%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : PUZ101^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n104.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 13:28:59 EDT 2014

% Result   : Timeout 300.07s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : PUZ101^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n104.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 08:18:21 CDT 2014
% % CPUTime  : 300.07 
% 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 0x2679488>, <kernel.Constant object at 0x28f0d40>) of role type named c1_type
% Using role type
% Declaring c1:fofType
% FOF formula (<kernel.Constant object at 0x236ce18>, <kernel.Single object at 0x28f0f38>) of role type named c2_type
% Using role type
% Declaring c2:fofType
% FOF formula (<kernel.Constant object at 0x2679488>, <kernel.Single object at 0x28f0ef0>) of role type named c3_type
% Using role type
% Declaring c3:fofType
% FOF formula (<kernel.Constant object at 0x2679488>, <kernel.Single object at 0x28f0d40>) of role type named c4_type
% Using role type
% Declaring c4:fofType
% FOF formula (<kernel.Constant object at 0x28f0e18>, <kernel.DependentProduct object at 0x2698dd0>) of role type named g_type
% Using role type
% Declaring g:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x28f0e60>, <kernel.DependentProduct object at 0x2698d88>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x28f0cf8>, <kernel.DependentProduct object at 0x2698d88>) of role type named cCKB6_BLACK_type
% Using role type
% Declaring cCKB6_BLACK:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x28f0b90>, <kernel.DependentProduct object at 0x2698d88>) of role type named cCKB6_H_type
% Using role type
% Declaring cCKB6_H:(fofType->(fofType->(fofType->(fofType->Prop))))
% FOF formula (<kernel.Constant object at 0x28f0cf8>, <kernel.DependentProduct object at 0x2698dd0>) of role type named cCKB_XPL_type
% Using role type
% Declaring cCKB_XPL:((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% FOF formula (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))) of role definition named cCKB6_BLACK_def
% A new definition: (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))))
% Defined: cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))
% FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) cCKB6_H) (fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB6_BLACK Xx) Xy)) ((or ((or ((or ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c1)) (((eq fofType) Xu) (s (s (s Xx)))))) (((eq fofType) Xv) (s Xy)))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c2)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) (s (s Xy)))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c3)) (((eq fofType) Xu) (s Xx)))) (((eq fofType) Xv) (s Xy))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c4)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) Xy)))))) of role definition named cCKB6_H_def
% A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) cCKB6_H) (fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB6_BLACK Xx) Xy)) ((or ((or ((or ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c1)) (((eq fofType) Xu) (s (s (s Xx)))))) (((eq fofType) Xv) (s Xy)))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c2)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) (s (s Xy)))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c3)) (((eq fofType) Xu) (s Xx)))) (((eq fofType) Xv) (s Xy))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c4)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) Xy))))))
% Defined: cCKB6_H:=(fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB6_BLACK Xx) Xy)) ((or ((or ((or ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c1)) (((eq fofType) Xu) (s (s (s Xx)))))) (((eq fofType) Xv) (s Xy)))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c2)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) (s (s Xy)))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c3)) (((eq fofType) Xu) (s Xx)))) (((eq fofType) Xv) (s Xy))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c4)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) Xy)))))
% FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))) of role definition named cCKB_XPL_def
% A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))))
% Defined: cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))
% FOF formula ((((cCKB_XPL cCKB6_H) cCKB6_BLACK) c1) c1) of role conjecture named cCKB6_L40000
% Conjecture to prove = ((((cCKB_XPL cCKB6_H) cCKB6_BLACK) c1) c1):Prop
% We need to prove ['((((cCKB_XPL cCKB6_H) cCKB6_BLACK) c1) c1)']
% Parameter fofType:Type.
% Parameter c1:fofType.
% Parameter c2:fofType.
% Parameter c3:fofType.
% Parameter c4:fofType.
% Parameter g:(fofType->(fofType->fofType)).
% Parameter s:(fofType->fofType).
% Definition cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))):(fofType->(fofType->Prop)).
% Definition cCKB6_H:=(fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB6_BLACK Xx) Xy)) ((or ((or ((or ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c1)) (((eq fofType) Xu) (s (s (s Xx)))))) (((eq fofType) Xv) (s Xy)))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c2)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) (s (s Xy)))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c3)) (((eq fofType) Xu) (s Xx)))) (((eq fofType) Xv) (s Xy))))) ((and ((and (((eq fofType) ((g (s (s Xx))) (s Xy))) c4)) (((eq fofType) Xu) (s (s Xx))))) (((eq fofType) Xv) Xy))))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% Definition cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))):((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% Trying to prove ((((cCKB_XPL cCKB6_H) cCKB6_BLACK) c1) c1)
% Found x0:((Xw c1) c1)
% Found (fun (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((Xw c1) c1)
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1))
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of (((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1)))
% Found (and_rect00 (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found ((and_rect0 ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (((fun (P:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (fun (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((Xw c1) c1)
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw c1) c1))
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((cCKB6_BLACK c1) c1)
% Found eq_ref00:=(eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))):(((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))
% Found (eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))):(((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))
% Found (eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found x:((cCKB6_BLACK Xx) Xy)
% Instantiate: x0:=Xx:fofType;x1:=Xy:fofType
% Found x as proof of ((cCKB6_BLACK x0) x1)
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% 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) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))
% Found x0:((Xw c1) c1)
% Found (fun (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((Xw c1) c1)
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1))
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of (((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1)))
% Found (and_rect00 (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found ((and_rect0 ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (fun (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((Xw c1) c1)
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw c1) c1))
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((cCKB6_BLACK c1) c1)
% Found ((conj00 (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)))) iff_refl) as proof of ((and ((cCKB6_BLACK c1) c1)) b)
% Found (((conj0 b) (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)))) iff_refl) as proof of ((and ((cCKB6_BLACK c1) c1)) b)
% Found ((((conj ((cCKB6_BLACK c1) c1)) b) (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)))) iff_refl) as proof of ((and ((cCKB6_BLACK c1) c1)) b)
% Found ((((conj ((cCKB6_BLACK c1) c1)) b) (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)))) iff_refl) as proof of ((and ((cCKB6_BLACK c1) c1)) b)
% Found ((((conj ((cCKB6_BLACK c1) c1)) b) (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)))) iff_refl) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: a:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of ((ex fofType) a)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: a:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of ((ex fofType) a)
% Found x:((cCKB6_BLACK Xx) Xy)
% Instantiate: x0:=Xx:fofType;x1:=Xy:fofType
% Found x as proof of ((cCKB6_BLACK x0) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 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 x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found eq_ref00:=(eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% 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) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) (fun (x:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) x)) ((cCKB6_BLACK x0) x))) (((and (((eq fofType) x0) c1)) (((eq fofType) x) c1))->False))))
% Found (eta_expansion00 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found x:((cCKB6_BLACK Xx) Xy)
% Instantiate: x0:=Xx:fofType;x1:=Xy:fofType
% Found x as proof of ((cCKB6_BLACK x0) x1)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x:((cCKB6_BLACK Xx) Xy)
% Instantiate: x2:=Xy:fofType;x0:=Xx:fofType
% Found x as proof of ((cCKB6_BLACK x0) x2)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found conj10:=(conj1 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))):(((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))))
% Instantiate: b:=(((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))))):Prop
% Found conj10 as proof of b
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found x0:((Xw c1) c1)
% Found (fun (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((Xw c1) c1)
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of ((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1))
% Found (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0) as proof of (((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->((Xw c1) c1)))
% Found (and_rect00 (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found ((and_rect0 ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0)) as proof of ((Xw c1) c1)
% Found (fun (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((Xw c1) c1)
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw c1) c1))
% Found (fun (Xw:(fofType->(fofType->Prop))) (x:((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))))=> (((fun (P0:Type) (x0:(((Xw c1) c1)->((forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))->P0)))=> (((((and_rect ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk)))))) P0) x0) x)) ((Xw c1) c1)) (fun (x0:((Xw c1) c1)) (x1:(forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))=> x0))) as proof of ((cCKB6_BLACK c1) c1)
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))->((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found ((eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (ex fofType)) as proof of (P (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found eq_ref00:=(eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))):(((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))))))
% Found (eq_ref0 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))->((and ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))))) b)
% Found conj10:=(conj1 (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))):(((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))))
% Instantiate: b:=(((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) (forall (Xj:fofType) (Xk:fofType), (((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))->((and ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))))):Prop
% Found conj10 as proof of b
% Found x:((cCKB6_BLACK Xx) Xy)
% Instantiate: x2:=Xy:fofType;x1:=Xx:fofType
% Found x as proof of ((cCKB6_BLACK x1) x2)
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion_dep00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (((eq_trans000 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((((eq_trans00 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (((((eq_trans0 (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((((((eq_trans Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (((eq_trans000 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((((eq_trans00 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (((((eq_trans0 (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found ((((((eq_trans Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found x10:(P0 (f x0))
% Found (fun (x10:(P0 (f x0)))=> x10) as proof of (P0 (f x0))
% Found (fun (x10:(P0 (f x0)))=> x10) as proof of (P1 (f x0))
% Found x10:(P0 (f x0))
% Found (fun (x10:(P0 (f x0)))=> x10) as proof of (P0 (f x0))
% Found (fun (x10:(P0 (f x0)))=> x10) as proof of (P1 (f x0))
% Found conj00:=(conj0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))):(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))))
% Instantiate: b:=(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))):Prop
% Found conj00 as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% 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) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 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 x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: b:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found x5:(((and (((eq fofType) x0) c1)) (((eq fofType) x1) c1))->False)
% Found x5 as proof of (((and (((eq fofType) x0) c1)) (((eq fofType) x1) c1))->False)
% Found x5:(((and (((eq fofType) x0) c1)) (((eq fofType) x1) c1))->False)
% Found x5 as proof of (((and (((eq fofType) x0) c1)) (((eq fofType) x1) c1))->False)
% Found conj00:=(conj0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))):(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))))
% Instantiate: b:=(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))):Prop
% Found conj00 as proof of b
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found conj00:=(conj0 (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))):(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))))))
% Instantiate: b:=(((cCKB6_BLACK c1) c1)->((forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))->((and ((cCKB6_BLACK c1) c1)) (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xx) Xy) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))))))):Prop
% Found conj00 as proof of b
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) c1)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) c1)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) c1)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) c1)
% Found eta_expansion000:=(eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x) Xv)) ((cCKB6_BLACK x) Xv))) (((and (((eq fofType) x) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eta_expansion00 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found (eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))) b)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Instantiate: f:=(fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))):(fofType->Prop)
% Found x1 as proof of (P 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 (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H c1) c1) x1) Xv)) ((cCKB6_BLACK x1) Xv))) (((and (((eq fofType) x1) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x3:((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Instantiate: a:=(fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))):(fofType->Prop)
% Found x3 as proof of ((ex fofType) a)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s (s Xj))) Xk) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) Xu) Xv)) ((cCKB6_BLACK Xu) Xv))) (((and (((eq fofType) Xu) c1)) (((eq fofType) Xv) c1))->False))))))
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H Xj) Xk) x2) Xv)) ((cCKB6_BLACK x2) Xv))) (((and (((eq fofType) x2) c1)) (((eq fofType) Xv) c1))->False)))) b)
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))):(((eq Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False)))))
% Found (eq_ref0 ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) as proof of (((eq Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((cCKB6_H (s Xj)) (s Xk)) x0) Xv)) ((cCKB6_BLACK x0) Xv))) (((and (((eq fofType) x0) c1)) (((eq fofType) Xv) c1))->False))))) as proof of (((e
% EOF
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