TSTP Solution File: SEV364^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV364^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n106.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 13:34:06 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV364^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.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 08:57:46 CDT 2014
% % CPUTime : 300.03
% 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 0x1d67950>, <kernel.Constant object at 0x1d67710>) of role type named g
% Using role type
% Declaring g:fofType
% FOF formula (<kernel.Constant object at 0x2124560>, <kernel.Single object at 0x1d67680>) of role type named f
% Using role type
% Declaring f:fofType
% FOF formula (<kernel.Constant object at 0x1d67ef0>, <kernel.Single object at 0x1d67a70>) of role type named z
% Using role type
% Declaring z:fofType
% FOF formula (<kernel.Constant object at 0x1d67950>, <kernel.DependentProduct object at 0x1d67518>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1d677a0>, <kernel.DependentProduct object at 0x2144200>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1d67a70>, <kernel.DependentProduct object at 0x2144908>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1d67518>, <kernel.DependentProduct object at 0x2144a70>) of role type named cGVB_COMPOSE
% Using role type
% Declaring cGVB_COMPOSE:(fofType->(fofType->fofType))
% FOF formula ((iff ((cGVB_IN z) ((cGVB_COMPOSE g) f))) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))) of role conjecture named cGVB_AX_COMPOSE
% Conjecture to prove = ((iff ((cGVB_IN z) ((cGVB_COMPOSE g) f))) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))):Prop
% We need to prove ['((iff ((cGVB_IN z) ((cGVB_COMPOSE g) f))) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))))']
% Parameter fofType:Type.
% Parameter g:fofType.
% Parameter f:fofType.
% Parameter z:fofType.
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_COMPOSE:(fofType->(fofType->fofType)).
% Trying to prove ((iff ((cGVB_IN z) ((cGVB_COMPOSE g) f))) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))):(((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found (eq_ref0 ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))):(((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found (eq_ref0 ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found (eq_ref0 (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found (eq_ref0 (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x) Xy)))) ((cGVB_IN ((cGVB_OP x) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x) Xy)))) ((cGVB_IN ((cGVB_OP x) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x) Xy)))) ((cGVB_IN ((cGVB_OP x) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x) Xy)))) ((cGVB_IN ((cGVB_OP x) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of b
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))
% Found iff_sym0:=(iff_sym ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))):(forall (B:Prop), (((iff ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))) B)->((iff B) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))))))
% Instantiate: b:=(forall (B:Prop), (((iff ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))) B)->((iff B) ((and (cGVB_M z)) ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))))))))):Prop
% Found iff_sym0 as proof of b
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M Xx)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP Xx) Xy)))) ((cGVB_IN ((cGVB_OP Xx) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g))))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M Xy))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) Xy)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) Xy)) g)))))) b)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of a
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x)) g))))))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x)) g))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_COMPOSE g) f)):(((eq fofType) ((cGVB_COMPOSE g) f)) ((cGVB_COMPOSE g) f))
% Found (eq_ref0 ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found ((eq_ref fofType) ((cGVB_COMPOSE g) f)) as proof of (((eq fofType) ((cGVB_COMPOSE g) f)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) f)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of a
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x)) g))))))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x1))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x1)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x1)) g)))))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and ((and (cGVB_M x0)) (cGVB_M x))) (cGVB_M Xw))) (((eq fofType) z) ((cGVB_OP x0) x)))) ((cGVB_IN ((cGVB_OP x0) Xw)) f))) ((cGVB_IN ((cGVB_OP Xw) x)) g))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_COMPOSE g) f))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq
% EOF
%------------------------------------------------------------------------------