xb) Xc)
% Found (fun (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (((Y Xa) Xb) Xc)
% Found (fun (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))
% Found (fun (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (forall (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (forall (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc))))
% Found (fun (Y:(a->(b->(c->Prop)))) (x00:((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))) (Xa:a) (Xb:b) (Xc:c) (x000:(((x0 Xa) Xb) Xc))=> ((((((x000 Y) x00) x1) x4) x2) x3)) as proof of (forall (Y:(a->(b->(c->Prop)))), (((and (cCL Y)) (((eq (a->(b->(c->Prop)))) (cF Y)) Y))->(forall (Xa:a) (Xb:b) (Xc:c), ((((x0 Xa) Xb) Xc)->(((Y Xa) Xb) Xc)))))
% Found x6:(cCL Xx)
% Found (fun (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of (cCL Xx)
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx))
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx)))
% Found (and_rect20 (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found ((and_rect2 (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (fun (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (cCL Xx)
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx))
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (forall (Xx:(a->(b->(c->Prop)))), (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx)))
% Found (x20 (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x4)
% Found ((x2 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x4)
% Found ((x2 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x4)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (cF x0)):(((eq (a->(b->(c->Prop)))) (cF x0)) (fun (x:a)=> ((cF x0) x)))
% Found (eta_expansion_dep00 (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found ((eta_expansion_dep0 (fun (x2:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x2:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x2:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x2:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->(b->(c->Prop)))) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eta_expansion0 (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found x6:(cCL Xx)
% Found (fun (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of (cCL Xx)
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx))
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx)))
% Found (and_rect20 (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found ((and_rect2 (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (fun (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (cCL Xx)
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx))
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (forall (Xx:(a->(b->(c->Prop)))), (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx)))
% Found (x30 (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x0)
% Found ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x0)
% Found ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x0)
% Found x6:(cCL Xx)
% Found (fun (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of (cCL Xx)
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx))
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx)))
% Found (and_rect20 (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found ((and_rect2 (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (fun (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (cCL Xx)
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx))
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (forall (Xx:(a->(b->(c->Prop)))), (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx)))
% Found (x30 (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x2)
% Found ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x2)
% Found ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x2)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->(c->Prop)))) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found eta_expansion000:=(eta_expansion00 (cF x0)):(((eq (a->(b->(c->Prop)))) (cF x0)) (fun (x:a)=> ((cF x0) x)))
% Found (eta_expansion00 (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found ((eta_expansion0 (b->(c->Prop))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->(c->Prop)))) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x4)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x4)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x4)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x4)
% Found eta_expansion000:=(eta_expansion00 (cF x4)):(((eq (a->(b->(c->Prop)))) (cF x4)) (fun (x:a)=> ((cF x4) x)))
% Found (eta_expansion00 (cF x4)) as proof of (((eq (a->(b->(c->Prop)))) (cF x4)) b0)
% Found ((eta_expansion0 (b->(c->Prop))) (cF x4)) as proof of (((eq (a->(b->(c->Prop)))) (cF x4)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x4)) as proof of (((eq (a->(b->(c->Prop)))) (cF x4)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x4)) as proof of (((eq (a->(b->(c->Prop)))) (cF x4)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x4)) as proof of (((eq (a->(b->(c->Prop)))) (cF x4)) b0)
% Found eq_ref00:=(eq_ref0 (cF x2)):(((eq (a->(b->(c->Prop)))) (cF x2)) (cF x2))
% Found (eq_ref0 (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found ((eq_ref (a->(b->(c->Prop)))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found ((eq_ref (a->(b->(c->Prop)))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found ((eq_ref (a->(b->(c->Prop)))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->(b->(c->Prop)))) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found ((eta_expansion0 (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->(c->Prop)))) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x2)
% Found eta_expansion000:=(eta_expansion00 (cF x2)):(((eq (a->(b->(c->Prop)))) (cF x2)) (fun (x:a)=> ((cF x2) x)))
% Found (eta_expansion00 (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found ((eta_expansion0 (b->(c->Prop))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found (((eta_expansion a) (b->(c->Prop))) (cF x2)) as proof of (((eq (a->(b->(c->Prop)))) (cF x2)) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (cF x0)):(((eq (a->(b->(c->Prop)))) (cF x0)) (fun (x:a)=> ((cF x0) x)))
% Found (eta_expansion_dep00 (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found ((eta_expansion_dep0 (fun (x4:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x4:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x4:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found (((eta_expansion_dep a) (fun (x4:a)=> (b->(c->Prop)))) (cF x0)) as proof of (((eq (a->(b->(c->Prop)))) (cF x0)) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->(b->(c->Prop)))) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eta_expansion0 (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found (((eta_expansion a) (b->(c->Prop))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found x6:(cCL Xx)
% Found (fun (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of (cCL Xx)
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx))
% Found (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6) as proof of ((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->(cCL Xx)))
% Found (and_rect20 (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found ((and_rect2 (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)) as proof of (cCL Xx)
% Found (fun (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (cCL Xx)
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx))
% Found (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))) as proof of (forall (Xx:(a->(b->(c->Prop)))), (((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))->(cCL Xx)))
% Found (x30 (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x0)
% Found ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))) as proof of (cCL x0)
% Found (fun (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))))) as proof of (cCL x0)
% Found (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))))) as proof of ((forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))->(cCL x0))
% Found (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6))))) as proof of ((forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))->((forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))->(cCL x0)))
% Found (and_rect10 (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))))) as proof of (cCL x0)
% Found ((and_rect1 (cCL x0)) (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))))) as proof of (cCL x0)
% Found (((fun (P:Type) (x3:((forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))->((forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))->P)))=> (((((and_rect (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))) P) x3) x1)) (cCL x0)) (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))))) as proof of (cCL x0)
% Found (((fun (P:Type) (x3:((forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))->((forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))->P)))=> (((((and_rect (forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R))))) P) x3) x1)) (cCL x0)) (fun (x3:(forall (S:((a->(b->(c->Prop)))->Prop)), ((forall (Xx:(a->(b->(c->Prop)))), ((S Xx)->(cCL Xx)))->(cCL (fun (Xa:a) (Xb:b) (Xc:c)=> (forall (R:(a->(b->(c->Prop)))), ((S R)->(((R Xa) Xb) Xc)))))))) (x4:(forall (R:(a->(b->(c->Prop)))), ((cCL R)->(cCL (cF R)))))=> ((x3 (fun (x10:(a->(b->(c->Prop))))=> ((and (cCL x10)) (((eq (a->(b->(c->Prop)))) (cF x10)) x10)))) (fun (Xx:(a->(b->(c->Prop)))) (x5:((and (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)))=> (((fun (P:Type) (x6:((cCL Xx)->((((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)->P)))=> (((((and_rect (cCL Xx)) (((eq (a->(b->(c->Prop)))) (cF Xx)) Xx)) P) x6) x5)) (cCL Xx)) (fun (x6:(cCL Xx)) (x7:(((eq (a->(b->(c->Prop)))) (cF Xx)) Xx))=> x6)))))) as proof of (cCL x0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->(b->(c->Prop)))) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Prop)))) b0) x0)
% Found ((eq_ref (a->(b->(c->Prop)))) b0) as proof of (((eq (a->(b->(c->Pro
% EOF
%------------------------------------------------------------------------------