%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV177^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n188.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 13:33:50 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV177^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.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 08:21:31 CDT 2014
% % CPUTime  : 300.09 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (forall (Xh:((fofType->Prop)->fofType)) (Xd:(fofType->Prop)), ((((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))->(Xd (Xh Xd)))) of role conjecture named cTHM144_pme
% Conjecture to prove = (forall (Xh:((fofType->Prop)->fofType)) (Xd:(fofType->Prop)), ((((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))->(Xd (Xh Xd)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xh:((fofType->Prop)->fofType)) (Xd:(fofType->Prop)), ((((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))->(Xd (Xh Xd))))']
% Parameter fofType:Type.
% Trying to prove (forall (Xh:((fofType->Prop)->fofType)) (Xd:(fofType->Prop)), ((((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))->(Xd (Xh Xd))))
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) Xd)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) Xd))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh Xd))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) Xd)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a00:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a00) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a00:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq (fofType->Prop)) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 a00):(((eq (fofType->Prop)) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found ((eq_ref (fofType->Prop)) a00) as proof of (((eq (fofType->Prop)) a00) a0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a1:=Xd:(fofType->Prop);a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 (Xh Xd)):(((eq fofType) (Xh Xd)) (Xh Xd))
% Found (eq_ref0 (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found ((eq_ref fofType) (Xh Xd)) as proof of (((eq fofType) (Xh Xd)) b1)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a1):(((eq (fofType->Prop)) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found ((eq_ref (fofType->Prop)) a1) as proof of (((eq (fofType->Prop)) a1) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) Xd)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 (Xh a0)):(((eq fofType) (Xh a0)) (Xh a0))
% Found (eq_ref0 (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found ((eq_ref fofType) (Xh a0)) as proof of (((eq fofType) (Xh a0)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop);a0:=Xd:(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a:=Xd:(fofType->Prop);a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found x:(((eq (fofType->Prop)) Xd) (fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))))
% Instantiate: a0:=(fun (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and (not (Xt (Xh Xt)))) (((eq fofType) Xz) (Xh Xt)))))):(fofType->Prop)
% Found x as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found (x0 ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((x (fun (x1:(fofType->Prop))=> (((eq (fofType->Prop)) x1) a))) ((eq_ref (fofType->Prop)) Xd)) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 Xd):(((eq (fofType->Prop)) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofType->Prop)) Xd) a)
% Found ((eq_ref (fofType->Prop)) Xd) as proof of (((eq (fofTyp
% EOF
%------------------------------------------------------------------------------