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cocATP---0.2.0.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU961^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.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 13:33:26 EDT 2014

% Result   : Theorem 17.91s
% Output   : Proof 17.91s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU961^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 11:46:31 CDT 2014
% % CPUTime  : 17.91 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->(forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))) of role conjecture named cTHM196C_pme
% Conjecture to prove = (((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->(forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->(forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))))']
% Parameter fofType:Type.
% Trying to prove (((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->(forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))))
% Found eta_expansion000:=(eta_expansion00 Xk):(((eq (fofType->fofType)) Xk) (fun (x:fofType)=> (Xk x)))
% Found (eta_expansion00 Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found ((eta_expansion0 fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))):(((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk))))))
% Found (eq_ref0 ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))):(((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))
% Found (eq_ref0 ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))):(((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) ((fofType->fofType)->((Xp Xk)->(Xp Xk))))
% Found (eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found x2:(Xp Xj)
% Instantiate: b:=Xj:(fofType->fofType)
% Found x2 as proof of (P b)
% Found eta_expansion000:=(eta_expansion00 Xk):(((eq (fofType->fofType)) Xk) (fun (x:fofType)=> (Xk x)))
% Found (eta_expansion00 Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found ((eta_expansion0 fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found (((eta_expansion fofType) fofType) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found x2:(Xp Xj)
% Instantiate: b:=Xj:(fofType->fofType)
% Found (fun (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of (P b)
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P b))
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P b)))
% Found (and_rect00 (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P b)
% Found ((and_rect0 (P b)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P b)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P b)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P b)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P b)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (Xk x)))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (Xk x2))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (Xk x)))
% Found x200:=(x20 (Xk Xx)):(((eq fofType) (Xf Xx)) (Xk Xx))
% Found (x20 (Xk Xx)) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found ((x2 (Xf Xx)) (Xk Xx)) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx))) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx))) as proof of (forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xk Xx)))
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))):(((eq Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))))
% Found (eq_ref0 ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))->((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))) b)
% Found x2:(Xp Xj)
% Instantiate: f:=Xj:(fofType->fofType)
% Found x2 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq fofType) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (Xk x)))
% Found x2:(Xp Xj)
% Instantiate: f:=Xj:(fofType->fofType)
% Found x2 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq fofType) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (((eq fofType) (f x4)) (Xk x4))
% Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (Xk x)))
% Found eq_ref00:=(eq_ref0 Xk):(((eq (fofType->fofType)) Xk) Xk)
% Found (eq_ref0 Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found ((eq_ref (fofType->fofType)) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found ((eq_ref (fofType->fofType)) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found ((eq_ref (fofType->fofType)) Xk) as proof of (((eq (fofType->fofType)) Xk) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))):(((eq Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))))
% Found (eq_ref0 ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))))) b)
% Found x2:(Xp Xj)
% Instantiate: f:=Xj:(fofType->fofType)
% Found (fun (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of (P f)
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P f))
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P f)))
% Found (and_rect00 (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found ((and_rect0 (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found x2:(Xp Xj)
% Instantiate: f:=Xj:(fofType->fofType)
% Found (fun (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of (P f)
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P f))
% Found (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2) as proof of ((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(P f)))
% Found (and_rect00 (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found ((and_rect0 (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found (((fun (P0:Type) (x2:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P0)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P0) x2) x1)) (P f)) (fun (x2:(Xp Xj)) (x3:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> x2)) as proof of (P f)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))):(((eq Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))))
% Found (eq_ref0 ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))->((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))):(((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk))))))
% Found (eq_ref0 ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) as proof of (((eq Prop) ((fofType->fofType)->((forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))->(forall (Xp0:((fofType->fofType)->Prop)), (((and (Xp0 Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp0 Xj_1)->(Xp0 (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp0 Xk)))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))):(((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) ((fofType->fofType)->((Xp Xk)->(Xp Xk))))
% Found (eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))):(((eq Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))))
% Found (eq_ref0 ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->(((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))):(((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) ((fofType->fofType)->((Xp Xk)->(Xp Xk))))
% Found (eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))):(((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))
% Found (eq_ref0 ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) as proof of (((eq Prop) ((fofType->fofType)->((((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))->(((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))):(((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) ((fofType->fofType)->((Xp Xk)->(Xp Xk))))
% Found (eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found eq_ref00:=(eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))):(((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) ((fofType->fofType)->((Xp Xk)->(Xp Xk))))
% Found (eq_ref0 ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found ((eq_ref Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) as proof of (((eq Prop) ((fofType->fofType)->((Xp Xk)->(Xp Xk)))) b)
% Found x4:(Xp Xj)
% Instantiate: Xf:=Xj:(fofType->fofType)
% Found x4 as proof of (P Xf)
% Found x200:=(x20 (Xk Xx)):(((eq fofType) (Xf Xx)) (Xk Xx))
% Found (x20 (Xk Xx)) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found ((x2 (Xf Xx)) (Xk Xx)) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx))) as proof of (((eq fofType) (Xf Xx)) (Xk Xx))
% Found (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx))) as proof of (forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xk Xx)))
% Found ((x3000 (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx)))) x4) as proof of (Xp Xk)
% Found ((x3000 (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx)))) x4) as proof of (Xp Xk)
% Found (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xk Xx))))=> ((x300 x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xf Xx)) (Xk Xx)))) x4) as proof of (Xp Xk)
% Found (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> (((x30 Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4) as proof of (Xp Xk)
% Found (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4) as proof of (Xp Xk)
% Found (fun (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)) as proof of (Xp Xk)
% Found (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)) as proof of ((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk))
% Found (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)) as proof of ((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->(Xp Xk)))
% Found (and_rect10 (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))) as proof of (Xp Xk)
% Found ((and_rect1 (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))) as proof of (Xp Xk)
% Found (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))) as proof of (Xp Xk)
% Found (fun (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))) as proof of (Xp Xk)
% Found (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))) as proof of ((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk))
% Found (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))) as proof of ((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(Xp Xk)))
% Found (and_rect00 (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))))) as proof of (Xp Xk)
% Found ((and_rect0 (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))))) as proof of (Xp Xk)
% Found (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))))) as proof of (Xp Xk)
% Found (fun (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (Xp Xk)
% Found (fun (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))
% Found (fun (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))
% Found (fun (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))
% Found (fun (Xj:(fofType->fofType)) (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (forall (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))
% Found (fun (x:((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))) (Xj:(fofType->fofType)) (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk)))))
% Found (fun (x:((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))) (Xj:(fofType->fofType)) (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4)))))) as proof of (((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->(forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))->(Xp Xk))))))
% Got proof (fun (x:((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))) (Xj:(fofType->fofType)) (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))))))
% Time elapsed = 17.446773s
% node=2625 cost=1185.000000 depth=27
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:((and (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))) (Xj:(fofType->fofType)) (Xk:(fofType->fofType)) (x0:(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_0:(fofType->fofType)), ((Xp Xj_0)->(Xp (fun (Xx:fofType)=> (Xj (Xj_0 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))) (Xp:((fofType->fofType)->Prop)) (x1:((and (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))))=> (((fun (P:Type) (x2:((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->P)))=> (((((and_rect (forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))) P) x2) x)) (Xp Xk)) (fun (x2:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (x3:(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))=> (((fun (P:Type) (x4:((Xp Xj)->((forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))->P)))=> (((((and_rect (Xp Xj)) (forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx))))))) P) x4) x1)) (Xp Xk)) (fun (x4:(Xp Xj)) (x5:(forall (Xj_1:(fofType->fofType)), ((Xp Xj_1)->(Xp (fun (Xx:fofType)=> (Xj (Xj_1 Xx)))))))=> (((fun (x6:(forall (Xx:fofType), (((eq fofType) (Xj Xx)) (Xk Xx))))=> ((((fun (Xf:(fofType->fofType))=> ((x3 Xf) Xk)) Xj) x6) Xp)) (fun (Xx:fofType)=> ((x2 (Xj Xx)) (Xk Xx)))) x4))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------