%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU691^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n179.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 13:32:50 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU691^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 11:12:51 CDT 2014
% % CPUTime  : 300.02 
% 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 0x20bd248>, <kernel.DependentProduct object at 0x20bd170>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x21182d8>, <kernel.Single object at 0x20bd7e8>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x20bd170>, <kernel.DependentProduct object at 0x20bd050>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x20bdc68>, <kernel.DependentProduct object at 0x20bdcb0>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x20bd7e8>, <kernel.DependentProduct object at 0x20bb908>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x20bd050>, <kernel.DependentProduct object at 0x20bba70>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x20bd4d0>, <kernel.DependentProduct object at 0x20bba70>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x20bdc68>, <kernel.DependentProduct object at 0x20bb4d0>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (<kernel.Constant object at 0x20bd200>, <kernel.DependentProduct object at 0x20bb6c8>) of role type named ex1_type
% Using role type
% Declaring ex1:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0x20bd200>, <kernel.DependentProduct object at 0x20bbb00>) of role type named breln_type
% Using role type
% Declaring breln:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) of role definition named breln
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))))
% Defined: breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))
% FOF formula (<kernel.Constant object at 0x20bd050>, <kernel.DependentProduct object at 0x20bb6c8>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) of role definition named func
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))))
% Defined: func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))
% FOF formula (<kernel.Constant object at 0x1ba8638>, <kernel.DependentProduct object at 0x20bb950>) of role type named ap_type
% Using role type
% Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType))))
% FOF formula (<kernel.Constant object at 0x20bba28>, <kernel.Sort object at 0x1babab8>) of role type named funcGraphProp1_type
% Using role type
% Declaring funcGraphProp1:Prop
% FOF formula (((eq Prop) funcGraphProp1) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))) of role definition named funcGraphProp1
% A new definition: (((eq Prop) funcGraphProp1) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))))
% Defined: funcGraphProp1:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))
% FOF formula (<kernel.Constant object at 0x20bb998>, <kernel.Sort object at 0x1babab8>) of role type named funcGraphProp2_type
% Using role type
% Declaring funcGraphProp2:Prop
% FOF formula (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) of role definition named funcGraphProp2
% A new definition: (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))
% Defined: funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))
% FOF formula (<kernel.Constant object at 0x20bbd88>, <kernel.Sort object at 0x1babab8>) of role type named eqbreln_type
% Using role type
% Declaring eqbreln:Prop
% FOF formula (((eq Prop) eqbreln) (forall (A:fofType) (B:fofType) (R:fofType), ((((breln A) B) R)->(forall (S:fofType), ((((breln A) B) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) S)->((in ((kpair Xx) Xy)) R))))))->(((eq fofType) R) S)))))))) of role definition named eqbreln
% A new definition: (((eq Prop) eqbreln) (forall (A:fofType) (B:fofType) (R:fofType), ((((breln A) B) R)->(forall (S:fofType), ((((breln A) B) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) S)->((in ((kpair Xx) Xy)) R))))))->(((eq fofType) R) S))))))))
% Defined: eqbreln:=(forall (A:fofType) (B:fofType) (R:fofType), ((((breln A) B) R)->(forall (S:fofType), ((((breln A) B) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) S)->((in ((kpair Xx) Xy)) R))))))->(((eq fofType) R) S)))))))
% FOF formula (funcGraphProp1->(funcGraphProp2->(eqbreln->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))))) of role conjecture named funcext
% Conjecture to prove = (funcGraphProp1->(funcGraphProp2->(eqbreln->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))))):Prop
% We need to prove ['(funcGraphProp1->(funcGraphProp2->(eqbreln->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)).
% Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))).
% Definition func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))):(fofType->(fofType->(fofType->Prop))).
% Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))).
% Definition funcGraphProp1:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))):Prop.
% Definition funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))):Prop.
% Definition eqbreln:=(forall (A:fofType) (B:fofType) (R:fofType), ((((breln A) B) R)->(forall (S:fofType), ((((breln A) B) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) S)->((in ((kpair Xx) Xy)) R))))))->(((eq fofType) R) S))))))):Prop.
% Trying to prove (funcGraphProp1->(funcGraphProp2->(eqbreln->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))))
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x7:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x5:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x7:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x7:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x7:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x9:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x9:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found x7:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x7:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found x5:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(P Xf)
% Instantiate: b:=Xf:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xf)
% Found (fun (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of (((breln A) B) Xf)
% Found (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of ((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->(((breln A) B) Xf))
% Found (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of ((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->(((breln A) B) Xf)))
% Found (and_rect10 (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found ((and_rect1 (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found (((fun (P:Type) (x7:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x7) x2)) (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found (((fun (P:Type) (x7:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x7) x2)) (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found x7:(((breln A) B) Xf)
% Found (fun (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of (((breln A) B) Xf)
% Found (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of ((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->(((breln A) B) Xf))
% Found (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7) as proof of ((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->(((breln A) B) Xf)))
% Found (and_rect10 (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found ((and_rect1 (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found (((fun (P:Type) (x7:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x7) x2)) (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found (((fun (P:Type) (x7:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x7) x2)) (((breln A) B) Xf)) (fun (x7:(((breln A) B) Xf)) (x8:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> x7)) as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found x5:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x5:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) b)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found eq_ref000:=(eq_ref00 (in ((kpair Xx) Xy))):(((in ((kpair Xx) Xy)) Xf)->((in ((kpair Xx) Xy)) Xf))
% Found (eq_ref00 (in ((kpair Xx) Xy))) as proof of (P Xf)
% Found ((eq_ref0 Xf) (in ((kpair Xx) Xy))) as proof of (P Xf)
% Found (((eq_ref fofType) Xf) (in ((kpair Xx) Xy))) as proof of (P Xf)
% Found (((eq_ref fofType) Xf) (in ((kpair Xx) Xy))) as proof of (P Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) b)
% Found eq_ref00:=(eq_ref0 Xg):(((eq fofType) Xg) Xg)
% Found (eq_ref0 Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found ((eq_ref fofType) Xg) as proof of (((eq fofType) Xg) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xf)
% Found x7:(((breln A) B) Xg)
% Found x7 as proof of (((breln A) B) Xg)
% Found x5:(((breln A) B) Xg)
% Found x5 as proof of (((breln A) B) Xg)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xf)
% Found x7 as proof of (((breln A) B) Xf)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x9:(P Xg)
% Instantiate: b:=Xg:fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref000:=(eq_ref00 P):((P Xg)->(P Xg))
% Found (eq_ref00 P) as proof of (P0 Xg)
% Found ((eq_ref0 Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found (((eq_ref fofType) Xg) P) as proof of (P0 Xg)
% Found x5:(((breln A) B) Xf)
% Found x5 as proof of (((breln A) B) Xf)
% Found x7:(((breln A) B) Xg)
% Fou
% EOF
%------------------------------------------------------------------------------