TSTP Solution File: PUZ097^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ097^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n120.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 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:22:30 EDT 2015
% Result : Unknown 238.78s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.02 % Problem : PUZ097^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.01/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/1.07 % Computer : n120.star.cs.uiowa.edu
% 0.02/1.07 % Model : x86_64 x86_64
% 0.02/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.07 % Memory : 32286.75MB
% 0.02/1.07 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.02/1.07 % CPULimit : 300
% 0.02/1.07 % DateTime : Thu Apr 16 11:44:57 CDT 2015
% 0.02/1.07 % CPUTime :
% 0.02/1.08 Python 2.7.5
% 0.05/1.41 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2654638>, <kernel.Constant object at 0x2601098>) of role type named c1_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring c1:fofType
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x265d440>, <kernel.Single object at 0x2654638>) of role type named c2_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring c2:fofType
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2654758>, <kernel.Single object at 0x2601098>) of role type named c3_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring c3:fofType
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2654638>, <kernel.Single object at 0x2601fc8>) of role type named c4_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring c4:fofType
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2654638>, <kernel.DependentProduct object at 0x26017e8>) of role type named g_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring g:(fofType->(fofType->fofType))
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2601998>, <kernel.DependentProduct object at 0x26012d8>) of role type named s_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring s:(fofType->fofType)
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2601128>, <kernel.DependentProduct object at 0x2601638>) of role type named cCKB_BLACK_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring cCKB_BLACK:(fofType->(fofType->Prop))
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2601b48>, <kernel.DependentProduct object at 0x2601ab8>) of role type named cCKB_EVEN_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring cCKB_EVEN:(fofType->Prop)
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x26017e8>, <kernel.DependentProduct object at 0x265bdd0>) of role type named cCKB_H_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring cCKB_H:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2601758>, <kernel.DependentProduct object at 0x265b710>) of role type named cCKB_INJ_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring cCKB_INJ:((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)
% 0.05/1.41 FOF formula (<kernel.Constant object at 0x2601ab8>, <kernel.DependentProduct object at 0x265bc68>) of role type named cCKB_ODD_type
% 0.05/1.41 Using role type
% 0.05/1.41 Declaring cCKB_ODD:(fofType->Prop)
% 0.05/1.41 FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))) of role definition named cCKB_INJ_def
% 0.05/1.41 A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))))
% 0.05/1.41 Defined: cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))
% 0.05/1.41 FOF formula (((eq (fofType->Prop)) cCKB_EVEN) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1))))))))))) of role definition named cCKB_EVEN_def
% 0.05/1.41 A new definition: (((eq (fofType->Prop)) cCKB_EVEN) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1)))))))))))
% 0.05/1.41 Defined: cCKB_EVEN:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1))))))))))
% 0.05/1.41 FOF formula (((eq (fofType->Prop)) cCKB_ODD) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1)))))))))) of role definition named cCKB_ODD_def
% 0.05/1.43 A new definition: (((eq (fofType->Prop)) cCKB_ODD) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1))))))))))
% 0.05/1.43 Defined: cCKB_ODD:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1)))))))))
% 0.05/1.43 FOF formula (((eq (fofType->(fofType->Prop))) cCKB_BLACK) (fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv))))) of role definition named cCKB_BLACK_def
% 0.05/1.43 A new definition: (((eq (fofType->(fofType->Prop))) cCKB_BLACK) (fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv)))))
% 0.05/1.43 Defined: cCKB_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv))))
% 0.05/1.43 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) cCKB_H) (fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB_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 cCKB_H_def
% 0.05/1.43 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) cCKB_H) (fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB_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))))))
% 0.05/1.43 Defined: cCKB_H:=(fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB_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)))))
% 0.05/1.43 FOF formula (cCKB_INJ cCKB_H) of role conjecture named cL2500
% 0.05/1.43 Conjecture to prove = (cCKB_INJ cCKB_H):Prop
% 0.05/1.43 We need to prove ['(cCKB_INJ cCKB_H)']
% 0.05/1.43 Parameter fofType:Type.
% 0.05/1.43 Parameter c1:fofType.
% 0.05/1.43 Parameter c2:fofType.
% 0.05/1.43 Parameter c3:fofType.
% 0.05/1.43 Parameter c4:fofType.
% 0.05/1.43 Parameter g:(fofType->(fofType->fofType)).
% 0.05/1.43 Parameter s:(fofType->fofType).
% 0.05/1.43 Definition cCKB_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv)))):(fofType->(fofType->Prop)).
% 0.05/1.43 Definition cCKB_EVEN:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1)))))))))):(fofType->Prop).
% 0.05/1.43 Definition cCKB_H:=(fun (Xx:fofType) (Xy:fofType) (Xu:fofType) (Xv:fofType)=> ((and ((cCKB_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)))).
% 94.43/95.53 Definition cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))):((fofType->(fofType->(fofType->(fofType->Prop))))->Prop).
% 94.43/95.53 Definition cCKB_ODD:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1))))))))):(fofType->Prop).
% 94.43/95.53 Trying to prove (cCKB_INJ cCKB_H)
% 94.43/95.53 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 94.43/95.53 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 94.43/95.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 94.43/95.53 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 94.43/95.53 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 94.43/95.53 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 94.43/95.53 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 94.43/95.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 94.43/95.53 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 94.43/95.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 94.43/95.53 Found x20:(P Xy1)
% 94.43/95.53 Found (fun (x20:(P Xy1))=> x20) as proof of (P Xy1)
% 94.43/95.53 Found (fun (x20:(P Xy1))=> x20) as proof of (P0 Xy1)
% 94.43/95.53 Found x20:(P Xx1)
% 94.43/95.53 Found (fun (x20:(P Xx1))=> x20) as proof of (P Xx1)
% 94.43/95.53 Found (fun (x20:(P Xx1))=> x20) as proof of (P0 Xx1)
% 94.43/95.53 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 94.43/95.53 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 94.43/95.53 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 94.43/95.53 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 94.43/95.53 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 94.43/95.53 Found eq_ref000:=(eq_ref00 P):((P Xx1)->(P Xx1))
% 94.43/95.53 Found (eq_ref00 P) as proof of (P0 Xx1)
% 94.43/95.53 Found ((eq_ref0 Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found eq_ref000:=(eq_ref00 P):((P Xy1)->(P Xy1))
% 94.43/95.53 Found (eq_ref00 P) as proof of (P0 Xy1)
% 94.43/95.53 Found ((eq_ref0 Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 Found eq_ref000:=(eq_ref00 P):((P Xx1)->(P Xx1))
% 94.43/95.53 Found (eq_ref00 P) as proof of (P0 Xx1)
% 94.43/95.53 Found ((eq_ref0 Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 94.43/95.53 Found eq_ref000:=(eq_ref00 P):((P Xy1)->(P Xy1))
% 94.43/95.53 Found (eq_ref00 P) as proof of (P0 Xy1)
% 94.43/95.53 Found ((eq_ref0 Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 94.43/95.53 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)))
% 94.43/95.53 Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 94.43/95.53 Found eq_sym as proof of b
% 94.43/95.53 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 191.47/192.55 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.47/192.55 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 191.47/192.55 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.47/192.55 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 191.47/192.55 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.47/192.55 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 191.47/192.55 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.47/192.55 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 191.47/192.55 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found eq_ref00:=(eq_ref0 (((eq fofType) Xy1) Xy2)):(((eq Prop) (((eq fofType) Xy1) Xy2)) (((eq fofType) Xy1) Xy2))
% 191.47/192.55 Found (eq_ref0 (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found ((eq_ref Prop) (((eq fofType) Xy1) Xy2)) as proof of (((eq Prop) (((eq fofType) Xy1) Xy2)) b)
% 191.47/192.55 Found eq_ref000:=(eq_ref00 P):((P Xy1)->(P Xy1))
% 191.47/192.55 Found (eq_ref00 P) as proof of (P0 Xy1)
% 191.47/192.55 Found ((eq_ref0 Xy1) P) as proof of (P0 Xy1)
% 191.47/192.55 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 191.47/192.55 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 191.47/192.55 Found eq_ref000:=(eq_ref00 P):((P Xx1)->(P Xx1))
% 191.47/192.55 Found (eq_ref00 P) as proof of (P0 Xx1)
% 191.47/192.55 Found ((eq_ref0 Xx1) P) as proof of (P0 Xx1)
% 191.47/192.55 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 191.47/192.55 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 191.47/192.55 Found eq_ref000:=(eq_ref00 P):((P Xy1)->(P Xy1))
% 191.47/192.55 Found (eq_ref00 P) as proof of (P0 Xy1)
% 191.47/192.55 Found ((eq_ref0 Xy1) P) as proof of (P0 Xy1)
% 191.47/192.55 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 191.47/192.55 Found (((eq_ref fofType) Xy1) P) as proof of (P0 Xy1)
% 238.78/239.88 Found eq_ref000:=(eq_ref00 P):((P Xx1)->(P Xx1))
% 238.78/239.88 Found (eq_ref00 P) as proof of (P0 Xx1)
% 238.78/239.88 Found ((eq_ref0 Xx1) P) as proof of (P0 Xx1)
% 238.78/239.88 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 238.78/239.88 Found (((eq_ref fofType) Xx1) P) as proof of (P0 Xx1)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.78/239.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx1)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xx2):(((eq fofType) Xx2) Xx2)
% 238.78/239.88 Found (eq_ref0 Xx2) as proof of (((eq fofType) Xx2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx2) as proof of (((eq fofType) Xx2) b)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xy2):(((eq fofType) Xy2) Xy2)
% 238.78/239.88 Found (eq_ref0 Xy2) as proof of (((eq fofType) Xy2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy2) as proof of (((eq fofType) Xy2) b)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.78/239.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy1)
% 238.78/239.88 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 238.78/239.88 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 238.78/239.88 Found iff_sym as proof of b
% 238.78/239.88 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 238.78/239.88 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 238.78/239.88 Found iff_sym as proof of b
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 238.78/239.88 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.78/239.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xy2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy2)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 238.78/239.88 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.78/239.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% 238.78/239.88 Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) b)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.78/239.88 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx2)
% 238.78/239.88 Found eq_ref00:=(eq_ref0 Xy1):(((eq fofType) Xy1) Xy1)
% 238.78/239.88 Found (eq_ref0 Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Found ((eq_ref fofType) Xy1) as proof of (((eq fofType) Xy1) b)
% 238.78/239.88 Fo
%------------------------------------------------------------------------------