TSTP Solution File: NUM021^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM021^1 : TPTP v7.0.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n144.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 13:10:13 EST 2018
% Result : Timeout 290.02s
% 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 : NUM021^1 : TPTP v7.0.0. Released v3.6.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n144.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Thu Jan 4 14:50:32 CST 2018
% 0.07/0.23 % CPUTime :
% 0.07/0.26 Python 2.7.13
% 0.33/0.76 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.33/0.76 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77adcf8>, <kernel.DependentProduct object at 0x2aace7ecbc20>) of role type named zero
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring zero:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad170>, <kernel.DependentProduct object at 0x2aace77ad368>) of role type named one
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring one:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ecbc20>, <kernel.DependentProduct object at 0x2aace77ad368>) of role type named two
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring two:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744c6c8>) of role type named three
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring three:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744cbd8>) of role type named four
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring four:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad368>, <kernel.DependentProduct object at 0x2aace744c368>) of role type named five
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring five:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744c4d0>) of role type named six
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring six:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named seven
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring seven:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744c6c8>) of role type named eight
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring eight:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744cbd8>) of role type named nine
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring nine:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744c320>) of role type named ten
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring ten:((fofType->fofType)->(fofType->fofType))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ea4ea8>, <kernel.DependentProduct object at 0x2aace744c320>) of role type named succ
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ea4fc8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named plus
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77fe6c8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named mult
% 0.33/0.76 Using role type
% 0.33/0.76 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax
% 0.33/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y))
% 0.33/0.76 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y)
% 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax
% 0.33/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)))
% 0.33/0.76 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))
% 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))))
% 0.33/0.77 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))
% 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))))
% 0.33/0.77 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))
% 0.33/0.77 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
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))))
% 0.33/0.77 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))
% 0.33/0.77 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
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))))
% 0.33/0.77 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))
% 0.33/0.77 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
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))))
% 0.33/0.77 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))
% 0.33/0.77 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
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))))
% 0.33/0.77 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))
% 0.33/0.77 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
% 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))))
% 0.33/0.77 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))
% 0.33/0.77 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
% 0.33/0.77 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)))))))))))
% 0.33/0.77 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))
% 0.33/0.77 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
% 0.33/0.77 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))))))))))))
% 0.33/0.77 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.33/0.77 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
% 0.33/0.77 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))))
% 0.33/0.77 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))
% 0.33/0.77 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
% 0.33/0.78 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))))
% 0.33/0.78 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))
% 0.33/0.78 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
% 0.33/0.78 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)))
% 0.33/0.78 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))
% 0.33/0.78 FOF formula ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) of role conjecture named thm
% 0.33/0.78 Conjecture to prove = ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))):Prop
% 0.33/0.78 Parameter fofType_DUMMY:fofType.
% 0.33/0.78 We need to prove ['((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))']
% 0.33/0.78 Parameter fofType:Type.
% 0.33/0.78 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.33/0.78 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)).
% 8.16/8.60 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)).
% 8.16/8.60 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))).
% 8.16/8.60 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)))).
% 8.16/8.60 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)))).
% 8.16/8.60 Trying to prove ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 8.16/8.60 Found eq_ref00:=(eq_ref0 ((x two) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) ((x two) three))
% 8.16/8.60 Found (eq_ref0 ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)
% 8.16/8.60 Found eq_ref00:=(eq_ref0 ((x one) two)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) ((x one) two))
% 8.16/8.60 Found (eq_ref0 ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)
% 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)
% 8.16/8.60 Found eta_expansion000:=(eta_expansion00 (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))))
% 8.16/8.60 Found (eta_expansion00 (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b)
% 8.16/8.61 Found ((eta_expansion0 Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b)
% 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b)
% 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b)
% 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b)
% 21.31/21.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.31/21.76 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))), (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))))
% 21.31/21.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.31/21.76 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))
% 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))), (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))))
% 21.31/21.76 Found x01:(P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 21.31/21.76 Found x01:(P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 21.31/21.76 Found x01:(P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 21.31/21.76 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 21.31/21.76 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three)
% 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three)
% 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three)
% 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three)
% 47.72/48.19 Found eq_ref00:=(eq_ref0 ((x one) two)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) ((x one) two))
% 47.72/48.19 Found (eq_ref0 ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b)
% 47.72/48.19 Found x01:(P ((x one) two))
% 47.72/48.19 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 47.72/48.19 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 47.72/48.19 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 47.72/48.19 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two))
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two))
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two))
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two))
% 47.72/48.19 Found eq_ref00:=(eq_ref0 three):(((eq ((fofType->fofType)->(fofType->fofType))) three) three)
% 47.72/48.19 Found (eq_ref0 three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b)
% 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b)
% 47.72/48.19 Found x01:(P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three)
% 47.72/48.19 Found x01:(P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three)
% 47.72/48.19 Found x11:(P (((x one) two) x0))
% 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 47.72/48.19 Found x11:(P (((x one) two) x0))
% 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 47.72/48.19 Found x01:(P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three)
% 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three)
% 47.72/48.19 Found eta_expansion000:=(eta_expansion00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1)))
% 47.72/48.19 Found (eta_expansion00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 47.72/48.19 Found ((eta_expansion0 fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 47.72/48.19 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 47.72/48.19 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 47.72/48.19 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found eq_ref00:=(eq_ref0 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (((x one) two) x0))
% 100.79/101.29 Found (eq_ref0 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 100.79/101.29 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 100.79/101.29 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 100.79/101.29 Found x11:(P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 100.79/101.29 Found x11:(P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 100.79/101.29 Found x11:(P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 100.79/101.29 Found x11:(P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 100.79/101.29 Found x11:(P ((((x one) two) x0) y))
% 100.79/101.29 Found (fun (x11:(P ((((x one) two) x0) y)))=> x11) as proof of (P ((((x one) two) x0) y))
% 100.79/101.29 Found (fun (x11:(P ((((x one) two) x0) y)))=> x11) as proof of (P0 ((((x one) two) x0) y))
% 100.79/101.29 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) y)):(((eq fofType) ((((x one) two) x0) y)) ((((x one) two) x0) y))
% 100.79/101.29 Found (eq_ref0 ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 100.79/101.29 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.79/101.29 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) y))
% 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 100.79/101.29 Found x11:(P (three x0))
% 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 100.79/101.29 Found x11:(P (three x0))
% 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 100.79/101.29 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 100.79/101.29 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 100.79/101.29 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 100.79/101.29 Found eta_expansion000:=(eta_expansion00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x)))
% 100.79/101.29 Found (eta_expansion00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eta_expansion0 fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found eq_ref00:=(eq_ref0 (three x0)):(((eq (fofType->fofType)) (three x0)) (three x0))
% 102.76/103.25 Found (eq_ref0 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found eta_expansion000:=(eta_expansion00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x)))
% 102.76/103.25 Found (eta_expansion00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eta_expansion0 fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found eta_expansion_dep000:=(eta_expansion_dep00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x)))
% 102.76/103.25 Found (eta_expansion_dep00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b)
% 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x11:(P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0))
% 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0))
% 120.05/120.56 Found x21:(P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1))
% 120.05/120.56 Found x21:(P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1))
% 120.05/120.56 Found x21:(P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1))
% 120.05/120.56 Found x21:(P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1))
% 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1))
% 120.05/120.56 Found x11:(P ((three x0) y))
% 120.05/120.56 Found (fun (x11:(P ((three x0) y)))=> x11) as proof of (P ((three x0) y))
% 120.05/120.56 Found (fun (x11:(P ((three x0) y)))=> x11) as proof of (P0 ((three x0) y))
% 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1))
% 120.05/120.56 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 120.05/120.56 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1))
% 120.05/120.56 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 120.05/120.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 120.05/120.56 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1))
% 200.88/201.41 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1))
% 200.88/201.41 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b)
% 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1))
% 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found eq_ref00:=(eq_ref0 ((three x0) y)):(((eq fofType) ((three x0) y)) ((three x0) y))
% 200.88/201.41 Found (eq_ref0 ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found eq_ref00:=(eq_ref0 ((three x0) y)):(((eq fofType) ((three x0) y)) ((three x0) y))
% 200.88/201.41 Found (eq_ref0 ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b)
% 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y))
% 200.88/201.41 Found eta_expansion_dep000:=(eta_expansion_dep00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1)))
% 200.88/201.41 Found (eta_expansion_dep00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 200.88/201.41 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 207.35/207.92 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 207.35/207.92 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0))
% 207.35/207.92 Found eta_expansion000:=(eta_expansion00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1)))
% 207.35/207.92 Found (eta_expansion00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found ((eta_expansion0 fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b)
% 207.35/207.92 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> (a x)))
% 207.35/207.92 Found (eta_expansion_dep00 a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b)
% 207.35/207.92 Found ((eta_expansion_dep0 (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b)
% 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b)
% 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b)
% 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b)
% 207.35/207.92 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> (b x)))
% 207.52/208.12 Found (eta_expansion_dep00 b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 207.52/208.12 Found ((eta_expansion_dep0 (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 207.52/208.12 Found eq_ref00:=(eq_ref0 b):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) b)
% 207.52/208.12 Found (eq_ref0 b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))
% 229.87/230.41 Found x11:(P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 229.87/230.41 Found x11:(P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 229.87/230.41 Found x11:(P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 229.87/230.41 Found x11:(P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0))
% 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0))
% 229.87/230.41 Found eq_ref00:=(eq_ref0 (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)):(((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))
% 229.87/230.41 Found (eq_ref0 (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b)
% 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b)
% 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b)
% 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b)
% 229.87/230.41 Found x21:(P ((three x0) x1))
% 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 229.87/230.41 Found x21:(P ((three x0) x1))
% 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found x21:(P ((three x0) x1))
% 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found x21:(P ((three x0) x1))
% 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found x21:(P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 236.28/236.81 Found x21:(P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 236.28/236.81 Found x21:(P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 236.28/236.81 Found x21:(P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1))
% 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1))
% 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1))
% 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b)
% 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1))
% 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) y))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y))
% 290.02/290.60 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) y)):(((eq fofType) ((((x one) two) x0) y)) ((((x one) two) x0) y))
% 290.02/290.60 Found (eq_ref0 ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b)
% 290.02/290.60 Found x01:(P ((x one) two))
% 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 290.02/290.60 Found x01:(P ((x one) two))
% 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two))
% 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two))
% 290.02/290.60 Found x0:(P ((x one) two))
% 290.02/290.60 Instantiate: b:=((x one) two):((fofType->fofType)->(fofType->fofType))
% 290.02/290.60 Found x0 as proof of (P0 b)
% 290.02/290.60 Found eta_expansion000:=(eta_expansion00 three):(((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (x:(fofType->fofType))=> (three x)))
% 290.02/290.60 Found (eta_expansion00
%------------------------------------------------------------------------------