TSTP Solution File: PUZ125^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ125^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n105.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 13:29:01 EDT 2014
% Result : Timeout 300.11s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : PUZ125^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 08:25:46 CDT 2014
% % CPUTime : 300.11
% 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 0x25d2ef0>, <kernel.Constant object at 0x25d2638>) of role type named c1_type
% Using role type
% Declaring c1:fofType
% FOF formula (<kernel.Constant object at 0x25d2a28>, <kernel.Single object at 0x25d29e0>) of role type named c2_type
% Using role type
% Declaring c2:fofType
% FOF formula (<kernel.Constant object at 0x25d2248>, <kernel.Single object at 0x25d20e0>) of role type named c3_type
% Using role type
% Declaring c3:fofType
% FOF formula (<kernel.Constant object at 0x25d2ef0>, <kernel.Single object at 0x25d2440>) of role type named c4_type
% Using role type
% Declaring c4:fofType
% FOF formula (<kernel.Constant object at 0x25d2a28>, <kernel.DependentProduct object at 0x2578f80>) of role type named g_type
% Using role type
% Declaring g:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x25d2ef0>, <kernel.DependentProduct object at 0x2578b48>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x25d2a28>, <kernel.DependentProduct object at 0x2578b48>) of role type named cCKB6_BLACK_type
% Using role type
% Declaring cCKB6_BLACK:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x25d2440>, <kernel.DependentProduct object at 0x2578e18>) of role type named cCKB6_H_type
% Using role type
% Declaring cCKB6_H:(fofType->(fofType->(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 (forall (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType), (((((cCKB6_H Xx) Xy) Xu) Xv)->((or ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) (((eq fofType) ((g Xu) Xv)) c4)))) of role conjecture named cCKB6_L30000
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType), (((((cCKB6_H Xx) Xy) Xu) Xv)->((or ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) (((eq fofType) ((g Xu) Xv)) c4)))):Prop
% We need to prove ['(forall (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType), (((((cCKB6_H Xx) Xy) Xu) Xv)->((or ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) (((eq fofType) ((g Xu) Xv)) c4))))']
% 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)))).
% Trying to prove (forall (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType), (((((cCKB6_H Xx) Xy) Xu) Xv)->((or ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) (((eq fofType) ((g Xu) Xv)) c4))))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 c4):(((eq fofType) c4) c4)
% Found (eq_ref0 c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found x00:(P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P ((g Xu) Xv))
% Found (fun (x00:(P ((g Xu) Xv)))=> x00) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c2)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 (((eq fofType) ((g Xu) Xv)) c4)):(((eq Prop) (((eq fofType) ((g Xu) Xv)) c4)) (((eq fofType) ((g Xu) Xv)) c4))
% Found (eq_ref0 (((eq fofType) ((g Xu) Xv)) c4)) as proof of (((eq Prop) (((eq fofType) ((g Xu) Xv)) c4)) b)
% Found ((eq_ref Prop) (((eq fofType) ((g Xu) Xv)) c4)) as proof of (((eq Prop) (((eq fofType) ((g Xu) Xv)) c4)) b)
% Found ((eq_ref Prop) (((eq fofType) ((g Xu) Xv)) c4)) as proof of (((eq Prop) (((eq fofType) ((g Xu) Xv)) c4)) b)
% Found ((eq_ref Prop) (((eq fofType) ((g Xu) Xv)) c4)) as proof of (((eq Prop) (((eq fofType) ((g Xu) Xv)) c4)) b)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 c4):(((eq fofType) c4) c4)
% Found (eq_ref0 c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 c4):(((eq fofType) c4) c4)
% Found (eq_ref0 c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found eq_ref00:=(eq_ref0 c3):(((eq fofType) c3) c3)
% Found (eq_ref0 c3) as proof of (((eq fofType) c3) b)
% Found ((eq_ref fofType) c3) as proof of (((eq fofType) c3) b)
% Found ((eq_ref fofType) c3) as proof of (((eq fofType) c3) b)
% Found ((eq_ref fofType) c3) as proof of (((eq fofType) c3) b)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c3)
% Found eq_ref00:=(eq_ref0 ((g Xu) Xv)):(((eq fofType) ((g Xu) Xv)) ((g Xu) Xv))
% Found (eq_ref0 ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found ((eq_ref fofType) ((g Xu) Xv)) as proof of (((eq fofType) ((g Xu) Xv)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c4)
% Found eq_ref00:=(eq_ref0 c4):(((eq fofType) c4) c4)
% Found (eq_ref0 c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found ((eq_ref fofType) c4) as proof of (((eq fofType) c4) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((g Xu) Xv))
% Found or_intror00:=(or_intror0 ((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)))):(((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)))->((or ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))))
% Found (or_intror0 ((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)))) as proof of (((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)))->(P b))
% Found ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))) as proof of (((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)))->(P b))
% Found ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))) as proof of (((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)))->(P b))
% Found (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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))))) as proof of (((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)))->(P b))
% Found (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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))))) as proof of (((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)))->(P b)))
% Found (and_rect00 (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))))) as proof of (P b)
% Found ((and_rect0 (P b)) (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))))) as proof of (P b)
% Found (((fun (P0:Type) (x0:(((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)))->P0)))=> (((((and_rect ((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)))) P0) x0) x)) (P b)) (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))))) as proof of (P b)
% Found (((fun (P0:Type) (x0:(((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)))->P0)))=> (((((and_rect ((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)))) P0) x0) x)) (P b)) (fun (x0:((cCKB6_BLACK Xx) Xy))=> ((or_intror ((or ((or (((eq fofType) ((g Xu) Xv)) c1)) (((eq fofType) ((g Xu) Xv)) c2))) (((eq fofType) ((g Xu) Xv)) c3))) ((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)))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (P0 ((g Xu) Xv))
% Found ((eq_ref0 ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found (((eq_ref fofType) ((g Xu) Xv)) P) as proof of (P0 ((g Xu) Xv))
% Found eq_ref000:=(eq_ref00 P):((P ((g Xu) Xv))->(P ((g Xu) Xv)))
% Found (eq_ref00 P) as proof of (
% EOF
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