TSTP Solution File: SEV300^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV300^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n106.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 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:27:25 EDT 2015
% Result : Timeout 288.01s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV300^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/1.07 % Computer : n106.star.cs.uiowa.edu
% 0.02/1.07 % Model : x86_64 x86_64
% 0.02/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.07 % Memory : 32286.75MB
% 0.02/1.07 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.02/1.07 % CPULimit : 300
% 0.02/1.07 % DateTime : Thu Apr 16 12:24:07 CDT 2015
% 0.02/1.07 % CPUTime :
% 0.02/1.09 Python 2.7.5
% 4.54/5.65 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 4.54/5.65 FOF formula (<kernel.Constant object at 0x8fea28>, <kernel.DependentProduct object at 0x8fecb0>) of role type named cONE_type
% 4.54/5.65 Using role type
% 4.54/5.65 Declaring cONE:((fofType->Prop)->Prop)
% 4.54/5.65 FOF formula (<kernel.Constant object at 0xd36ea8>, <kernel.DependentProduct object at 0x8fe6c8>) of role type named cSUCC_type
% 4.54/5.65 Using role type
% 4.54/5.65 Declaring cSUCC:(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))
% 4.54/5.65 FOF formula (<kernel.Constant object at 0x8fe9e0>, <kernel.DependentProduct object at 0x8fea28>) of role type named cZERO_type
% 4.54/5.65 Using role type
% 4.54/5.65 Declaring cZERO:((fofType->Prop)->Prop)
% 4.54/5.65 FOF formula (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))) of role definition named cZERO_def
% 4.54/5.65 A new definition: (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)))
% 4.54/5.65 Defined: cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))
% 4.54/5.65 FOF formula (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))) of role definition named cSUCC_def
% 4.54/5.65 A new definition: (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))))
% 4.54/5.65 Defined: cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))
% 4.54/5.65 FOF formula (((eq ((fofType->Prop)->Prop)) cONE) (cSUCC cZERO)) of role definition named cONE_def
% 4.54/5.65 A new definition: (((eq ((fofType->Prop)->Prop)) cONE) (cSUCC cZERO))
% 4.54/5.65 Defined: cONE:=(cSUCC cZERO)
% 4.54/5.65 FOF formula ((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(((eq ((fofType->Prop)->Prop)) cONE) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) Xx) Xy)) Xy))))))) of role conjecture named cX6101_EXT_pme
% 4.54/5.65 Conjecture to prove = ((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(((eq ((fofType->Prop)->Prop)) cONE) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) Xx) Xy)) Xy))))))):Prop
% 4.54/5.65 Parameter fofType_DUMMY:fofType.
% 4.54/5.65 We need to prove ['((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(((eq ((fofType->Prop)->Prop)) cONE) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) Xx) Xy)) Xy)))))))']
% 4.54/5.65 Parameter fofType:Type.
% 4.54/5.65 Definition cONE:=(cSUCC cZERO):((fofType->Prop)->Prop).
% 4.54/5.65 Definition cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))):(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)).
% 4.54/5.65 Definition cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)):((fofType->Prop)->Prop).
% 4.54/5.65 Trying to prove ((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg)))->(((eq ((fofType->Prop)->Prop)) cONE) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) Xx) Xy)) Xy)))))))
% 4.54/5.65 Found eq_ref000:=(eq_ref00 P):((P cONE)->(P cONE))
% 8.85/9.92 Found (eq_ref00 P) as proof of (P0 cONE)
% 8.85/9.92 Found ((eq_ref0 cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P cONE)->(P (fun (x:(fofType->Prop))=> (cONE x))))
% 8.85/9.92 Found (eta_expansion_dep000 P) as proof of (P0 cONE)
% 8.85/9.92 Found ((eta_expansion_dep00 cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found eq_ref000:=(eq_ref00 P):((P cONE)->(P cONE))
% 8.85/9.92 Found (eq_ref00 P) as proof of (P0 cONE)
% 8.85/9.92 Found ((eq_ref0 cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) cONE) P) as proof of (P0 cONE)
% 8.85/9.92 Found eta_expansion_dep000:=(eta_expansion_dep00 cONE):(((eq ((fofType->Prop)->Prop)) cONE) (fun (x:(fofType->Prop))=> (cONE x)))
% 8.85/9.92 Found (eta_expansion_dep00 cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 8.85/9.92 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 8.85/9.92 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 8.85/9.92 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 8.85/9.92 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 8.85/9.92 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 8.85/9.92 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 8.85/9.92 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 8.85/9.92 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 8.85/9.92 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 8.85/9.92 Found eq_ref000:=(eq_ref00 P):((P (cSUCC cZERO))->(P (cSUCC cZERO)))
% 8.85/9.92 Found (eq_ref00 P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found ((eq_ref0 (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found eq_ref000:=(eq_ref00 P):((P (cSUCC cZERO))->(P (cSUCC cZERO)))
% 8.85/9.92 Found (eq_ref00 P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found ((eq_ref0 (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found (((eq_ref ((fofType->Prop)->Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (cSUCC cZERO))->(P (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x))))
% 8.85/9.92 Found (eta_expansion_dep000 P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found ((eta_expansion_dep00 (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 8.85/9.92 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 18.34/19.47 Found eta_expansion000:=(eta_expansion00 (cSUCC cZERO)):(((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x)))
% 18.34/19.47 Found (eta_expansion00 (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 18.34/19.47 Found ((eta_expansion0 Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 18.34/19.47 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 18.34/19.47 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 18.34/19.47 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 18.34/19.47 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 18.34/19.47 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 18.34/19.47 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 18.34/19.47 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) cONE)
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) cONE)
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) cONE)
% 18.34/19.47 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) cONE)
% 18.34/19.47 Found eta_expansion000:=(eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 18.34/19.48 Found (eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 18.34/19.48 Found ((eta_expansion0 Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 18.34/19.48 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 18.34/19.48 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 18.34/19.48 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 20.85/21.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))->(P (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))))
% 20.85/21.96 Found (eta_expansion_dep000 P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((eta_expansion_dep00 (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))->(P (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))))
% 20.85/21.96 Found (eta_expansion000 P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((eta_expansion00 (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found (((eta_expansion0 Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((((eta_expansion (fofType->Prop)) Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found ((((eta_expansion (fofType->Prop)) Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 20.85/21.96 Found eq_ref000:=(eq_ref00 P):((P (cONE x0))->(P (cONE x0)))
% 20.85/21.96 Found (eq_ref00 P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found ((eq_ref0 (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found (((eq_ref Prop) (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found (((eq_ref Prop) (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found eq_ref000:=(eq_ref00 P):((P (cONE x0))->(P (cONE x0)))
% 25.44/26.53 Found (eq_ref00 P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found ((eq_ref0 (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found (((eq_ref Prop) (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found (((eq_ref Prop) (cONE x0)) P) as proof of (P0 (cONE x0))
% 25.44/26.53 Found eq_ref00:=(eq_ref0 (cONE x0)):(((eq Prop) (cONE x0)) (cONE x0))
% 25.44/26.53 Found (eq_ref0 (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 25.44/26.53 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found eq_ref00:=(eq_ref0 (cONE x0)):(((eq Prop) (cONE x0)) (cONE x0))
% 25.44/26.53 Found (eq_ref0 (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 25.44/26.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 25.44/26.53 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 25.44/26.53 Found eq_ref00:=(eq_ref0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 25.44/26.53 Found (eq_ref0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 25.44/26.53 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 25.44/26.53 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 25.44/26.53 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 28.85/29.96 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 28.85/29.96 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (cSUCC cZERO))
% 28.85/29.96 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (cSUCC cZERO))
% 28.85/29.96 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (cSUCC cZERO))
% 28.85/29.96 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (cSUCC cZERO))
% 28.85/29.96 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (cSUCC cZERO))
% 28.85/29.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy))))))->(P (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy)))))))
% 28.85/29.96 Found (eta_expansion_dep000 P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((eta_expansion_dep00 (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy))))))->(P (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy)))))))
% 28.85/29.96 Found (eta_expansion000 P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((eta_expansion00 (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found (((eta_expansion0 Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((((eta_expansion (fofType->Prop)) Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found ((((eta_expansion (fofType->Prop)) Prop) (fun (P1:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P1) ((eq fofType) Xy)))))) P) as proof of (P0 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 28.85/29.96 Found eq_ref000:=(eq_ref00 P):((P ((cSUCC cZERO) x0))->(P ((cSUCC cZERO) x0)))
% 28.85/29.96 Found (eq_ref00 P) as proof of (P0 ((cSUCC cZERO) x0))
% 28.85/29.96 Found ((eq_ref0 ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 28.85/29.96 Found (((eq_ref Prop) ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found (((eq_ref Prop) ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found eq_ref000:=(eq_ref00 P):((P ((cSUCC cZERO) x0))->(P ((cSUCC cZERO) x0)))
% 52.66/53.73 Found (eq_ref00 P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found ((eq_ref0 ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found (((eq_ref Prop) ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found (((eq_ref Prop) ((cSUCC cZERO) x0)) P) as proof of (P0 ((cSUCC cZERO) x0))
% 52.66/53.73 Found eq_ref00:=(eq_ref0 ((cSUCC cZERO) x0)):(((eq Prop) ((cSUCC cZERO) x0)) ((cSUCC cZERO) x0))
% 52.66/53.73 Found (eq_ref0 ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.66/53.73 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found eq_ref00:=(eq_ref0 ((cSUCC cZERO) x0)):(((eq Prop) ((cSUCC cZERO) x0)) ((cSUCC cZERO) x0))
% 52.66/53.73 Found (eq_ref0 ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 52.66/53.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.66/53.73 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 52.66/53.73 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 52.66/53.73 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 52.66/53.73 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 52.66/53.73 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 52.66/53.73 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 52.66/53.73 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 52.66/53.73 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.65/58.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.65/58.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 57.65/58.76 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 57.65/58.76 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 57.65/58.76 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 71.47/72.52 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.47/72.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 71.47/72.52 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 71.47/72.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.47/72.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cONE x0))
% 71.47/72.52 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 71.47/72.52 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 71.47/72.52 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 76.06/77.15 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.06/77.15 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.06/77.15 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 76.06/77.15 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 76.06/77.15 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 76.06/77.15 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 80.28/81.31 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.28/81.31 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 80.28/81.31 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) b)
% 80.28/81.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.28/81.31 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cSUCC cZERO) x0))
% 80.28/81.31 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 80.28/81.31 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 80.28/81.31 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 80.28/81.31 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 83.46/84.55 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 83.46/84.55 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 85.67/86.72 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 85.67/86.72 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 105.68/106.78 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 105.68/106.78 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 105.68/106.78 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (eq_ref00 P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 (P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found eq_ref000:=(eq_ref00 P):((P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))->(P ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))))
% 121.67/122.76 Found (eq_ref00 P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found ((eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found (((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))) P) as proof of (P0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 121.67/122.76 Found x0:(P cONE)
% 121.67/122.76 Instantiate: b:=cONE:((fofType->Prop)->Prop)
% 121.67/122.76 Found x0 as proof of (P0 b)
% 121.67/122.76 Found eta_expansion000:=(eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 131.57/132.64 Found (eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 131.57/132.64 Found ((eta_expansion0 Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 131.57/132.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 131.57/132.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 131.57/132.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 131.57/132.64 Found x0:(P cONE)
% 131.57/132.64 Instantiate: f:=cONE:((fofType->Prop)->Prop)
% 131.57/132.64 Found x0 as proof of (P0 f)
% 131.57/132.64 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 131.57/132.64 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 131.57/132.64 Found x0:(P cONE)
% 131.57/132.64 Instantiate: f:=cONE:((fofType->Prop)->Prop)
% 131.57/132.64 Found x0 as proof of (P0 f)
% 131.57/132.64 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 131.57/132.64 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 131.57/132.64 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 144.57/145.64 Found x0:(P (cSUCC cZERO))
% 144.57/145.64 Instantiate: b:=(cSUCC cZERO):((fofType->Prop)->Prop)
% 144.57/145.64 Found x0 as proof of (P0 b)
% 144.57/145.64 Found eta_expansion000:=(eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy))))))
% 144.57/145.64 Found (eta_expansion00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 144.57/145.64 Found ((eta_expansion0 Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 144.57/145.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 144.57/145.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 144.57/145.64 Found (((eta_expansion (fofType->Prop)) Prop) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 144.57/145.64 Found eq_ref00:=(eq_ref0 (cONE x0)):(((eq Prop) (cONE x0)) (cONE x0))
% 144.57/145.64 Found (eq_ref0 (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.57/145.64 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found eq_ref00:=(eq_ref0 (cONE x0)):(((eq Prop) (cONE x0)) (cONE x0))
% 144.57/145.64 Found (eq_ref0 (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found ((eq_ref Prop) (cONE x0)) as proof of (((eq Prop) (cONE x0)) b)
% 144.57/145.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.57/145.64 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 144.57/145.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 151.78/152.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 151.78/152.83 Found eta_expansion_dep000:=(eta_expansion_dep00 cONE):(((eq ((fofType->Prop)->Prop)) cONE) (fun (x:(fofType->Prop))=> (cONE x)))
% 151.78/152.83 Found (eta_expansion_dep00 cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 151.78/152.83 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found eta_expansion0000:=(eta_expansion000 P):((P cONE)->(P (fun (x:(fofType->Prop))=> (cONE x))))
% 151.78/152.83 Found (eta_expansion000 P) as proof of (P0 cONE)
% 151.78/152.83 Found ((eta_expansion00 cONE) P) as proof of (P0 cONE)
% 151.78/152.83 Found (((eta_expansion0 Prop) cONE) P) as proof of (P0 cONE)
% 151.78/152.83 Found ((((eta_expansion (fofType->Prop)) Prop) cONE) P) as proof of (P0 cONE)
% 151.78/152.83 Found ((((eta_expansion (fofType->Prop)) Prop) cONE) P) as proof of (P0 cONE)
% 151.78/152.83 Found eta_expansion000:=(eta_expansion00 cONE):(((eq ((fofType->Prop)->Prop)) cONE) (fun (x:(fofType->Prop))=> (cONE x)))
% 151.78/152.83 Found (eta_expansion00 cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found ((eta_expansion0 Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 151.78/152.83 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 151.78/152.83 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 151.78/152.83 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 177.09/178.12 Found x0:(P (cSUCC cZERO))
% 177.09/178.12 Instantiate: f:=(cSUCC cZERO):((fofType->Prop)->Prop)
% 177.09/178.12 Found x0 as proof of (P0 f)
% 177.09/178.12 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 177.09/178.12 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy))))))
% 177.09/178.12 Found x0:(P (cSUCC cZERO))
% 177.09/178.12 Instantiate: f:=(cSUCC cZERO):((fofType->Prop)->Prop)
% 177.09/178.12 Found x0 as proof of (P0 f)
% 177.09/178.12 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 177.09/178.12 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x1) ((eq fofType) Xy)))))
% 177.09/178.12 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy))))))
% 177.09/178.12 Found eta_expansion000:=(eta_expansion00 (cSUCC cZERO)):(((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x)))
% 177.09/178.12 Found (eta_expansion00 (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 177.09/178.12 Found ((eta_expansion0 Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 177.09/178.12 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 177.09/178.12 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 177.09/178.12 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 177.09/178.12 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found eta_expansion0000:=(eta_expansion000 P):((P (cSUCC cZERO))->(P (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x))))
% 190.68/191.79 Found (eta_expansion000 P) as proof of (P0 (cSUCC cZERO))
% 190.68/191.79 Found ((eta_expansion00 (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 190.68/191.79 Found (((eta_expansion0 Prop) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 190.68/191.79 Found ((((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 190.68/191.79 Found ((((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) P) as proof of (P0 (cSUCC cZERO))
% 190.68/191.79 Found eta_expansion000:=(eta_expansion00 (cSUCC cZERO)):(((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x)))
% 190.68/191.79 Found (eta_expansion00 (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 190.68/191.79 Found ((eta_expansion0 Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 190.68/191.79 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 190.68/191.79 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 190.68/191.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.68/191.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 190.68/191.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 190.68/191.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 190.68/191.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 190.68/191.79 Found eq_ref00:=(eq_ref0 ((cSUCC cZERO) x0)):(((eq Prop) ((cSUCC cZERO) x0)) ((cSUCC cZERO) x0))
% 190.68/191.79 Found (eq_ref0 ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found eq_ref00:=(eq_ref0 ((cSUCC cZERO) x0)):(((eq Prop) ((cSUCC cZERO) x0)) ((cSUCC cZERO) x0))
% 190.68/191.79 Found (eq_ref0 ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found ((eq_ref Prop) ((cSUCC cZERO) x0)) as proof of (((eq Prop) ((cSUCC cZERO) x0)) b)
% 190.68/191.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.68/191.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 190.68/191.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 195.38/196.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 195.38/196.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))))
% 195.38/196.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 195.38/196.46 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 195.38/196.46 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 195.38/196.46 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 195.38/196.46 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 199.38/200.43 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 199.38/200.43 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 199.38/200.43 Found (eq_ref0 b) as proof of (P b)
% 199.38/200.43 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (P b)
% 199.38/200.43 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (P b)
% 199.38/200.43 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (P b)
% 199.38/200.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 199.38/200.43 Found (eta_expansion_dep00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 199.38/200.43 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 199.38/200.43 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 199.38/200.43 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 205.08/206.18 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))) b)
% 205.08/206.18 Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 205.08/206.18 Found (eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 205.08/206.18 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 205.08/206.18 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 205.08/206.18 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 205.08/206.18 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 205.08/206.18 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 205.08/206.18 Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0)))))
% 205.08/206.18 Found (eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 205.08/206.18 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 209.78/210.82 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 209.78/210.82 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 209.78/210.82 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 209.78/210.82 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 209.78/210.82 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 209.78/210.82 Found x0:(P (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 209.78/210.82 Instantiate: b:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):((fofType->Prop)->Prop)
% 209.78/210.82 Found x0 as proof of (P0 b)
% 209.78/210.82 Found eta_expansion000:=(eta_expansion00 cONE):(((eq ((fofType->Prop)->Prop)) cONE) (fun (x:(fofType->Prop))=> (cONE x)))
% 209.78/210.82 Found (eta_expansion00 cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 209.78/210.82 Found ((eta_expansion0 Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 209.78/210.82 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 209.78/210.82 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 209.78/210.82 Found (((eta_expansion (fofType->Prop)) Prop) cONE) as proof of (((eq ((fofType->Prop)->Prop)) cONE) b)
% 209.78/210.82 Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 209.78/210.82 Found (eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 209.78/210.82 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 231.38/232.40 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 231.38/232.40 Found (eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 231.38/232.40 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 231.38/232.40 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 231.38/232.40 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) b)
% 231.38/232.40 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 231.38/232.40 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 231.38/232.40 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 231.38/232.40 Found (eta_expansion000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 231.38/232.40 Found ((eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 231.38/232.40 Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 232.88/233.97 Found (eta_expansion000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 232.88/233.97 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 232.88/233.97 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 232.88/233.97 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 235.09/236.14 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 235.09/236.14 Found (eta_expansion000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 235.09/236.14 Found (eta_expansion000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 235.09/236.14 Found ((eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) x) Xy0))))))
% 264.00/265.08 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))
% 264.00/265.08 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 264.00/265.08 Found (eta_expansion_dep00 b) as proof of (P b)
% 264.00/265.08 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (P b)
% 264.00/265.08 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (P b)
% 264.00/265.08 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (P b)
% 264.00/265.08 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (P b)
% 264.00/265.08 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))):(((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) (fun (x:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x) ((eq fofType) Xy))))))
% 264.00/265.08 Found (eta_expansion_dep00 (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 264.00/265.08 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 264.00/265.08 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 274.40/275.44 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 274.40/275.44 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy)))))) b)
% 274.40/275.44 Found x0:(P (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))))
% 274.40/275.44 Instantiate: b:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) ((eq fofType) Xy))))):((fofType->Prop)->Prop)
% 274.40/275.44 Found x0 as proof of (P0 b)
% 274.40/275.44 Found eta_expansion000:=(eta_expansion00 (cSUCC cZERO)):(((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) (fun (x:(fofType->Prop))=> ((cSUCC cZERO) x)))
% 274.40/275.44 Found (eta_expansion00 (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 274.40/275.44 Found ((eta_expansion0 Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 274.40/275.44 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 274.40/275.44 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 274.40/275.44 Found (((eta_expansion (fofType->Prop)) Prop) (cSUCC cZERO)) as proof of (((eq ((fofType->Prop)->Prop)) (cSUCC cZERO)) b)
% 274.40/275.44 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x)))))
% 274.40/275.44 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 274.40/275.44 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 274.40/275.44 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 274.40/275.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 274.40/275.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 274.40/275.44 Found eta_expansion0000:=(eta_expansion000 P):((P b)->(P (fun (x:(fofType->Prop))=> (b x))))
% 274.40/275.44 Found (eta_expansion000 P) as proof of (P0 b)
% 274.40/275.44 Found ((eta_expansion00 b) P) as proof of (P0 b)
% 274.40/275.44 Found (((eta_expansion0 Prop) b) P) as proof of (P0 b)
% 274.40/275.44 Found ((((eta_expansion (fofType->Prop)) Prop) b) P) as proof of (P0 b)
% 274.40/275.44 Found ((((eta_expansion (fofType->Prop)) Prop) b) P) as proof of (P0 b)
% 274.40/275.44 Found x0:(P (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 274.40/275.44 Instantiate: f:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):((fofType->Prop)->Prop)
% 274.40/275.44 Found x0 as proof of (P0 f)
% 274.40/275.44 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 274.40/275.44 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 274.40/275.44 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 274.40/275.44 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 274.40/275.44 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cONE x1))
% 279.42/280.42 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (cONE x)))
% 279.42/280.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x)))))
% 279.42/280.42 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found x0:(P (fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))))
% 279.42/280.42 Instantiate: f:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) P) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):((fofType->Prop)->Prop)
% 279.42/280.42 Found x0 as proof of (P0 f)
% 279.42/280.42 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 279.42/280.42 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 279.42/280.42 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 279.42/280.42 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (cONE x1))
% 279.42/280.42 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (cONE x1))
% 279.42/280.42 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (cONE x)))
% 279.42/280.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x)))))
% 279.42/280.42 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))->(P (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x)))))
% 279.42/280.42 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 279.42/280.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 282.82/283.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) P) as proof of (P0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 282.82/283.84 Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x))))
% 282.82/283.84 Found (eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 282.82/283.84 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 282.82/283.84 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 282.82/283.84 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 282.82/283.84 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 282.82/283.84 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 282.82/283.84 Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x))))
% 282.82/283.84 Found (eta_expansion00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 282.82/283.84 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 282.82/283.84 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 287.21/288.25 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 287.21/288.25 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 287.21/288.25 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 287.21/288.25 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 287.21/288.25 Found x1:(P (cONE x0))
% 287.21/288.25 Instantiate: b:=(cONE x0):Prop
% 287.21/288.25 Found x1 as proof of (P0 b)
% 287.21/288.25 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 287.21/288.25 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found x1:(P (cONE x0))
% 287.21/288.25 Instantiate: b:=(cONE x0):Prop
% 287.21/288.25 Found x1 as proof of (P0 b)
% 287.21/288.25 Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))):(((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0))))))
% 287.21/288.25 Found (eq_ref0 ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found ((eq_ref Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) (fun (Xy0:fofType)=> (((eq fofType) Xy) Xy0)))))) b)
% 287.21/288.25 Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy))))
% 288.01/289.03 Found (eq_ref0 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 288.01/289.03 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) (fun (x:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) x))))
% 288.01/289.03 Found (eta_expansion_dep00 (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> (((eq (fofType->Prop)) x0) ((eq fofType) Xy)))) b)
% 288.01/289.03 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 288.01/289.03 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and (x0 Xx)) (cZERO (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (x0 Xt)))))))
% 288.01/289.03 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X
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