TSTP Solution File: SEU645^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU645^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n101.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 13:32:42 EDT 2014
% Result : Timeout 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU645^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n101.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 11:01:11 CDT 2014
% % CPUTime : 300.06
% 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 0x23d6e60>, <kernel.DependentProduct object at 0x215e440>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1fa5440>, <kernel.Single object at 0x23d6f38>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x1fa5440>, <kernel.DependentProduct object at 0x215e4d0>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x23d6f38>, <kernel.DependentProduct object at 0x215e5f0>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x23d6e60>, <kernel.DependentProduct object at 0x215e170>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x23d6f38>, <kernel.Sort object at 0x2238878>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0x1e6a050>, <kernel.DependentProduct object at 0x215e4d0>) of role type named iskpair_type
% Using role type
% Declaring iskpair:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) iskpair) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))))))) of role definition named iskpair
% A new definition: (((eq (fofType->Prop)) iskpair) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))))))))
% Defined: iskpair:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))))))
% FOF formula (<kernel.Constant object at 0x217dcf8>, <kernel.DependentProduct object at 0x215e440>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))) of role definition named kpair
% A new definition: (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))
% Defined: kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))
% FOF formula (<kernel.Constant object at 0x217d950>, <kernel.Sort object at 0x2238878>) of role type named kpairp_type
% Using role type
% Declaring kpairp:Prop
% FOF formula (((eq Prop) kpairp) (forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy)))) of role definition named kpairp
% A new definition: (((eq Prop) kpairp) (forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy))))
% Defined: kpairp:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x217d950>, <kernel.DependentProduct object at 0x215e320>) 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 0x217d830>, <kernel.Sort object at 0x2238878>) of role type named setukpairinjL1_type
% Using role type
% Declaring setukpairinjL1:Prop
% FOF formula (((eq Prop) setukpairinjL1) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))->(((eq fofType) Xx) Xz)))) of role definition named setukpairinjL1
% A new definition: (((eq Prop) setukpairinjL1) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))->(((eq fofType) Xx) Xz))))
% Defined: setukpairinjL1:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))->(((eq fofType) Xx) Xz)))
% FOF formula (<kernel.Constant object at 0x23df878>, <kernel.Sort object at 0x2238878>) of role type named kfstsingleton_type
% Using role type
% Declaring kfstsingleton:Prop
% FOF formula (((eq Prop) kfstsingleton) (forall (Xu:fofType), ((iskpair Xu)->(singleton ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu))))))) of role definition named kfstsingleton
% A new definition: (((eq Prop) kfstsingleton) (forall (Xu:fofType), ((iskpair Xu)->(singleton ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu)))))))
% Defined: kfstsingleton:=(forall (Xu:fofType), ((iskpair Xu)->(singleton ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu))))))
% FOF formula (<kernel.Constant object at 0x215e320>, <kernel.Sort object at 0x2238878>) of role type named theprop_type
% Using role type
% Declaring theprop:Prop
% FOF formula (((eq Prop) theprop) (forall (X:fofType), ((singleton X)->((in (setunion X)) X)))) of role definition named theprop
% A new definition: (((eq Prop) theprop) (forall (X:fofType), ((singleton X)->((in (setunion X)) X))))
% Defined: theprop:=(forall (X:fofType), ((singleton X)->((in (setunion X)) X)))
% FOF formula (<kernel.Constant object at 0x215e4d0>, <kernel.DependentProduct object at 0x217cb00>) of role type named kfst_type
% Using role type
% Declaring kfst:(fofType->fofType)
% FOF formula (((eq (fofType->fofType)) kfst) (fun (Xu:fofType)=> (setunion ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu)))))) of role definition named kfst
% A new definition: (((eq (fofType->fofType)) kfst) (fun (Xu:fofType)=> (setunion ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu))))))
% Defined: kfst:=(fun (Xu:fofType)=> (setunion ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu)))))
% FOF formula (dsetconstrER->(kpairp->(setukpairinjL1->(kfstsingleton->(theprop->(forall (Xx:fofType) (Xy:fofType), (((eq fofType) (kfst ((kpair Xx) Xy))) Xx))))))) of role conjecture named kfstpairEq
% Conjecture to prove = (dsetconstrER->(kpairp->(setukpairinjL1->(kfstsingleton->(theprop->(forall (Xx:fofType) (Xy:fofType), (((eq fofType) (kfst ((kpair Xx) Xy))) Xx))))))):Prop
% We need to prove ['(dsetconstrER->(kpairp->(setukpairinjL1->(kfstsingleton->(theprop->(forall (Xx:fofType) (Xy:fofType), (((eq fofType) (kfst ((kpair Xx) Xy))) Xx)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter setunion:(fofType->fofType).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Definition iskpair:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))))))):(fofType->Prop).
% Definition kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))):(fofType->(fofType->fofType)).
% Definition kpairp:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy))):Prop.
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition setukpairinjL1:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))->(((eq fofType) Xx) Xz))):Prop.
% Definition kfstsingleton:=(forall (Xu:fofType), ((iskpair Xu)->(singleton ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu)))))):Prop.
% Definition theprop:=(forall (X:fofType), ((singleton X)->((in (setunion X)) X))):Prop.
% Definition kfst:=(fun (Xu:fofType)=> (setunion ((dsetconstr (setunion Xu)) (fun (Xx:fofType)=> ((in ((setadjoin Xx) emptyset)) Xu))))):(fofType->fofType).
% Trying to prove (dsetconstrER->(kpairp->(setukpairinjL1->(kfstsingleton->(theprop->(forall (Xx:fofType) (Xy:fofType), (((eq fofType) (kfst ((kpair Xx) Xy))) Xx)))))))
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P (kfst ((kpair Xx) Xy)))
% Instantiate: b:=(kfst ((kpair Xx) Xy)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x40:(P b)
% Found (fun (x40:(P b))=> x40) as proof of (P b)
% Found (fun (x40:(P b))=> x40) as proof of (P0 b)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b0)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b0)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b0)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x4:(P (kfst ((kpair Xx) Xy)))
% Instantiate: b:=(kfst ((kpair Xx) Xy)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P (kfst ((kpair Xx) Xy)))
% Instantiate: Xx0:=(kfst ((kpair Xx) Xy)):fofType
% Found x4 as proof of (P0 Xx0)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P (kfst ((kpair Xx) Xy)))
% Instantiate: a:=(kfst ((kpair Xx) Xy)):fofType
% Found x4 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found x4:(P Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of (P0 Xx0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P1 Xx)
% Instantiate: b:=Xx:fofType
% Found x4 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x40:(P b)
% Found (fun (x40:(P b))=> x40) as proof of (P b)
% Found (fun (x40:(P b))=> x40) as proof of (P0 b)
% Found x40:(P b)
% Found (fun (x40:(P b))=> x40) as proof of (P b)
% Found (fun (x40:(P b))=> x40) as proof of (P0 b)
% Found x4:(P b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x50:(P1 Xx)
% Found (fun (x50:(P1 Xx))=> x50) as proof of (P1 Xx)
% Found (fun (x50:(P1 Xx))=> x50) as proof of (P2 Xx)
% Found x40:(P1 Xx)
% Found (fun (x40:(P1 Xx))=> x40) as proof of (P1 Xx)
% Found (fun (x40:(P1 Xx))=> x40) as proof of (P2 Xx)
% Found x4:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (kfst ((kpair Xx) Xy))):(((eq fofType) (kfst ((kpair Xx) Xy))) (kfst ((kpair Xx) Xy)))
% Found (eq_ref0 (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found ((eq_ref fofType) (kfst ((kpair Xx) Xy))) as proof of (((eq fofType) (kfst ((kpair Xx) Xy))) b)
% Found x4:(P Xx)
% Instantiate: a:=Xx:fofType
% Found x4 as proof of (P0 a)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x40:(P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P Xx)
% Found (fun (x40:(P Xx))=> x40) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (kfst ((kpair Xx) Xy)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_
% EOF
%------------------------------------------------------------------------------