TSTP Solution File: SEU947^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU947^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n102.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 13:33:25 EDT 2014
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU947^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n102.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 11:44:51 CDT 2014
% % CPUTime : 300.07
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1a96ef0>, <kernel.DependentProduct object at 0x1a96b00>) of role type named cFIXPOINT_type
% Using role type
% Declaring cFIXPOINT:((fofType->fofType)->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1588c68>, <kernel.DependentProduct object at 0x1a96f80>) of role type named cUNIQUE_FIXPOINT_type
% Using role type
% Declaring cUNIQUE_FIXPOINT:((fofType->fofType)->(fofType->Prop))
% FOF formula (((eq ((fofType->fofType)->(fofType->Prop))) cFIXPOINT) (fun (Xg:(fofType->fofType)) (Xx:fofType)=> (((eq fofType) (Xg Xx)) Xx))) of role definition named cFIXPOINT_def
% A new definition: (((eq ((fofType->fofType)->(fofType->Prop))) cFIXPOINT) (fun (Xg:(fofType->fofType)) (Xx:fofType)=> (((eq fofType) (Xg Xx)) Xx)))
% Defined: cFIXPOINT:=(fun (Xg:(fofType->fofType)) (Xx:fofType)=> (((eq fofType) (Xg Xx)) Xx))
% FOF formula (((eq ((fofType->fofType)->(fofType->Prop))) cUNIQUE_FIXPOINT) (fun (Xg:(fofType->fofType)) (Xx:fofType)=> ((and ((cFIXPOINT Xg) Xx)) (forall (Xz:fofType), (((cFIXPOINT Xg) Xz)->(((eq fofType) Xx) Xz)))))) of role definition named cUNIQUE_FIXPOINT_def
% A new definition: (((eq ((fofType->fofType)->(fofType->Prop))) cUNIQUE_FIXPOINT) (fun (Xg:(fofType->fofType)) (Xx:fofType)=> ((and ((cFIXPOINT Xg) Xx)) (forall (Xz:fofType), (((cFIXPOINT Xg) Xz)->(((eq fofType) Xx) Xz))))))
% Defined: cUNIQUE_FIXPOINT:=(fun (Xg:(fofType->fofType)) (Xx:fofType)=> ((and ((cFIXPOINT Xg) Xx)) (forall (Xz:fofType), (((cFIXPOINT Xg) Xz)->(((eq fofType) Xx) Xz)))))
% FOF formula (forall (Xf:(fofType->fofType)), (((ex (fofType->fofType)) (fun (Xg:(fofType->fofType))=> ((and (forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xf)) (forall (Xj:(fofType->fofType)), ((Xp Xj)->(Xp (fun (Xx:fofType)=> (Xf (Xj Xx)))))))->(Xp Xg)))) ((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT Xg) Xx))))))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))))) of role conjecture named cTHM15B_V2_pme
% Conjecture to prove = (forall (Xf:(fofType->fofType)), (((ex (fofType->fofType)) (fun (Xg:(fofType->fofType))=> ((and (forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xf)) (forall (Xj:(fofType->fofType)), ((Xp Xj)->(Xp (fun (Xx:fofType)=> (Xf (Xj Xx)))))))->(Xp Xg)))) ((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT Xg) Xx))))))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xf:(fofType->fofType)), (((ex (fofType->fofType)) (fun (Xg:(fofType->fofType))=> ((and (forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xf)) (forall (Xj:(fofType->fofType)), ((Xp Xj)->(Xp (fun (Xx:fofType)=> (Xf (Xj Xx)))))))->(Xp Xg)))) ((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT Xg) Xx))))))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))']
% Parameter fofType:Type.
% Definition cFIXPOINT:=(fun (Xg:(fofType->fofType)) (Xx:fofType)=> (((eq fofType) (Xg Xx)) Xx)):((fofType->fofType)->(fofType->Prop)).
% Definition cUNIQUE_FIXPOINT:=(fun (Xg:(fofType->fofType)) (Xx:fofType)=> ((and ((cFIXPOINT Xg) Xx)) (forall (Xz:fofType), (((cFIXPOINT Xg) Xz)->(((eq fofType) Xx) Xz))))):((fofType->fofType)->(fofType->Prop)).
% Trying to prove (forall (Xf:(fofType->fofType)), (((ex (fofType->fofType)) (fun (Xg:(fofType->fofType))=> ((and (forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xf)) (forall (Xj:(fofType->fofType)), ((Xp Xj)->(Xp (fun (Xx:fofType)=> (Xf (Xj Xx)))))))->(Xp Xg)))) ((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT Xg) Xx))))))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))
% Found x3:((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)))
% Instantiate: b:=(fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)):(fofType->Prop)
% Found x3 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))
% Found (eq_ref0 (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))) b)
% Found x3:((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)))
% Instantiate: f:=(fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)):(fofType->Prop)
% Found x3 as proof of (P f)
% Found x3:((ex fofType) (fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)))
% Instantiate: f:=(fun (Xx:fofType)=> ((cUNIQUE_FIXPOINT x0) Xx)):(fofType->Prop)
% Found x3 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((cFIXPOINT Xf) x)))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((cFIXPOINT Xf) x)))
% Found x3:((ex fofType) ((unique fofType) (cFIXPOINT x0)))
% Instantiate: b:=((unique fofType) (cFIXPOINT x0)):(fofType->Prop)
% Found x3 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cFIXPOINT Xf)):(((eq (fofType->Prop)) (cFIXPOINT Xf)) (cFIXPOINT Xf))
% Found (eq_ref0 (cFIXPOINT Xf)) as proof of (((eq (fofType->Prop)) (cFIXPOINT Xf)) b)
% Found ((eq_ref (fofType->Prop)) (cFIXPOINT Xf)) as proof of (((eq (fofType->Prop)) (cFIXPOINT Xf)) b)
% Found ((eq_ref (fofType->Prop)) (cFIXPOINT Xf)) as proof of (((eq (fofType->Prop)) (cFIXPOINT Xf)) b)
% Found ((eq_ref (fofType->Prop)) (cFIXPOINT Xf)) as proof of (((eq (fofType->Prop)) (cFIXPOINT Xf)) b)
% Found x3:((ex fofType) ((unique fofType) (cFIXPOINT x0)))
% Instantiate: f:=((unique fofType) (cFIXPOINT x0)):(fofType->Prop)
% Found x3 as proof of (P f)
% Found x3:((ex fofType) ((unique fofType) (cFIXPOINT x0)))
% Instantiate: f:=((unique fofType) (cFIXPOINT x0)):(fofType->Prop)
% Found x3 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((cFIXPOINT Xf) x)))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((cFIXPOINT Xf) x8))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((cFIXPOINT Xf) x)))
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found x6:((cFIXPOINT x0) x4)
% Instantiate: x8:=x4:fofType
% Found x6 as proof of ((cFIXPOINT x0) x8)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy))))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))->((ex fofType) (fun (Xy:fofType)=> ((cFIXPOINT Xf) Xy)))))) b)
% Found x7:((cFIXPOINT x0) x4)
% Instantiate: x6:=x4:fofType
% Found x7 as proof of ((cFIXPOINT x0) x6)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x4:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x0) x4)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x2) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x2) x0)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x2:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x1) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x4:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x4)
% Found x7:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x4)
% Instantiate: x6:=x4:fofType
% Found x8 as proof of ((cFIXPOINT x0) x6)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x2:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x0) x5)
% Instantiate: x4:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x0) x4)
% Found x8:((cFIXPOINT x1) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf)))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found x8:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x6:((cFIXPOINT x0) x4)
% Instantiate: x8:=x4:fofType
% Found x6 as proof of ((cFIXPOINT x0) x8)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf)))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))):(((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf)))))
% Found (eq_ref0 ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) as proof of (((eq Prop) ((fofType->fofType)->(((ex fofType) (cFIXPOINT Xf))->((ex fofType) (cFIXPOINT Xf))))) b)
% Found x6:((cFIXPOINT x0) x4)
% Instantiate: x8:=x4:fofType;b:=(x0 x4):fofType
% Found x6 as proof of (((eq fofType) b) x8)
% Found eq_ref00:=(eq_ref0 (Xf x8)):(((eq fofType) (Xf x8)) (Xf x8))
% Found (eq_ref0 (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found x7:((cFIXPOINT x0) x4)
% Instantiate: x6:=x4:fofType
% Found x7 as proof of ((cFIXPOINT x0) x6)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x4:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x0) x4)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x2) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x2) x0)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x2:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x1) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x4:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x4)
% Found x7:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType
% Found x7 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x4)
% Instantiate: x6:=x4:fofType
% Found x8 as proof of ((cFIXPOINT x0) x6)
% Found x8:((cFIXPOINT x0) x6)
% Instantiate: x2:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x0) x5)
% Instantiate: x4:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x0) x4)
% Found x8:((cFIXPOINT x1) x6)
% Instantiate: x0:=x6:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x8:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x0) x2)
% Found x8:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType
% Found x8 as proof of ((cFIXPOINT x1) x0)
% Found x7:((cFIXPOINT x0) x4)
% Instantiate: b:=(x0 x4):fofType;x6:=x4:fofType
% Found x7 as proof of (((eq fofType) b) x6)
% Found eq_ref00:=(eq_ref0 (Xf x6)):(((eq fofType) (Xf x6)) (Xf x6))
% Found (eq_ref0 (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: b:=(x0 x5):fofType;x4:=x5:fofType
% Found x7 as proof of (((eq fofType) b) x4)
% Found eq_ref00:=(eq_ref0 (Xf x4)):(((eq fofType) (Xf x4)) (Xf x4))
% Found (eq_ref0 (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType;b:=(x0 x5):fofType
% Found x7 as proof of (((eq fofType) b) x2)
% Found eq_ref00:=(eq_ref0 (Xf x2)):(((eq fofType) (Xf x2)) (Xf x2))
% Found (eq_ref0 (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found x7:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType;b:=(x1 x5):fofType
% Found x7 as proof of (((eq fofType) b) x0)
% Found eq_ref00:=(eq_ref0 (Xf x0)):(((eq fofType) (Xf x0)) (Xf x0))
% Found (eq_ref0 (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found x6:((cFIXPOINT x0) x4)
% Instantiate: x8:=x4:fofType;b:=(x0 x4):fofType
% Found x6 as proof of (((eq fofType) b) x8)
% Found eq_ref00:=(eq_ref0 (Xf x8)):(((eq fofType) (Xf x8)) (Xf x8))
% Found (eq_ref0 (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found ((eq_ref fofType) (Xf x8)) as proof of (((eq fofType) (Xf x8)) b)
% Found x7:((cFIXPOINT x0) x4)
% Instantiate: b:=(x0 x4):fofType;x6:=x4:fofType
% Found x7 as proof of (((eq fofType) b) x6)
% Found eq_ref00:=(eq_ref0 (Xf x6)):(((eq fofType) (Xf x6)) (Xf x6))
% Found (eq_ref0 (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found ((eq_ref fofType) (Xf x6)) as proof of (((eq fofType) (Xf x6)) b)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: b:=(x0 x5):fofType;x4:=x5:fofType
% Found x7 as proof of (((eq fofType) b) x4)
% Found eq_ref00:=(eq_ref0 (Xf x4)):(((eq fofType) (Xf x4)) (Xf x4))
% Found (eq_ref0 (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found ((eq_ref fofType) (Xf x4)) as proof of (((eq fofType) (Xf x4)) b)
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: x2:=x5:fofType;b:=(x0 x5):fofType
% Found x7 as proof of (((eq fofType) b) x2)
% Found eq_ref00:=(eq_ref0 (Xf x2)):(((eq fofType) (Xf x2)) (Xf x2))
% Found (eq_ref0 (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found ((eq_ref fofType) (Xf x2)) as proof of (((eq fofType) (Xf x2)) b)
% Found x7:((cFIXPOINT x1) x5)
% Instantiate: x0:=x5:fofType;b:=(x1 x5):fofType
% Found x7 as proof of (((eq fofType) b) x0)
% Found eq_ref00:=(eq_ref0 (Xf x0)):(((eq fofType) (Xf x0)) (Xf x0))
% Found (eq_ref0 (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found ((eq_ref fofType) (Xf x0)) as proof of (((eq fofType) (Xf x0)) b)
% Found x9:(P x8)
% Instantiate: x8:=x4:fofType
% Found x9 as proof of (P0 x4)
% Found x9:(P x6)
% Instantiate: x6:=x4:fofType
% Found x9 as proof of (P0 x4)
% Found x9:(P x4)
% Instantiate: x4:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found x9:(P x2)
% Instantiate: x2:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found x9:(P x0)
% Instantiate: x0:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found x9:(P x8)
% Instantiate: x8:=x4:fofType
% Found x9 as proof of (P0 x4)
% Found eq_ref000:=(eq_ref00 P):((P (Xf x8))->(P (Xf x8)))
% Found (eq_ref00 P) as proof of ((P (Xf x8))->(P (Xf x8)))
% Found ((eq_ref0 (Xf x8)) P) as proof of ((P (Xf x8))->(P (Xf x8)))
% Found (((eq_ref fofType) (Xf x8)) P) as proof of ((P (Xf x8))->(P (Xf x8)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x8)) P)) as proof of ((P (Xf x8))->(P (Xf x8)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x8)) P)) as proof of ((fofType->fofType)->((P (Xf x8))->(P (Xf x8))))
% Found x6:((cFIXPOINT x0) x4)
% Instantiate: x8:=(x0 x4):fofType;b:=x4:fofType
% Found x6 as proof of (((eq fofType) x8) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xf x8))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x8))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x8))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x8))
% Found x9:(P x6)
% Instantiate: x6:=x4:fofType
% Found x9 as proof of (P0 x4)
% Found eq_ref000:=(eq_ref00 P):((P (Xf x6))->(P (Xf x6)))
% Found (eq_ref00 P) as proof of ((P (Xf x6))->(P (Xf x6)))
% Found ((eq_ref0 (Xf x6)) P) as proof of ((P (Xf x6))->(P (Xf x6)))
% Found (((eq_ref fofType) (Xf x6)) P) as proof of ((P (Xf x6))->(P (Xf x6)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x6)) P)) as proof of ((P (Xf x6))->(P (Xf x6)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x6)) P)) as proof of ((fofType->fofType)->((P (Xf x6))->(P (Xf x6))))
% Found x9:(P x4)
% Instantiate: x4:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found eq_ref000:=(eq_ref00 P):((P (Xf x4))->(P (Xf x4)))
% Found (eq_ref00 P) as proof of ((P (Xf x4))->(P (Xf x4)))
% Found ((eq_ref0 (Xf x4)) P) as proof of ((P (Xf x4))->(P (Xf x4)))
% Found (((eq_ref fofType) (Xf x4)) P) as proof of ((P (Xf x4))->(P (Xf x4)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x4)) P)) as proof of ((P (Xf x4))->(P (Xf x4)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x4)) P)) as proof of ((fofType->fofType)->((P (Xf x4))->(P (Xf x4))))
% Found x9:(P x2)
% Instantiate: x2:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found eq_ref000:=(eq_ref00 P):((P (Xf x2))->(P (Xf x2)))
% Found (eq_ref00 P) as proof of ((P (Xf x2))->(P (Xf x2)))
% Found ((eq_ref0 (Xf x2)) P) as proof of ((P (Xf x2))->(P (Xf x2)))
% Found (((eq_ref fofType) (Xf x2)) P) as proof of ((P (Xf x2))->(P (Xf x2)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x2)) P)) as proof of ((P (Xf x2))->(P (Xf x2)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x2)) P)) as proof of ((fofType->fofType)->((P (Xf x2))->(P (Xf x2))))
% Found x9:(P x0)
% Instantiate: x0:=x5:fofType
% Found x9 as proof of (P0 x5)
% Found eq_ref000:=(eq_ref00 P):((P (Xf x0))->(P (Xf x0)))
% Found (eq_ref00 P) as proof of ((P (Xf x0))->(P (Xf x0)))
% Found ((eq_ref0 (Xf x0)) P) as proof of ((P (Xf x0))->(P (Xf x0)))
% Found (((eq_ref fofType) (Xf x0)) P) as proof of ((P (Xf x0))->(P (Xf x0)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x0)) P)) as proof of ((P (Xf x0))->(P (Xf x0)))
% Found (fun (Xj:(fofType->fofType))=> (((eq_ref fofType) (Xf x0)) P)) as proof of ((fofType->fofType)->((P (Xf x0))->(P (Xf x0))))
% Found x7:((cFIXPOINT x0) x4)
% Instantiate: b:=x4:fofType;x6:=(x0 x4):fofType
% Found x7 as proof of (((eq fofType) x6) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xf x6))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x6))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x6))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf x6))
% Found x7:((cFIXPOINT x0) x5)
% Instantiate: b:=x5:fofType;x4:=(x0 x5):fofType
% Found x7 as proof of (((eq fofType) x4) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xf x4))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf
% EOF
%------------------------------------------------------------------------------