TSTP Solution File: NUM799^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM799^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n029.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:47 EST 2018
% Result : Timeout 287.28s
% 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 : NUM799^1 : TPTP v7.0.0. Released v3.7.0.
% 0.01/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n029.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 14:21:49 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.26 Python 2.7.13
% 0.25/0.70 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.25/0.70 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443411b8>, <kernel.DependentProduct object at 0x2abc443412d8>) of role type named zero
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring zero:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44429488>, <kernel.DependentProduct object at 0x2abc443412d8>) of role type named one
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring one:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44341ea8>, <kernel.DependentProduct object at 0x2abc44348560>) of role type named two
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring two:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443413f8>, <kernel.DependentProduct object at 0x2abc44348200>) of role type named three
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring three:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443412d8>, <kernel.DependentProduct object at 0x2abc44348248>) of role type named four
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring four:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443413f8>, <kernel.DependentProduct object at 0x2abc44348950>) of role type named five
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring five:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44341ea8>, <kernel.DependentProduct object at 0x2abc44348200>) of role type named six
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring six:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443413f8>, <kernel.DependentProduct object at 0x2abc44348950>) of role type named seven
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring seven:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443413f8>, <kernel.DependentProduct object at 0x2abc44348200>) of role type named eight
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring eight:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443488c0>, <kernel.DependentProduct object at 0x2abc44348950>) of role type named nine
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring nine:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44348290>, <kernel.DependentProduct object at 0x2abc44348200>) of role type named ten
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring ten:((fofType->fofType)->(fofType->fofType))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc443485a8>, <kernel.DependentProduct object at 0x2abc44348908>) of role type named succ
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44348998>, <kernel.DependentProduct object at 0x2abc44348440>) of role type named plus
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.25/0.70 FOF formula (<kernel.Constant object at 0x2abc44348950>, <kernel.DependentProduct object at 0x2abc443488c0>) of role type named mult
% 0.25/0.70 Using role type
% 0.25/0.70 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.25/0.70 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax
% 0.25/0.70 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y))
% 0.25/0.70 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y)
% 0.25/0.70 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax
% 0.25/0.70 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)))
% 0.25/0.70 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))
% 0.25/0.70 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))))
% 0.34/0.72 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))))
% 0.34/0.72 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) of role definition named four_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))))
% 0.34/0.72 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) of role definition named five_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))))
% 0.34/0.72 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) of role definition named six_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))))
% 0.34/0.72 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) of role definition named seven_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))))
% 0.34/0.72 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) of role definition named eight_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))))
% 0.34/0.72 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) of role definition named nine_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.34/0.72 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))
% 0.34/0.72 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) of role definition named ten_ax
% 0.34/0.72 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))))
% 0.34/0.72 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.34/0.72 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) of role definition named succ_ax
% 0.34/0.72 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))))
% 0.34/0.72 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))
% 0.34/0.72 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) of role definition named plus_ax
% 0.34/0.73 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))))
% 0.34/0.73 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))
% 0.34/0.73 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) of role definition named mult_ax
% 0.34/0.73 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)))
% 0.34/0.73 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))
% 0.34/0.73 FOF formula ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) of role conjecture named thm
% 0.34/0.73 Conjecture to prove = ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))):Prop
% 0.34/0.73 Parameter fofType_DUMMY:fofType.
% 0.34/0.73 We need to prove ['((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))']
% 0.34/0.73 Parameter fofType:Type.
% 0.34/0.73 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.34/0.73 Definition succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))).
% 0.34/0.73 Definition plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))).
% 2.35/2.80 Definition mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))).
% 2.35/2.80 Trying to prove ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 2.35/2.80 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 2.35/2.80 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 2.35/2.80 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 2.35/2.80 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 2.35/2.80 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 2.35/2.80 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.35/2.80 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 2.65/3.05 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 2.65/3.05 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 2.65/3.05 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 2.65/3.05 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.65/3.05 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 2.65/3.05 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.89/3.27 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.89/3.27 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.89/3.27 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 2.89/3.27 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 2.89/3.27 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 2.89/3.27 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 2.89/3.27 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.89/3.27 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 2.96/3.37 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 2.96/3.37 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 2.96/3.37 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 2.96/3.37 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 2.96/3.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 3.05/3.45 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 3.05/3.45 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 3.05/3.45 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.05/3.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 3.11/3.54 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 3.11/3.54 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 3.11/3.54 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 3.11/3.54 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 3.11/3.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 13.46/13.88 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 13.46/13.88 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 13.46/13.88 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 13.46/13.88 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 13.46/13.88 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 13.46/13.88 Found eq_ref00:=(eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 13.46/13.88 Found (eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) b)
% 16.44/16.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) b)
% 16.44/16.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) b)
% 16.44/16.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven)))) b)
% 16.44/16.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 16.44/16.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven))))
% 16.44/16.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 16.44/16.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven)))
% 16.44/16.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) seven))))
% 16.44/16.82 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 16.44/16.82 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.44/16.82 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.44/16.82 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.44/16.82 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.44/16.82 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 16.65/17.03 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 16.65/17.03 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 16.65/17.03 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 16.65/17.03 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 16.65/17.03 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 16.65/17.03 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 16.65/17.03 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 17.10/17.56 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 17.10/17.56 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 17.10/17.56 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 17.10/17.56 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 17.10/17.56 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.10/17.56 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.10/17.56 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.10/17.56 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.10/17.56 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 17.34/17.78 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 17.34/17.78 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 17.34/17.78 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.34/17.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 17.42/17.84 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 17.42/17.84 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 17.42/17.84 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 17.42/17.84 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.42/17.84 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 17.85/18.25 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 17.85/18.25 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 17.85/18.25 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 17.85/18.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 21.01/21.39 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 21.01/21.39 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.01/21.39 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.01/21.39 Found x01:(P ((mult x) four))
% 21.01/21.39 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 21.01/21.39 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 21.01/21.39 Found x01:(P ((mult x) four))
% 21.01/21.39 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 21.01/21.39 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 21.01/21.39 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 21.24/21.62 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 21.24/21.62 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 21.24/21.62 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 21.24/21.62 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 21.24/21.62 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.24/21.62 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 21.24/21.68 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 21.24/21.68 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.24/21.68 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.24/21.68 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.24/21.68 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 21.31/21.75 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 21.31/21.75 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.31/21.75 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.31/21.75 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.53/21.95 Found x01:(P ((mult x) four))
% 21.53/21.95 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 21.53/21.95 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 21.53/21.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 21.53/21.95 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 21.53/21.95 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 21.53/21.95 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 21.53/21.95 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.53/21.95 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 21.53/21.95 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.70/22.09 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.70/22.09 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 21.70/22.09 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 21.70/22.09 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 21.70/22.09 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.70/22.09 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.70/22.09 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.70/22.09 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 21.74/22.16 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 21.74/22.16 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 21.74/22.16 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 21.74/22.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 35.43/35.86 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 35.43/35.86 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 35.43/35.86 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 35.43/35.86 Found eq_ref00:=(eq_ref0 ((mult x) four)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((mult x) four))
% 35.43/35.86 Found (eq_ref0 ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 35.43/35.86 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 35.43/35.86 Found x01:(P ((mult x) four))
% 35.43/35.86 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 35.43/35.86 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 35.43/35.86 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 35.43/35.86 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 35.43/35.86 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 35.43/35.86 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.43/35.86 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 35.75/36.18 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 35.75/36.18 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 35.75/36.18 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 35.75/36.18 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 35.75/36.18 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 35.75/36.18 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 40.46/40.90 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 40.46/40.90 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 40.46/40.90 Found x01:(P ((plus five) seven))
% 40.46/40.90 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P ((plus five) seven))
% 40.46/40.90 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P0 ((plus five) seven))
% 40.46/40.90 Found x01:(P ((plus five) seven))
% 40.46/40.90 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P ((plus five) seven))
% 40.46/40.90 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P0 ((plus five) seven))
% 40.46/40.90 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 40.46/40.90 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 40.46/40.90 Found eq_ref00:=(eq_ref0 ((plus five) seven)):(((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) ((plus five) seven))
% 40.46/40.90 Found (eq_ref0 ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 40.46/40.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 40.46/40.90 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 40.46/40.90 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.46/40.90 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 40.69/41.08 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 40.69/41.08 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 40.69/41.08 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 40.69/41.08 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.69/41.08 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 40.75/41.16 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 40.75/41.16 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 40.75/41.16 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 40.75/41.16 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.75/41.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 40.83/41.24 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 40.83/41.24 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 40.83/41.24 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 40.83/41.24 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 40.83/41.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 46.45/46.85 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (b x0)))
% 46.45/46.85 Found x11:(P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 46.45/46.85 Found x11:(P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 46.45/46.85 Found x01:(P ((plus five) seven))
% 46.45/46.85 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P ((plus five) seven))
% 46.45/46.85 Found (fun (x01:(P ((plus five) seven)))=> x01) as proof of (P0 ((plus five) seven))
% 46.45/46.85 Found x11:(P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 46.45/46.85 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 46.45/46.85 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 46.45/46.85 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 46.45/46.85 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 46.45/46.85 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 46.45/46.85 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 46.45/46.85 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) ((eq_ref (fofType->fofType)) b)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 47.43/47.87 Found (((eq_trans000 (fun (Y:fofType)=> ((x (four x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (four x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 47.43/47.87 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((plus five) seven) x0))) (fun (Y:fofType)=> ((x (four x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (four x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 47.43/47.87 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) four) x0)) b) (((plus five) seven) x0))) (fun (Y:fofType)=> ((x (four x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (four x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 47.43/47.87 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) four) x0)) b) (((plus five) seven) x0))) (fun (Y:fofType)=> ((x (four x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (four x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 47.43/47.87 Found x11:(P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 47.43/47.87 Found x11:(P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 47.43/47.87 Found x11:(P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P (((mult x) four) x0))
% 47.43/47.87 Found (fun (x11:(P (((mult x) four) x0)))=> x11) as proof of (P0 (((mult x) four) x0))
% 47.43/47.87 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 47.43/47.87 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 47.43/47.87 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 47.43/47.87 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 47.43/47.87 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 47.43/47.87 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 47.43/47.87 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 47.43/47.87 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 47.43/47.87 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 47.43/47.87 Found ((eq_trans0000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found (((eq_trans000 (fun (x11:fofType)=> ((x (four x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (four x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((plus five) seven) x0))) (fun (x11:fofType)=> ((x (four x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (four x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) four) x0)) b) (((plus five) seven) x0))) (fun (x11:fofType)=> ((x (four x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (four x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) four) x0)) b) (((plus five) seven) x0))) (fun (x11:fofType)=> ((x (four x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (four x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found x11:(P ((((mult x) four) x0) y))
% 51.71/52.12 Found (fun (x11:(P ((((mult x) four) x0) y)))=> x11) as proof of (P ((((mult x) four) x0) y))
% 51.71/52.12 Found (fun (x11:(P ((((mult x) four) x0) y)))=> x11) as proof of (P0 ((((mult x) four) x0) y))
% 51.71/52.12 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 51.71/52.12 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 51.71/52.12 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 51.71/52.12 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.71/52.12 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 51.84/52.26 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 51.84/52.26 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 51.84/52.26 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 51.84/52.26 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 51.84/52.26 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 51.84/52.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 52.01/52.43 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 52.01/52.43 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 52.01/52.43 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 52.01/52.43 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 52.01/52.43 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.01/52.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 52.24/52.65 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 52.24/52.65 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 52.24/52.65 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 52.24/52.65 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.24/52.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 52.31/52.73 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 52.31/52.73 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 52.31/52.73 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 52.31/52.73 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 52.31/52.73 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 55.54/55.94 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 55.54/55.94 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 55.54/55.94 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 55.54/55.94 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) y)):(((eq fofType) ((((mult x) four) x0) y)) ((((mult x) four) x0) y))
% 55.54/55.94 Found (eq_ref0 ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 55.54/55.94 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 55.54/55.94 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 55.54/55.94 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 55.54/55.94 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 55.54/55.94 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 55.54/55.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 55.54/55.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 55.54/55.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 55.54/55.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 55.54/55.94 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 55.54/55.94 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.54/55.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 55.54/55.94 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 55.61/56.02 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 55.61/56.02 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 55.61/56.02 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.61/56.02 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 55.71/56.10 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 55.71/56.10 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 55.71/56.10 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.71/56.10 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 55.74/56.20 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 55.74/56.20 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 55.74/56.20 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 55.74/56.20 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 55.74/56.20 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.05/56.43 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 56.05/56.43 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.05/56.43 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 56.05/56.43 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.05/56.51 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.05/56.51 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.05/56.51 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 56.05/56.51 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.05/56.51 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 56.05/56.51 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.05/56.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.20/56.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.20/56.59 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.20/56.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 56.20/56.59 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((eta_expansion_dep00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.20/56.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 56.20/56.59 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.20/56.59 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.89 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.50/56.89 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.89 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.50/56.89 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.89 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.89 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.50/56.96 Found (eq_ref00 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((eq_ref0 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.96 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x0))->(P (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 56.50/56.96 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((eta_expansion00 (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 56.50/56.96 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 56.50/56.96 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))):((P (((mult x) four) x0))->(P (((mult x) four) x0)))
% 56.50/56.96 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 56.50/56.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 59.35/59.82 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 59.35/59.82 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0)))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 59.35/59.82 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of ((P (((mult x) four) x0))->(P (((plus five) seven) x0)))
% 59.35/59.82 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 59.35/59.82 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 59.35/59.82 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 59.35/59.82 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.35/59.82 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 59.50/59.89 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 59.50/59.89 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 59.50/59.89 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.50/59.89 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 59.65/60.04 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 59.65/60.04 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 59.65/60.04 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 59.65/60.04 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 59.65/60.04 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 62.04/62.43 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 62.04/62.43 Found eta_expansion0000:=(eta_expansion000 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1))))
% 62.04/62.43 Found (eta_expansion000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.43 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.43 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.43 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.43 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.43 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 62.04/62.47 Found (eta_expansion000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 62.04/62.47 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.04/62.47 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.14/62.56 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found eq_ref000:=(eq_ref00 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.14/62.56 Found (eq_ref00 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.14/62.56 Found eta_expansion0000:=(eta_expansion000 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1))))
% 62.21/62.59 Found (eta_expansion000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 62.21/62.59 Found (eta_expansion000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 62.21/62.59 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.21/62.59 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.28/62.67 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.28/62.67 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1))))
% 62.28/62.67 Found (eta_expansion_dep000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 62.31/62.71 Found (eta_expansion_dep000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 62.31/62.71 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.31/62.71 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.31/62.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found eq_ref000:=(eq_ref00 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.44/62.88 Found (eq_ref00 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1))))
% 62.44/62.88 Found (eta_expansion_dep000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 62.44/62.88 Found (eta_expansion_dep000 P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 62.44/62.88 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 62.44/62.88 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 62.44/62.88 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P (((plus five) seven) x0)))
% 64.60/64.99 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 64.60/64.99 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.60/64.99 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.60/64.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.60/64.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.60/64.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.60/64.99 Found (eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.60/64.99 Found (eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.60/64.99 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((eq_sym100 x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.60/64.99 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((eq_sym10 (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.60/64.99 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.60/64.99 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 64.99/65.40 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found (eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((eq_sym100 x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((eq_sym10 (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) P)) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 64.99/65.40 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 64.99/65.40 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 64.99/65.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 65.03/65.51 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 65.03/65.51 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.03/65.51 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.03/65.51 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 65.81/66.25 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 65.81/66.25 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.81/66.25 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 65.81/66.25 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.81/66.25 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 65.95/66.36 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 65.95/66.36 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 65.95/66.36 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 65.95/66.36 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 89.59/89.98 Found x11:(P (((plus five) seven) x0))
% 89.59/89.98 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 89.59/89.98 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 89.59/89.98 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 89.59/89.98 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 89.59/89.98 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 89.59/89.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 89.59/89.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 89.59/89.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 89.59/89.98 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((eq_sym100 x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((eq_sym10 (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) (((eta_expansion fofType) fofType) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 89.59/89.98 Found x11:(P (((plus five) seven) x0))
% 89.59/89.98 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 89.59/89.98 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 89.59/89.98 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 98.04/98.46 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 98.04/98.46 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((eq_sym100 x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((eq_sym10 (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> ((((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11)) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x1:(((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) x1) (fun (x2:(fofType->fofType))=> ((P (((plus five) seven) x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) (fun (x11:(P (((plus five) seven) x0)))=> x11))) as proof of ((P (((plus five) seven) x0))->(P (((mult x) four) x0)))
% 98.04/98.46 Found eq_ref00:=(eq_ref0 (((plus five) seven) x0)):(((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus five) seven) x0))
% 98.04/98.46 Found (eq_ref0 (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 98.04/98.46 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 98.04/98.46 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 98.04/98.46 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 98.04/98.46 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 98.04/98.46 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 98.04/98.46 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 98.04/98.46 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found eq_ref00:=(eq_ref0 (((plus five) seven) x0)):(((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus five) seven) x0))
% 99.54/99.95 Found (eq_ref0 (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found ((eq_ref (fofType->fofType)) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 99.54/99.95 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 99.54/99.95 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found eta_expansion000:=(eta_expansion00 (((plus five) seven) x0)):(((eq (fofType->fofType)) (((plus five) seven) x0)) (fun (x:fofType)=> ((((plus five) seven) x0) x)))
% 99.54/99.95 Found (eta_expansion00 (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found ((eta_expansion0 fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 99.54/99.95 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 99.54/99.95 Found eta_expansion000:=(eta_expansion00 (((plus five) seven) x0)):(((eq (fofType->fofType)) (((plus five) seven) x0)) (fun (x:fofType)=> ((((plus five) seven) x0) x)))
% 99.54/99.95 Found (eta_expansion00 (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found ((eta_expansion0 fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 99.54/99.95 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 112.38/112.79 Found (((eta_expansion fofType) fofType) (((plus five) seven) x0)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x11:(P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P (((plus five) seven) x0))
% 112.38/112.79 Found (fun (x11:(P (((plus five) seven) x0)))=> x11) as proof of (P0 (((plus five) seven) x0))
% 112.38/112.79 Found x21:(P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P0 ((((mult x) four) x0) x1))
% 112.38/112.79 Found x21:(P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P0 ((((mult x) four) x0) x1))
% 112.38/112.79 Found x21:(P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P0 ((((mult x) four) x0) x1))
% 112.38/112.79 Found x21:(P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P ((((mult x) four) x0) x1))
% 112.38/112.79 Found (fun (x21:(P ((((mult x) four) x0) x1)))=> x21) as proof of (P0 ((((mult x) four) x0) x1))
% 112.38/112.79 Found x11:(P ((((plus five) seven) x0) y))
% 112.38/112.79 Found (fun (x11:(P ((((plus five) seven) x0) y)))=> x11) as proof of (P ((((plus five) seven) x0) y))
% 112.38/112.79 Found (fun (x11:(P ((((plus five) seven) x0) y)))=> x11) as proof of (P0 ((((plus five) seven) x0) y))
% 112.38/112.79 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 112.38/112.79 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 112.38/112.79 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 112.38/112.79 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 112.38/112.79 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 112.38/112.79 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) y)):(((eq fofType) ((((plus five) seven) x0) y)) ((((plus five) seven) x0) y))
% 112.38/112.79 Found (eq_ref0 ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 112.38/112.79 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 112.38/112.79 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 112.38/112.79 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 115.42/115.82 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 115.42/115.82 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 115.42/115.82 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 115.42/115.82 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 115.42/115.82 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 115.42/115.82 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 115.42/115.82 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 115.42/115.82 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 115.42/115.82 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 115.42/115.82 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 115.42/115.82 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) y)):(((eq fofType) ((((plus five) seven) x0) y)) ((((plus five) seven) x0) y))
% 115.42/115.82 Found (eq_ref0 ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 115.42/115.82 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 132.17/132.56 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 132.17/132.56 Found ((eq_ref fofType) ((((plus five) seven) x0) y)) as proof of (((eq fofType) ((((plus five) seven) x0) y)) b)
% 132.17/132.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 132.17/132.56 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 132.17/132.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 132.17/132.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 132.17/132.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) y))
% 132.17/132.56 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 132.17/132.56 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.17/132.56 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.17/132.56 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.17/132.56 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.17/132.56 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.17/132.56 Found (eq_sym010 (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.17/132.56 Found ((eq_sym01 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.17/132.56 Found (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.17/132.56 Found (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.17/132.56 Found ((eq_trans0000 (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) b))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found (((eq_trans000 (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.17/132.56 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 132.25/132.64 Found ((eq_sym00 (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 132.25/132.64 Found (((eq_sym0 (((plus five) seven) x0)) (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 132.25/132.64 Found ((((eq_sym (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) ((((eq_sym (fofType->fofType)) (x (four x0))) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (x (four x0))))) (((eta_expansion fofType) fofType) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 132.25/132.64 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 132.25/132.64 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.25/132.64 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.25/132.64 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.25/132.64 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.25/132.64 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) seven) x0))
% 132.25/132.64 Found (eq_sym010 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.25/132.64 Found ((eq_sym01 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.25/132.64 Found (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.25/132.64 Found (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) b)
% 132.25/132.64 Found ((eq_trans0000 (((eq_sym0 b) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.25/132.64 Found (((eq_trans000 (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.25/132.64 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 132.25/132.64 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 133.59/134.05 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 133.59/134.05 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 133.59/134.05 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 133.59/134.05 Found ((eq_sym00 (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 133.59/134.05 Found (((eq_sym0 (((plus five) seven) x0)) (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) (((eq_sym0 (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 133.59/134.05 Found ((((eq_sym (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (x (four x0))) ((((eq_sym (fofType->fofType)) (x (four x0))) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x0))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 133.59/134.05 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 133.59/134.05 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 133.59/134.05 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.59/134.05 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 133.89/134.34 Found (eta_expansion_dep00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 133.89/134.34 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 133.89/134.34 Found (eta_expansion_dep00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 133.89/134.34 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eq_ref00:=(eq_ref0 (b x0)):(((eq (fofType->fofType)) (b x0)) (b x0))
% 133.89/134.34 Found (eq_ref0 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 133.89/134.34 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 142.84/143.28 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 142.84/143.28 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found eq_ref00:=(eq_ref0 (b x0)):(((eq (fofType->fofType)) (b x0)) (b x0))
% 142.84/143.28 Found (eq_ref0 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 142.84/143.28 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 142.84/143.28 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 142.84/143.28 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 142.84/143.28 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 142.84/143.28 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 142.84/143.28 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 142.84/143.28 Found ((eq_sym10 b) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 142.84/143.28 Found (((eq_sym1 (((mult x) four) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 142.84/143.28 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 142.84/143.28 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 142.84/143.28 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 142.84/143.28 Found (((eq_trans000 (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 142.84/143.28 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) seven) x0)) b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 143.50/143.90 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 143.50/143.90 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 143.50/143.90 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 143.50/143.90 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 143.50/143.90 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) b)
% 143.50/143.90 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 143.50/143.90 Found ((eq_sym10 b) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 143.50/143.90 Found (((eq_sym1 (((mult x) four) x0)) b) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 143.50/143.90 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 143.50/143.90 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x0))
% 143.50/143.90 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) b) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found (((eq_trans000 (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 143.50/143.90 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) seven) x0)) b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 145.30/145.74 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) seven) x0)) b) (((mult x) four) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) ((eq_ref (fofType->fofType)) (((plus five) seven) x0))) ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) Y)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x0)))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 145.30/145.74 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 145.30/145.74 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.30/145.74 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.30/145.74 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.30/145.74 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.30/145.74 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.30/145.74 Found (eq_sym100 (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.30/145.74 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.30/145.74 Found (((eq_sym1 (b x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.30/145.74 Found ((((eq_sym (fofType->fofType)) (b x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.30/145.74 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 145.30/145.74 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((eta_expansion_dep00 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 145.30/145.74 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.30/145.74 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 145.67/146.06 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 145.67/146.06 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 145.67/146.06 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 145.67/146.06 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 145.67/146.06 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 145.67/146.06 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 145.67/146.06 Found ((eq_sym10 (b x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 145.67/146.06 Found (((eq_sym1 (((mult x) four) x0)) (b x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 145.67/146.06 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (b x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 145.67/146.06 Found eq_ref000:=(eq_ref00 P):((P (b x0))->(P (b x0)))
% 145.67/146.06 Found (eq_ref00 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found ((eq_ref0 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.67/146.06 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 145.67/146.06 Found (eta_expansion_dep00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.67/146.06 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.67/146.06 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.67/146.06 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.67/146.06 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (((plus five) seven) x0))
% 145.67/146.06 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.83/146.23 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.83/146.23 Found (((eq_sym1 (b x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.83/146.23 Found ((((eq_sym (fofType->fofType)) (b x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (b x0))
% 145.83/146.23 Found eta_expansion0000:=(eta_expansion000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 145.83/146.23 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((eta_expansion00 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (((eta_expansion0 fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 145.83/146.23 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 145.83/146.23 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found eta_expansion0000:=(eta_expansion000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 145.83/146.23 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found ((eta_expansion00 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.83/146.23 Found (((eta_expansion0 fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 145.89/146.33 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 145.89/146.33 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found eq_ref000:=(eq_ref00 P):((P (b x0))->(P (b x0)))
% 145.89/146.33 Found (eq_ref00 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((eq_ref0 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 145.89/146.33 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((eta_expansion_dep00 (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 145.89/146.33 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 146.02/146.44 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P)) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 146.02/146.44 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (((plus five) seven) x0)))
% 146.02/146.44 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 146.02/146.44 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 146.02/146.44 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 146.02/146.44 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 146.02/146.44 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 146.02/146.44 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (b x0))
% 146.02/146.44 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 146.02/146.44 Found ((eq_sym10 (b x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 146.02/146.44 Found (((eq_sym1 (((mult x) four) x0)) (b x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 146.02/146.44 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (b x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) four) x0))
% 164.58/164.99 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 164.58/164.99 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion fofType) fofType) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 164.58/164.99 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.58/164.99 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) seven) x0))->(P (((mult x) four) x0))))
% 164.58/164.99 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 164.58/164.99 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 164.64/165.07 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 164.64/165.07 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 164.64/165.07 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 164.64/165.07 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 178.53/178.95 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found (((eq_sym1 (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((mult x) four) x0))
% 178.53/178.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 178.53/178.95 Found (eta_expansion_dep00 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.98 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.98 Found ((eq_sym10 (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.99 Found (((eq_sym1 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.99 Found ((((eq_sym (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.99 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.99 Found (eq_ref0 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.99 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.99 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.99 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0))
% 178.53/178.99 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 178.53/178.99 Found ((eq_sym10 (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 189.38/189.86 Found (((eq_sym1 (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 189.38/189.86 Found ((((eq_sym (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus five) seven) x0)) ((eq_ref (fofType->fofType)) (((plus zero) (fun (x30:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))) as proof of (((eq (fofType->fofType)) (((plus five) seven) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 189.38/189.86 Found x21:(P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P0 ((((plus five) seven) x0) x1))
% 189.38/189.86 Found x21:(P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P0 ((((plus five) seven) x0) x1))
% 189.38/189.86 Found x21:(P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P0 ((((plus five) seven) x0) x1))
% 189.38/189.86 Found x21:(P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (fun (x21:(P ((((plus five) seven) x0) x1)))=> x21) as proof of (P0 ((((plus five) seven) x0) x1))
% 189.38/189.86 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 189.38/189.86 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 189.38/189.86 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 189.38/189.86 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 189.38/189.86 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 189.38/189.86 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.27/191.67 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.27/191.67 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 191.27/191.67 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 191.27/191.67 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.27/191.67 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 191.27/191.67 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.27/191.67 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 191.27/191.67 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 191.27/191.67 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 191.27/191.67 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 202.57/202.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 202.57/202.98 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found eq_ref00:=(eq_ref0 ((((plus five) seven) x0) x1)):(((eq fofType) ((((plus five) seven) x0) x1)) ((((plus five) seven) x0) x1))
% 202.57/202.98 Found (eq_ref0 ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((plus five) seven) x0) x1)) as proof of (((eq fofType) ((((plus five) seven) x0) x1)) b)
% 202.57/202.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 202.57/202.98 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x0) x1))
% 202.57/202.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 202.57/202.98 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 202.57/202.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) y))
% 202.57/202.98 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) y)):(((eq fofType) ((((mult x) four) x0) y)) ((((mult x) four) x0) y))
% 202.57/202.98 Found (eq_ref0 ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 202.57/202.98 Found ((eq_ref fofType) ((((mult x) four) x0) y)) as proof of (((eq fofType) ((((mult x) four) x0) y)) b)
% 202.57/202.98 Found eq_ref00:=(eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven))))
% 202.57/202.98 Found (eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) b)
% 202.57/202.98 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) b)
% 202.57/202.98 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) b)
% 219.68/220.12 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (N (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))) b)
% 219.68/220.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 219.68/220.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven))))
% 219.68/220.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 219.68/220.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven)))
% 219.68/220.12 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus five) seven))))
% 219.68/220.12 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 219.68/220.12 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.68/220.12 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.68/220.12 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 219.83/220.31 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 219.83/220.31 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 219.83/220.31 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 219.83/220.31 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 219.83/220.31 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 219.83/220.31 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.28/220.74 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 220.28/220.74 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.28/220.74 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.28/220.74 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 220.28/220.74 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 220.28/220.74 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.28/220.74 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.28/220.74 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.40/220.81 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.40/220.81 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.40/220.81 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.40/220.81 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.58/221.02 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 220.58/221.02 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.58/221.02 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.58/221.02 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.58/221.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.66/221.10 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.66/221.10 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 220.66/221.10 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.66/221.10 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.66/221.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.88/221.33 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.88/221.33 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.88/221.33 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.88/221.33 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.95/221.37 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.95/221.37 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 220.95/221.37 Found (eta_expansion00 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 220.95/221.37 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 220.95/221.37 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 227.32/227.73 Found (eq_ref0 (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.32/227.73 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 227.32/227.73 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 227.32/227.73 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.32/227.73 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.32/227.73 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.41/227.88 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 227.41/227.88 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 227.41/227.88 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.41/227.88 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.41/227.88 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 227.55/227.96 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 227.55/227.96 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.55/227.96 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.55/227.96 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 227.62/228.05 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 227.62/228.05 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.62/228.05 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.62/228.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 227.92/228.37 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 227.92/228.37 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 227.92/228.37 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 227.92/228.37 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 227.92/228.37 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.00/228.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.00/228.42 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.00/228.42 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.00/228.42 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.00/228.42 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.00/228.42 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.00/228.42 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.16/228.60 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.16/228.60 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.16/228.60 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.16/228.60 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.16/228.60 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.16/228.60 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.16/228.60 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.16/228.60 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.22/228.68 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.22/228.68 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.22/228.68 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.22/228.68 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.22/228.68 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.22/228.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.30/228.77 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.30/228.77 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.30/228.77 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.30/228.77 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.30/228.77 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.30/228.77 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.30/228.77 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.37/228.83 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.37/228.83 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.37/228.83 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.37/228.83 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.37/228.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.53/228.94 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.53/228.94 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.53/228.94 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.53/228.94 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.53/228.94 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.53/228.94 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.53/228.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.60/229.02 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.60/229.02 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.60/229.02 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.60/229.02 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.60/229.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.60/229.02 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.60/229.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.60/229.05 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.60/229.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.60/229.05 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.60/229.05 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.82/229.24 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 228.82/229.24 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.82/229.24 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 228.82/229.24 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 228.82/229.24 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 228.82/229.24 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 228.82/229.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 231.76/232.20 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 231.76/232.20 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 231.76/232.20 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x0))->(P (((plus five) seven) x0))))
% 231.76/232.20 Found x01:(P ((mult x) four))
% 231.76/232.20 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 231.76/232.20 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 231.76/232.20 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 231.76/232.20 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 231.76/232.20 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.76/232.20 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 231.82/232.30 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 231.82/232.30 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 231.82/232.30 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.82/232.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 231.97/232.45 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 231.97/232.45 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 231.97/232.45 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 231.97/232.45 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 233.29/233.71 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 233.29/233.71 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 233.29/233.71 Found eq_ref00:=(eq_ref0 a):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) a)
% 233.29/233.71 Found (eq_ref0 a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 233.29/233.71 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 233.29/233.71 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 233.29/233.71 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 233.29/233.71 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (x:((fofType->fofType)->(fofType->fofType)))=> (b x)))
% 233.29/233.71 Found (eta_expansion_dep00 b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 233.29/233.71 Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 241.10/241.53 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 241.10/241.53 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 241.10/241.53 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) seven))))
% 241.10/241.53 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 241.10/241.53 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 241.10/241.53 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 241.10/241.53 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 241.10/241.53 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.10/241.53 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 241.20/241.63 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 241.20/241.63 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.63 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 241.20/241.64 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 241.20/241.64 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.20/241.64 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 241.26/241.74 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 241.26/241.74 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.74 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 241.26/241.75 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.26/241.75 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 241.26/241.75 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.80 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.80 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.80 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)))
% 241.36/241.81 Found (eq_ref00 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)))
% 241.36/241.81 Found (eq_ref00 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.36/241.81 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 241.42/241.89 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 241.42/241.89 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.89 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 241.42/241.90 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 241.42/241.90 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.42/241.90 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.72/242.16 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.72/242.16 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 241.72/242.16 Found x01:(P ((mult x) four))
% 241.72/242.16 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 241.72/242.16 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 241.72/242.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 241.72/242.16 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 241.72/242.16 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 241.72/242.16 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 241.72/242.16 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.72/242.16 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.85/242.36 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 241.85/242.36 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.85/242.36 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.85/242.36 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.85/242.36 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 241.85/242.36 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 241.85/242.36 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 241.85/242.36 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 241.85/242.36 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 241.85/242.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 242.01/242.46 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 242.01/242.46 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 242.01/242.46 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 242.01/242.46 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.01/242.46 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.15/242.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.15/242.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.15/242.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.15/242.58 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.15/242.58 Found x01:(P ((mult x) four))
% 242.15/242.58 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 242.15/242.58 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 242.15/242.58 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 242.15/242.58 Found (eta_expansion_dep00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 242.15/242.58 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found eq_ref00:=(eq_ref0 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (((mult x) four) x0))
% 242.15/242.58 Found (eq_ref0 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.15/242.58 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x0)):(((eq (fofType->fofType)) (((mult x) four) x0)) (fun (x1:fofType)=> ((((mult x) four) x0) x1)))
% 242.15/242.58 Found (eta_expansion00 (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found ((eta_expansion0 fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found (((eta_expansion fofType) fofType) (((mult x) four) x0)) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 242.31/242.77 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x0)) (((plus five) seven) x0))
% 242.31/242.77 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 242.31/242.77 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((eta_expansion00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found (((eta_expansion0 fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 242.31/242.77 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 242.31/242.77 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.31/242.77 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 242.39/242.87 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((eq_ref0 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x0))->(P1 (fun (x1:fofType)=> ((((mult x) four) x0) x1))))
% 242.39/242.87 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((eta_expansion_dep00 (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x0)) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 242.39/242.87 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 242.39/242.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))):((P1 (((mult x) four) x0))->(P1 (((mult x) four) x0)))
% 250.35/250.78 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0)))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x0))))) as proof of ((P1 (((mult x) four) x0))->(P1 (((plus five) seven) x0)))
% 250.35/250.78 Found x0:(P ((mult x) four))
% 250.35/250.78 Instantiate: b:=((mult x) four):((fofType->fofType)->(fofType->fofType))
% 250.35/250.78 Found x0 as proof of (P0 b)
% 250.35/250.78 Found eq_ref00:=(eq_ref0 ((plus five) seven)):(((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) ((plus five) seven))
% 250.35/250.78 Found (eq_ref0 ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) seven)) b)
% 250.35/250.78 Found x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))))
% 250.35/250.78 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 250.35/250.78 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 250.35/250.78 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 250.35/250.78 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 250.35/250.78 Found eq_ref00:=(eq_ref0 ((mult x) four)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((mult x) four))
% 250.35/250.78 Found (eq_ref0 ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 250.35/250.78 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 254.25/254.68 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 254.25/254.68 Found x01:(P ((mult x) four))
% 254.25/254.68 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P ((mult x) four))
% 254.25/254.68 Found (fun (x01:(P ((mult x) four)))=> x01) as proof of (P0 ((mult x) four))
% 254.25/254.68 Found x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))))
% 254.25/254.68 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 254.25/254.68 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 254.25/254.68 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 254.25/254.68 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 254.25/254.68 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.25/254.68 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 254.31/254.80 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 254.31/254.80 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 254.31/254.80 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.31/254.80 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 254.31/254.80 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.31/254.80 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 254.39/254.84 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 254.39/254.84 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.39/254.84 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 254.45/254.91 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 254.45/254.91 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.91 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 254.45/254.94 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 254.45/254.94 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.45/254.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 254.55/254.98 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.55/254.98 Found eq_ref000:=(eq_ref00 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)))
% 254.74/255.18 Found (eq_ref00 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.74/255.18 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.74/255.18 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.74/255.18 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.74/255.18 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.74/255.18 Found x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))))
% 254.74/255.18 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 254.74/255.18 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 254.74/255.18 Found eta_expansion000:=(eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 254.74/255.18 Found (eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found ((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found (((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 254.74/255.18 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.74/255.18 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0) x1)))
% 254.83/255.26 Found (eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x))))))))
% 254.83/255.26 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found eq_ref00:=(eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)):(((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))
% 254.83/255.26 Found (eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.83/255.26 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.91/255.40 Found ((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)) as proof of (((eq (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) (((plus five) seven) x0))
% 254.91/255.40 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 254.91/255.40 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((eta_expansion00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (((eta_expansion0 fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 254.91/255.40 Found (eta_expansion000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 254.91/255.40 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 254.91/255.40 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 254.91/255.40 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (fun (x1:fofType)=> ((((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0) x1))))
% 255.06/255.50 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((eta_expansion_dep00 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))))
% 255.06/255.50 Found (eta_expansion_dep000 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType)) (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType)) (x:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x)))))))) x0)))
% 255.06/255.51 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> x1)) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))
% 255.06/255.51 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 255.06/255.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0)))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 ((seven x0) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))) x0))))) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found eq_ref000:=(eq_ref00 P1):((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)))
% 261.28/261.73 Found (eq_ref00 P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found ((eq_ref0 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0)) P1)) as proof of ((P1 (((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))) x0))->(P1 (((plus five) seven) x0)))
% 261.28/261.73 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 261.28/261.73 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) seven))
% 261.28/261.73 Found eq_ref00:=(eq_ref0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))):(((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 261.28/261.73 Found (eq_ref0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) b)
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) b)
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) b)
% 261.28/261.73 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1)))))) b)
% 264.89/265.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 264.89/265.42 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 264.89/265.42 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 264.89/265.42 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 264.89/265.42 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 264.89/265.42 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 264.89/265.42 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 264.89/265.42 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) seven) x0) x1))
% 264.89/265.42 Found eq_ref00:=(eq_ref0 ((((mult x) four) x0) x1)):(((eq fofType) ((((mult x) four) x0) x1)) ((((mult x) four) x0) x1))
% 264.89/265.42 Found (eq_ref0 ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found ((eq_ref fofType) ((((mult x) four) x0) x1)) as proof of (((eq fofType) ((((mult x) four) x0) x1)) b)
% 264.89/265.42 Found x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10))))))
% 264.89/265.42 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 278.18/278.65 Found (fun (x01:(P ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x10:fofType)=> x10)))))))=> x01) as proof of (P0 ((plus zero) (fun (x3:(fofType->fofType))=> (x (eight (fun (x1:fofType)=> x1))))))
% 278.18/278.65 Found x0:(P ((mult x) four))
% 278.18/278.65 Instantiate: f:=((mult x) four):((fofType->fofType)->(fofType->fofType))
% 278.18/278.65 Found x0 as proof of (P0 f)
% 278.18/278.65 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 278.18/278.65 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (forall (x:(fofType->fofType)), (((eq (fofType->fofType)) (f x)) (((plus five) seven) x)))
% 278.18/278.65 Found x0:(P ((mult x) four))
% 278.18/278.65 Instantiate: f:=((mult x) four):((fofType->fofType)->(fofType->fofType))
% 278.18/278.65 Found x0 as proof of (P0 f)
% 278.18/278.65 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 278.18/278.65 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (forall (x:(fofType->fofType)), (((eq (fofType->fofType)) (f x)) (((plus five) seven) x)))
% 278.18/278.65 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 278.18/278.65 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 278.18/278.65 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found eta_expansion000:=(eta_expansion00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 278.18/278.65 Found (eta_expansion00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eta_expansion0 fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x))))))))
% 278.18/278.65 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.18/278.65 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 278.25/278.76 Found (eta_expansion_dep00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x))))))))
% 278.25/278.76 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 278.25/278.76 Found (eta_expansion_dep00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x))))))))
% 278.25/278.76 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found eta_expansion000:=(eta_expansion00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 278.25/278.76 Found (eta_expansion00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found ((eta_expansion0 fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 278.25/278.76 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x))))))))
% 287.28/287.73 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (((plus five) seven) x1))
% 287.28/287.73 Found x0:(P ((mult x) four))
% 287.28/287.73 Instantiate: f:=((mult x) four):((fofType->fofType)->(fofType->fofType))
% 287.28/287.73 Found x0 as proof of (P0 f)
% 287.28/287.73 Found eq_ref00:=(eq_ref0 ((f x1) y)):(((eq fofType) ((f x1) y)) ((f x1) y))
% 287.28/287.73 Found (eq_ref0 ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((((plus five) seven) x1) y))
% 287.28/287.73 Found ((eq_ref fofType) ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((((plus five) seven) x1) y))
% 287.28/287.73 Found ((eq_ref fofType) ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((((plus five) seven) x1) y))
% 287.28/287.73 Found (fun (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (((eq fofType) ((f x1) y)) ((((plus five) seven) x1) y))
% 287.28/287.73 Found (fun (x1:(fofType->fofType)) (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (forall (y:fofType), (((eq fofType) ((f x1) y)) ((((plus five) seven) x1) y)))
% 287.28/287.73 Found (fun (x1:(fofType->fofType)) (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (forall (x:(fofType->fofType)) (y:fofType), (((eq fofType) ((f x) y)) ((((plus five) seven) x) y)))
% 287.28/287.73 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 287.28/287.73 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((eta_expansion00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found (((eta_expansion0 fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x)))))))))
% 287.28/287.73 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.28/287.73 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 287.28/287.73 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 287.36/287.81 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((eta_expansion00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (((eta_expansion0 fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x)))))))))
% 287.36/287.81 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 287.36/287.81 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.36/287.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 287.48/287.98 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((eta_expansion_dep00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x)))))))))
% 287.48/287.98 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 287.48/287.98 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 287.48/287.98 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found ((eta_expansion_dep00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.48/287.98 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x)))))))))
% 287.78/288.25 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 287.78/288.25 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((seven x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found eq_ref000:=(eq_ref00 P1):((P1 (f x1))->(P1 (f x1)))
% 287.78/288.25 Found (eq_ref00 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((eq_ref0 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found eq_ref000:=(eq_ref00 P1):((P1 (f x1))->(P1 (f x1)))
% 287.78/288.25 Found (eq_ref00 P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found ((eq_ref0 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five) seven) x1)))
% 287.78/288.25 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (((plus five
%------------------------------------------------------------------------------