TSTP Solution File: NUM016^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM016^5 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n101.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 294.09s
% 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 : NUM016^5 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n101.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 14:57:16 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.24 Python 2.7.13
% 0.07/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab34819c5f0>, <kernel.Constant object at 0x2ab34819cc68>) of role type named a
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring a:fofType
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab348893b00>, <kernel.DependentProduct object at 0x2ab3488ba5f0>) of role type named factorial_plus_one
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring factorial_plus_one:(fofType->fofType)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab34819c1b8>, <kernel.DependentProduct object at 0x2ab3488ba5f0>) of role type named less
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring less:(fofType->(fofType->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab34819cf38>, <kernel.DependentProduct object at 0x2ab3488ba878>) of role type named prime
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring prime:(fofType->Prop)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab34819c5f0>, <kernel.DependentProduct object at 0x2ab3488ae6c8>) of role type named prime_divisor
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring prime_divisor:(fofType->fofType)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2ab3488ae6c8>, <kernel.DependentProduct object at 0x2ab34819c5f0>) of role type named divides
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring divides:(fofType->(fofType->Prop))
% 0.07/0.51 FOF formula (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a))) (forall (X:fofType), ((or ((or ((prime X)->False)) (((less a) X)->False))) ((less (factorial_plus_one a)) X))))->False) of role conjecture named cNUM016_1
% 0.07/0.51 Conjecture to prove = (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a))) (forall (X:fofType), ((or ((or ((prime X)->False)) (((less a) X)->False))) ((less (factorial_plus_one a)) X))))->False):Prop
% 0.07/0.51 We need to prove ['(((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a))) (forall (X:fofType), ((or ((or ((prime X)->False)) (((less a) X)->False))) ((less (factorial_plus_one a)) X))))->False)']
% 8.39/8.64 Parameter fofType:Type.
% 8.39/8.64 Parameter a:fofType.
% 8.39/8.64 Parameter factorial_plus_one:(fofType->fofType).
% 8.39/8.64 Parameter less:(fofType->(fofType->Prop)).
% 8.39/8.64 Parameter prime:(fofType->Prop).
% 8.39/8.64 Parameter prime_divisor:(fofType->fofType).
% 8.39/8.64 Parameter divides:(fofType->(fofType->Prop)).
% 8.39/8.64 Trying to prove (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a))) (forall (X:fofType), ((or ((or ((prime X)->False)) (((less a) X)->False))) ((less (factorial_plus_one a)) X))))->False)
% 8.39/8.64 Found x3:(prime a)
% 8.39/8.64 Instantiate: X:=a:fofType
% 8.39/8.64 Found x3 as proof of (prime X)
% 8.39/8.64 Found (x5 x3) as proof of False
% 8.39/8.64 Found (fun (x5:((prime X)->False))=> (x5 x3)) as proof of False
% 8.39/8.64 Found (fun (x5:((prime X)->False))=> (x5 x3)) as proof of (((prime X)->False)->False)
% 8.39/8.64 Found x3:(prime a)
% 8.39/8.64 Instantiate: X:=a:fofType
% 8.39/8.64 Found x3 as proof of (prime X)
% 8.39/8.64 Found (x5 x3) as proof of False
% 8.39/8.64 Found (fun (x5:(not (prime X)))=> (x5 x3)) as proof of False
% 8.39/8.64 Found (fun (x5:(not (prime X)))=> (x5 x3)) as proof of ((not (prime X))->False)
% 8.39/8.64 Found x3:((prime X)->False)
% 8.39/8.64 Instantiate: X:=a:fofType
% 8.39/8.64 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of ((prime a)->False)
% 8.39/8.64 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 8.39/8.64 Found (and_rect10 (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 8.39/8.64 Found ((and_rect1 False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 8.39/8.64 Found (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 8.39/8.65 Found (fun (x3:((prime X)->False))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of False
% 8.39/8.65 Found (fun (x3:((prime X)->False))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of (((prime X)->False)->False)
% 10.33/10.57 Found x3:(not (prime X))
% 10.33/10.57 Instantiate: X:=a:fofType
% 10.33/10.57 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of ((prime a)->False)
% 10.33/10.57 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 10.33/10.57 Found (and_rect10 (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 10.33/10.57 Found ((and_rect1 False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 10.33/10.57 Found (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 10.33/10.58 Found (fun (x3:(not (prime X)))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of False
% 10.33/10.58 Found (fun (x3:(not (prime X)))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of ((not (prime X))->False)
% 27.81/28.03 Found x4:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x4 as proof of (prime X)
% 27.81/28.03 Found (x5 x4) as proof of False
% 27.81/28.03 Found (fun (x5:((prime X)->False))=> (x5 x4)) as proof of False
% 27.81/28.03 Found (fun (x5:((prime X)->False))=> (x5 x4)) as proof of (((prime X)->False)->False)
% 27.81/28.03 Found x3:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x3 as proof of (prime X)
% 27.81/28.03 Found (x7 x3) as proof of False
% 27.81/28.03 Found (fun (x7:((prime X)->False))=> (x7 x3)) as proof of False
% 27.81/28.03 Found (fun (x7:((prime X)->False))=> (x7 x3)) as proof of (((prime X)->False)->False)
% 27.81/28.03 Found x4:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x4 as proof of (prime X)
% 27.81/28.03 Found (x5 x4) as proof of False
% 27.81/28.03 Found (fun (x5:(not (prime X)))=> (x5 x4)) as proof of False
% 27.81/28.03 Found (fun (x5:(not (prime X)))=> (x5 x4)) as proof of ((not (prime X))->False)
% 27.81/28.03 Found x3:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x3 as proof of (prime X)
% 27.81/28.03 Found (x7 x3) as proof of False
% 27.81/28.03 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of False
% 27.81/28.03 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of ((not (prime X))->False)
% 27.81/28.03 Found x3:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x3 as proof of (prime X)
% 27.81/28.03 Found (x7 x3) as proof of False
% 27.81/28.03 Found (fun (x7:((prime X)->False))=> (x7 x3)) as proof of False
% 27.81/28.03 Found (fun (x7:((prime X)->False))=> (x7 x3)) as proof of (((prime X)->False)->False)
% 27.81/28.03 Found x3:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x3 as proof of (prime X)
% 27.81/28.03 Found (x9 x3) as proof of False
% 27.81/28.03 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of False
% 27.81/28.03 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of (((prime X)->False)->False)
% 27.81/28.03 Found x3:(prime a)
% 27.81/28.03 Instantiate: X:=a:fofType
% 27.81/28.03 Found x3 as proof of (prime X)
% 27.81/28.03 Found (x7 x3) as proof of False
% 27.81/28.03 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of False
% 27.81/28.03 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of ((not (prime X))->False)
% 27.81/28.03 Found x30:False
% 27.81/28.03 Found (fun (x5:(prime a))=> x30) as proof of False
% 27.81/28.03 Found (fun (x5:(prime a))=> x30) as proof of ((prime a)->False)
% 27.81/28.03 Found x30:False
% 27.81/28.03 Found (fun (x5:(prime a))=> x30) as proof of False
% 27.81/28.03 Found (fun (x5:(prime a))=> x30) as proof of ((prime a)->False)
% 27.81/28.03 Found x30:False
% 27.81/28.03 Found (fun (x5:(prime a))=> x30) as proof of False
% 27.81/28.03 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (x5:(prime a))=> x30) as proof of ((prime a)->False)
% 28.78/29.03 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (x5:(prime a))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 28.78/29.03 Found x30:False
% 28.78/29.03 Found (fun (x5:(prime a))=> x30) as proof of False
% 28.78/29.03 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (x5:(prime a))=> x30) as proof of ((prime a)->False)
% 28.78/29.03 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (x5:(prime a))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 47.70/48.00 Found x3:(prime a)
% 47.70/48.00 Instantiate: X:=a:fofType
% 47.70/48.00 Found x3 as proof of (prime X)
% 47.70/48.00 Found (x9 x3) as proof of False
% 47.70/48.00 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of False
% 47.70/48.00 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of ((not (prime X))->False)
% 47.70/48.00 Found x4:(prime a)
% 47.70/48.00 Instantiate: X:=a:fofType
% 47.70/48.00 Found x4 as proof of (prime X)
% 47.70/48.00 Found (x7 x4) as proof of False
% 47.70/48.00 Found (fun (x7:((prime X)->False))=> (x7 x4)) as proof of False
% 47.70/48.00 Found (fun (x7:((prime X)->False))=> (x7 x4)) as proof of (((prime X)->False)->False)
% 47.70/48.00 Found x4:(prime a)
% 47.70/48.00 Instantiate: X:=a:fofType
% 47.70/48.00 Found x4 as proof of (prime X)
% 47.70/48.00 Found (x7 x4) as proof of False
% 47.70/48.00 Found (fun (x7:(not (prime X)))=> (x7 x4)) as proof of False
% 47.70/48.00 Found (fun (x7:(not (prime X)))=> (x7 x4)) as proof of ((not (prime X))->False)
% 47.70/48.00 Found x3:(prime a)
% 47.70/48.00 Instantiate: X:=a:fofType
% 47.70/48.00 Found x3 as proof of (prime X)
% 47.70/48.00 Found (x9 x3) as proof of False
% 47.70/48.00 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of False
% 47.70/48.00 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of (((prime X)->False)->False)
% 47.70/48.00 Found x50:False
% 47.70/48.00 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 47.70/48.00 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 47.70/48.00 Found x50:False
% 47.70/48.00 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 47.70/48.00 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 47.70/48.00 Found x50:False
% 47.70/48.00 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 47.70/48.00 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 47.70/48.00 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 50.58/50.88 Found x3:(prime a)
% 50.58/50.88 Instantiate: X:=a:fofType
% 50.58/50.88 Found x3 as proof of (prime X)
% 50.58/50.88 Found (x9 x3) as proof of False
% 50.58/50.88 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of False
% 50.58/50.88 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of ((not (prime X))->False)
% 50.58/50.88 Found x50:False
% 50.58/50.88 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 50.58/50.88 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 50.58/50.88 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 50.58/50.88 Found x3:(prime a)
% 50.58/50.88 Instantiate: X:=a:fofType
% 50.58/50.88 Found x3 as proof of (prime X)
% 50.58/50.88 Found (x12 x3) as proof of False
% 50.58/50.88 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of False
% 50.58/50.88 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of (((prime X)->False)->False)
% 63.07/63.31 Found x3:(prime a)
% 63.07/63.31 Instantiate: X:=a:fofType
% 63.07/63.31 Found x3 as proof of (prime X)
% 63.07/63.31 Found (x9 x3) as proof of False
% 63.07/63.31 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of False
% 63.07/63.31 Found (fun (x9:((prime X)->False))=> (x9 x3)) as proof of (((prime X)->False)->False)
% 63.07/63.31 Found x30:False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 63.07/63.31 Found x30:False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 63.07/63.31 Found x3:(prime a)
% 63.07/63.31 Instantiate: X:=a:fofType
% 63.07/63.31 Found x3 as proof of (prime X)
% 63.07/63.31 Found (x12 x3) as proof of False
% 63.07/63.31 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of False
% 63.07/63.31 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of ((not (prime X))->False)
% 63.07/63.31 Found x30:False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of False
% 63.07/63.31 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 63.07/63.31 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 63.07/63.31 Found x30:False
% 63.07/63.31 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of False
% 63.07/63.31 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 68.30/68.61 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 68.30/68.61 Found x50:False
% 68.30/68.61 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 68.30/68.61 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 68.30/68.61 Found x50:False
% 68.30/68.61 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 68.30/68.61 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 68.30/68.61 Found x50:False
% 68.30/68.61 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 68.30/68.61 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 71.17/71.47 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 71.17/71.47 Found x3:(prime a)
% 71.17/71.47 Instantiate: X:=a:fofType
% 71.17/71.47 Found x3 as proof of (prime X)
% 71.17/71.47 Found (x9 x3) as proof of False
% 71.17/71.47 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of False
% 71.17/71.47 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of ((not (prime X))->False)
% 71.17/71.47 Found x3:(prime a)
% 71.17/71.47 Instantiate: X:=a:fofType
% 71.17/71.47 Found x3 as proof of (prime X)
% 71.17/71.47 Found (x5 x3) as proof of False
% 71.17/71.47 Found (fun (x5:(not (prime X)))=> (x5 x3)) as proof of False
% 71.17/71.47 Found (fun (x5:(not (prime X)))=> (x5 x3)) as proof of ((not (prime X))->False)
% 71.17/71.47 Found x50:False
% 71.17/71.47 Found (fun (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of False
% 71.17/71.47 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False)
% 71.17/71.47 Found (fun (x6:((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (x7:(forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))->((forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))->False))
% 86.88/87.19 Found x3:(prime a)
% 86.88/87.19 Instantiate: X:=a:fofType
% 86.88/87.19 Found x3 as proof of (prime X)
% 86.88/87.19 Found (x12 x3) as proof of False
% 86.88/87.19 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of False
% 86.88/87.19 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of (((prime X)->False)->False)
% 86.88/87.19 Found x4:(prime a)
% 86.88/87.19 Instantiate: X:=a:fofType
% 86.88/87.19 Found x4 as proof of (prime X)
% 86.88/87.19 Found (x9 x4) as proof of False
% 86.88/87.19 Found (fun (x9:((prime X)->False))=> (x9 x4)) as proof of False
% 86.88/87.19 Found (fun (x9:((prime X)->False))=> (x9 x4)) as proof of (((prime X)->False)->False)
% 86.88/87.19 Found x70:False
% 86.88/87.19 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 86.88/87.19 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 86.88/87.19 Found x70:False
% 86.88/87.19 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 86.88/87.19 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 86.88/87.19 Found x70:False
% 86.88/87.19 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 86.88/87.19 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 86.88/87.19 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 89.46/89.77 Found x3:(not (prime X))
% 89.46/89.77 Instantiate: X:=a:fofType
% 89.46/89.77 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of ((prime a)->False)
% 89.46/89.77 Found (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 89.46/89.77 Found (and_rect10 (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 89.46/89.77 Found ((and_rect1 False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 89.46/89.77 Found (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3)) as proof of False
% 89.46/89.77 Found (fun (x3:(not (prime X)))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of False
% 89.55/89.78 Found (fun (x3:(not (prime X)))=> (((fun (P:Type) (x4:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x4) x0)) False) (fun (x4:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x3))) as proof of ((not (prime X))->False)
% 109.24/109.55 Found x70:False
% 109.24/109.55 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 109.24/109.55 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 109.24/109.55 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 109.24/109.55 Found x3:(prime a)
% 109.24/109.55 Instantiate: X:=a:fofType
% 109.24/109.55 Found x3 as proof of (prime X)
% 109.24/109.55 Found (x12 x3) as proof of False
% 109.24/109.55 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of False
% 109.24/109.55 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of ((not (prime X))->False)
% 109.24/109.55 Found x4:(prime a)
% 109.24/109.55 Instantiate: X:=a:fofType
% 109.24/109.55 Found x4 as proof of (prime X)
% 109.24/109.55 Found (x9 x4) as proof of False
% 109.24/109.55 Found (fun (x9:(not (prime X)))=> (x9 x4)) as proof of False
% 109.24/109.55 Found (fun (x9:(not (prime X)))=> (x9 x4)) as proof of ((not (prime X))->False)
% 109.24/109.55 Found x50:False
% 109.24/109.55 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 109.24/109.55 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 109.24/109.55 Found x3:(prime a)
% 109.24/109.55 Instantiate: X:=a:fofType
% 109.24/109.55 Found x3 as proof of (prime X)
% 109.24/109.55 Found (x14 x3) as proof of False
% 109.24/109.55 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of False
% 109.24/109.55 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of (((prime X)->False)->False)
% 109.24/109.55 Found x50:False
% 109.24/109.55 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 109.24/109.55 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 109.24/109.55 Found x4:(prime a)
% 109.24/109.55 Instantiate: X:=a:fofType
% 109.24/109.55 Found x4 as proof of (prime X)
% 109.24/109.55 Found (x5 x4) as proof of False
% 109.24/109.55 Found (fun (x5:(not (prime X)))=> (x5 x4)) as proof of False
% 117.05/117.36 Found (fun (x5:(not (prime X)))=> (x5 x4)) as proof of ((not (prime X))->False)
% 117.05/117.36 Found x50:False
% 117.05/117.36 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 117.05/117.36 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 117.05/117.36 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 117.05/117.36 Found x3:(prime a)
% 117.05/117.36 Instantiate: X:=a:fofType
% 117.05/117.36 Found x3 as proof of (prime X)
% 117.05/117.36 Found (x12 x3) as proof of False
% 117.05/117.36 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of False
% 117.05/117.36 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of (((prime X)->False)->False)
% 117.05/117.36 Found x50:False
% 117.05/117.36 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 117.05/117.36 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 117.05/117.36 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 124.68/124.94 Found x70:False
% 124.68/124.94 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 124.68/124.94 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 124.68/124.94 Found x3:(prime a)
% 124.68/124.94 Instantiate: X:=a:fofType
% 124.68/124.94 Found x3 as proof of (prime X)
% 124.68/124.94 Found (x7 x3) as proof of False
% 124.68/124.94 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of False
% 124.68/124.94 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of ((not (prime X))->False)
% 124.68/124.94 Found x70:False
% 124.68/124.94 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 124.68/124.94 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 124.68/124.94 Found x70:False
% 124.68/124.94 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 124.68/124.94 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 124.68/124.94 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 129.85/130.11 Found x30:False
% 129.85/130.11 Found (fun (x4:((less (factorial_plus_one a)) X0))=> x30) as proof of False
% 129.85/130.11 Found (fun (x4:((less (factorial_plus_one a)) X0))=> x30) as proof of (((less (factorial_plus_one a)) X0)->False)
% 129.85/130.11 Found x30:False
% 129.85/130.11 Found (fun (x4:((or ((prime X0)->False)) (((less a) X0)->False)))=> x30) as proof of False
% 129.85/130.11 Found (fun (x4:((or ((prime X0)->False)) (((less a) X0)->False)))=> x30) as proof of (((or ((prime X0)->False)) (((less a) X0)->False))->False)
% 129.85/130.11 Found x70:False
% 129.85/130.11 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 129.85/130.11 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 129.85/130.11 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 129.85/130.11 Found x3:(prime a)
% 129.85/130.11 Instantiate: X:=a:fofType
% 129.85/130.11 Found x3 as proof of (prime X)
% 129.85/130.11 Found (x14 x3) as proof of False
% 129.85/130.11 Found (fun (x14:(not (prime X)))=> (x14 x3)) as proof of False
% 129.85/130.11 Found (fun (x14:(not (prime X)))=> (x14 x3)) as proof of ((not (prime X))->False)
% 129.85/130.11 Found x30:False
% 129.85/130.11 Found (fun (x4:((less (factorial_plus_one a)) X0))=> x30) as proof of False
% 129.85/130.11 Found (fun (x4:((less (factorial_plus_one a)) X0))=> x30) as proof of (((less (factorial_plus_one a)) X0)->False)
% 129.85/130.11 Found x30:False
% 129.85/130.11 Found (fun (x4:((or ((prime X0)->False)) (((less a) X0)->False)))=> x30) as proof of False
% 129.85/130.11 Found (fun (x4:((or ((prime X0)->False)) (((less a) X0)->False)))=> x30) as proof of (((or ((prime X0)->False)) (((less a) X0)->False))->False)
% 145.87/146.17 Found x30:False
% 145.87/146.17 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of False
% 145.87/146.17 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 145.87/146.17 Found x3:(prime a)
% 145.87/146.17 Instantiate: X:=a:fofType
% 145.87/146.17 Found x3 as proof of (prime X)
% 145.87/146.17 Found (x12 x3) as proof of False
% 145.87/146.17 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of False
% 145.87/146.17 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of ((not (prime X))->False)
% 145.87/146.17 Found x3:(prime a)
% 145.87/146.17 Instantiate: X0:=a:fofType
% 145.87/146.17 Found x3 as proof of (prime X0)
% 145.87/146.17 Found (x6 x3) as proof of False
% 145.87/146.17 Found (fun (x6:((prime X0)->False))=> (x6 x3)) as proof of False
% 145.87/146.17 Found (fun (x6:((prime X0)->False))=> (x6 x3)) as proof of (((prime X0)->False)->False)
% 145.87/146.17 Found x30:False
% 145.87/146.17 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of False
% 145.87/146.17 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 145.87/146.17 Found x3:(prime a)
% 145.87/146.17 Instantiate: X0:=a:fofType
% 145.87/146.17 Found x3 as proof of (prime X0)
% 145.87/146.17 Found (x6 x3) as proof of False
% 145.87/146.17 Found (fun (x6:((prime X0)->False))=> (x6 x3)) as proof of False
% 145.87/146.17 Found (fun (x6:((prime X0)->False))=> (x6 x3)) as proof of (((prime X0)->False)->False)
% 145.87/146.17 Found x30:False
% 145.87/146.17 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of False
% 145.87/146.17 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 145.87/146.18 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 145.87/146.18 Found x30:False
% 145.87/146.18 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of False
% 145.87/146.18 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 155.74/156.01 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x30) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 155.74/156.01 Found x50:False
% 155.74/156.01 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 155.74/156.01 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 155.74/156.01 Found x50:False
% 155.74/156.01 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 155.74/156.01 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 155.74/156.01 Found x3:(prime a)
% 155.74/156.01 Instantiate: X:=a:fofType
% 155.74/156.01 Found x3 as proof of (prime X)
% 155.74/156.01 Found (x6 x3) as proof of False
% 155.74/156.01 Found (fun (x6:((prime X)->False))=> (x6 x3)) as proof of False
% 155.74/156.01 Found (fun (x6:((prime X)->False))=> (x6 x3)) as proof of (((prime X)->False)->False)
% 155.74/156.01 Found x3:(prime a)
% 155.74/156.01 Instantiate: X:=a:fofType
% 155.74/156.01 Found x3 as proof of (prime X)
% 155.74/156.01 Found (x6 x3) as proof of False
% 155.74/156.01 Found (fun (x6:((prime X)->False))=> (x6 x3)) as proof of False
% 155.74/156.01 Found (fun (x6:((prime X)->False))=> (x6 x3)) as proof of (((prime X)->False)->False)
% 155.74/156.01 Found x50:False
% 155.74/156.01 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 155.74/156.01 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 161.88/162.20 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 161.88/162.20 Found x3:(prime a)
% 161.88/162.20 Instantiate: X:=a:fofType
% 161.88/162.20 Found x3 as proof of (prime X)
% 161.88/162.20 Found (x12 x3) as proof of False
% 161.88/162.20 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of False
% 161.88/162.20 Found (fun (x12:((prime X)->False))=> (x12 x3)) as proof of (((prime X)->False)->False)
% 161.88/162.20 Found x50:False
% 161.88/162.20 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of False
% 161.88/162.20 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 161.88/162.20 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x50) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 173.76/174.06 Found x90:False
% 173.76/174.06 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 173.76/174.06 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 173.76/174.06 Found x3:(prime a)
% 173.76/174.06 Instantiate: X0:=a:fofType
% 173.76/174.06 Found x3 as proof of (prime X0)
% 173.76/174.06 Found (x6 x3) as proof of False
% 173.76/174.06 Found (fun (x6:(not (prime X0)))=> (x6 x3)) as proof of False
% 173.76/174.06 Found (fun (x6:(not (prime X0)))=> (x6 x3)) as proof of ((not (prime X0))->False)
% 173.76/174.06 Found x70:False
% 173.76/174.06 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 173.76/174.06 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 173.76/174.06 Found x3:(prime a)
% 173.76/174.06 Instantiate: X0:=a:fofType
% 173.76/174.06 Found x3 as proof of (prime X0)
% 173.76/174.06 Found (x6 x3) as proof of False
% 173.76/174.06 Found (fun (x6:(not (prime X0)))=> (x6 x3)) as proof of False
% 173.76/174.06 Found (fun (x6:(not (prime X0)))=> (x6 x3)) as proof of ((not (prime X0))->False)
% 173.76/174.06 Found x3:(prime a)
% 173.76/174.06 Instantiate: X:=a:fofType
% 173.76/174.06 Found x3 as proof of (prime X)
% 173.76/174.06 Found (x14 x3) as proof of False
% 173.76/174.06 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of False
% 173.76/174.06 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of (((prime X)->False)->False)
% 173.76/174.06 Found x90:False
% 173.76/174.06 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 173.76/174.06 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 173.76/174.06 Found x70:False
% 173.76/174.06 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 173.76/174.06 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 173.76/174.06 Found x90:False
% 173.76/174.06 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 173.76/174.06 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 173.76/174.06 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 178.31/178.60 Found x70:False
% 178.31/178.60 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 178.31/178.60 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 178.31/178.60 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 178.31/178.60 Found x90:False
% 178.31/178.60 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 178.31/178.60 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 178.31/178.60 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 183.47/183.74 Found x70:False
% 183.47/183.74 Found (fun (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of False
% 183.47/183.74 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False)
% 183.47/183.74 Found (fun (x8:((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (x9:(forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))=> x70) as proof of (((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))->((forall (X:fofType), ((or (prime X)) (prime (prime_divisor X))))->False))
% 183.47/183.74 Found x3:(prime a)
% 183.47/183.74 Instantiate: X:=a:fofType
% 183.47/183.74 Found x3 as proof of (prime X)
% 183.47/183.74 Found (x6 x3) as proof of False
% 183.47/183.74 Found (fun (x6:(not (prime X)))=> (x6 x3)) as proof of False
% 183.47/183.74 Found (fun (x6:(not (prime X)))=> (x6 x3)) as proof of ((not (prime X))->False)
% 183.47/183.74 Found x3:(prime a)
% 183.47/183.74 Instantiate: X:=a:fofType
% 183.47/183.74 Found x3 as proof of (prime X)
% 183.47/183.74 Found (x6 x3) as proof of False
% 183.47/183.74 Found (fun (x6:(not (prime X)))=> (x6 x3)) as proof of False
% 183.47/183.74 Found (fun (x6:(not (prime X)))=> (x6 x3)) as proof of ((not (prime X))->False)
% 209.23/209.50 Found x3:(prime a)
% 209.23/209.50 Instantiate: X:=a:fofType
% 209.23/209.50 Found x3 as proof of (prime X)
% 209.23/209.50 Found (x7 x3) as proof of False
% 209.23/209.50 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of False
% 209.23/209.50 Found (fun (x7:(not (prime X)))=> (x7 x3)) as proof of ((not (prime X))->False)
% 209.23/209.50 Found x3:(prime a)
% 209.23/209.50 Instantiate: X:=a:fofType
% 209.23/209.50 Found x3 as proof of (prime X)
% 209.23/209.50 Found (x12 x3) as proof of False
% 209.23/209.50 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of False
% 209.23/209.50 Found (fun (x12:(not (prime X)))=> (x12 x3)) as proof of ((not (prime X))->False)
% 209.23/209.50 Found x4:(prime a)
% 209.23/209.50 Instantiate: X0:=a:fofType
% 209.23/209.50 Found x4 as proof of (prime X0)
% 209.23/209.50 Found (x6 x4) as proof of False
% 209.23/209.50 Found (fun (x6:((prime X0)->False))=> (x6 x4)) as proof of False
% 209.23/209.50 Found (fun (x6:((prime X0)->False))=> (x6 x4)) as proof of (((prime X0)->False)->False)
% 209.23/209.50 Found x4:(prime a)
% 209.23/209.50 Instantiate: X0:=a:fofType
% 209.23/209.50 Found x4 as proof of (prime X0)
% 209.23/209.50 Found (x6 x4) as proof of False
% 209.23/209.50 Found (fun (x6:((prime X0)->False))=> (x6 x4)) as proof of False
% 209.23/209.50 Found (fun (x6:((prime X0)->False))=> (x6 x4)) as proof of (((prime X0)->False)->False)
% 209.23/209.50 Found x3:(prime a)
% 209.23/209.50 Instantiate: X:=a:fofType
% 209.23/209.50 Found x3 as proof of (prime X)
% 209.23/209.50 Found (x14 x3) as proof of False
% 209.23/209.50 Found (fun (x14:(not (prime X)))=> (x14 x3)) as proof of False
% 209.23/209.50 Found (fun (x14:(not (prime X)))=> (x14 x3)) as proof of ((not (prime X))->False)
% 209.23/209.50 Found x70:False
% 209.23/209.50 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of False
% 209.23/209.50 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 209.23/209.50 Found x4:((prime X0)->False)
% 209.23/209.50 Instantiate: X0:=a:fofType
% 209.23/209.50 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 209.23/209.50 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 209.23/209.50 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 209.23/209.50 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 209.23/209.50 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 209.23/209.51 Found (fun (x4:((prime X0)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 209.23/209.51 Found (fun (x4:((prime X0)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of (((prime X0)->False)->False)
% 210.75/211.07 Found x4:((prime X0)->False)
% 210.75/211.07 Instantiate: X0:=a:fofType
% 210.75/211.07 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 210.75/211.07 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 210.75/211.07 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 210.75/211.07 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 210.75/211.07 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 210.75/211.08 Found (fun (x4:((prime X0)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 210.75/211.08 Found (fun (x4:((prime X0)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of (((prime X0)->False)->False)
% 223.24/223.52 Found x70:False
% 223.24/223.52 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of False
% 223.24/223.52 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 223.24/223.52 Found x70:False
% 223.24/223.52 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of False
% 223.24/223.52 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 223.24/223.52 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 223.24/223.52 Found x4:(prime a)
% 223.24/223.52 Instantiate: X:=a:fofType
% 223.24/223.52 Found x4 as proof of (prime X)
% 223.24/223.52 Found (x12 x4) as proof of False
% 223.24/223.52 Found (fun (x12:((prime X)->False))=> (x12 x4)) as proof of False
% 235.49/235.79 Found (fun (x12:((prime X)->False))=> (x12 x4)) as proof of (((prime X)->False)->False)
% 235.49/235.79 Found x70:False
% 235.49/235.79 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of False
% 235.49/235.79 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 235.49/235.79 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x70) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 235.49/235.79 Found x3:(prime a)
% 235.49/235.79 Instantiate: X:=a:fofType
% 235.49/235.79 Found x3 as proof of (prime X)
% 235.49/235.79 Found (x9 x3) as proof of False
% 235.49/235.79 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of False
% 235.49/235.79 Found (fun (x9:(not (prime X)))=> (x9 x3)) as proof of ((not (prime X))->False)
% 235.49/235.79 Found x90:False
% 235.49/235.79 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 235.49/235.79 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 235.49/235.79 Found x4:(prime a)
% 235.49/235.79 Instantiate: X0:=a:fofType
% 235.49/235.79 Found x4 as proof of (prime X0)
% 235.49/235.79 Found (x6 x4) as proof of False
% 235.49/235.79 Found (fun (x6:(not (prime X0)))=> (x6 x4)) as proof of False
% 235.49/235.79 Found (fun (x6:(not (prime X0)))=> (x6 x4)) as proof of ((not (prime X0))->False)
% 235.49/235.79 Found x4:(prime a)
% 235.49/235.79 Instantiate: X0:=a:fofType
% 235.49/235.79 Found x4 as proof of (prime X0)
% 235.49/235.79 Found (x6 x4) as proof of False
% 235.49/235.79 Found (fun (x6:(not (prime X0)))=> (x6 x4)) as proof of False
% 235.49/235.79 Found (fun (x6:(not (prime X0)))=> (x6 x4)) as proof of ((not (prime X0))->False)
% 235.49/235.79 Found x4:((prime X)->False)
% 235.49/235.79 Instantiate: X:=a:fofType
% 235.49/235.79 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 235.49/235.80 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 235.49/235.80 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 235.49/235.80 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 235.49/235.80 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 235.52/235.80 Found (fun (x4:((prime X)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 236.85/237.17 Found (fun (x4:((prime X)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of (((prime X)->False)->False)
% 236.85/237.17 Found x4:((prime X)->False)
% 236.85/237.17 Instantiate: X:=a:fofType
% 236.85/237.17 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 236.85/237.17 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 236.85/237.17 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 236.85/237.17 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 236.85/237.17 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 236.85/237.17 Found (fun (x4:((prime X)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 240.14/240.44 Found (fun (x4:((prime X)->False))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of (((prime X)->False)->False)
% 240.14/240.44 Found x3:(prime a)
% 240.14/240.44 Instantiate: X:=a:fofType
% 240.14/240.44 Found x3 as proof of (prime X)
% 240.14/240.44 Found (x14 x3) as proof of False
% 240.14/240.44 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of False
% 240.14/240.44 Found (fun (x14:((prime X)->False))=> (x14 x3)) as proof of (((prime X)->False)->False)
% 240.14/240.44 Found x3:(prime a)
% 240.14/240.44 Instantiate: X:=a:fofType
% 240.14/240.44 Found x3 as proof of (prime X)
% 240.14/240.44 Found (x16 x3) as proof of False
% 240.14/240.44 Found (fun (x16:((prime X)->False))=> (x16 x3)) as proof of False
% 240.14/240.44 Found (fun (x16:((prime X)->False))=> (x16 x3)) as proof of (((prime X)->False)->False)
% 240.14/240.44 Found x130:=(x13 a):((less a) (factorial_plus_one a))
% 240.14/240.44 Found (x13 a) as proof of ((less a) X)
% 240.14/240.44 Found (x13 a) as proof of ((less a) X)
% 240.14/240.44 Found (x13 a) as proof of ((less a) X)
% 240.14/240.44 Found (x16 (x13 a)) as proof of False
% 240.14/240.44 Found (fun (x16:(((less a) X)->False))=> (x16 (x13 a))) as proof of False
% 240.14/240.44 Found (fun (x16:(((less a) X)->False))=> (x16 (x13 a))) as proof of ((((less a) X)->False)->False)
% 240.14/240.44 Found x50:False
% 240.14/240.44 Found (fun (x6:((or ((prime X0)->False)) (((less a) X0)->False)))=> x50) as proof of False
% 253.22/253.53 Found (fun (x6:((or ((prime X0)->False)) (((less a) X0)->False)))=> x50) as proof of (((or ((prime X0)->False)) (((less a) X0)->False))->False)
% 253.22/253.53 Found x50:False
% 253.22/253.53 Found (fun (x6:((less (factorial_plus_one a)) X0))=> x50) as proof of False
% 253.22/253.53 Found (fun (x6:((less (factorial_plus_one a)) X0))=> x50) as proof of (((less (factorial_plus_one a)) X0)->False)
% 253.22/253.53 Found x90:False
% 253.22/253.53 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 253.22/253.53 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 253.22/253.53 Found x90:False
% 253.22/253.53 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 253.22/253.53 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 253.22/253.53 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 253.22/253.53 Found x4:(prime a)
% 253.22/253.53 Instantiate: X:=a:fofType
% 253.22/253.53 Found x4 as proof of (prime X)
% 253.22/253.53 Found (x6 x4) as proof of False
% 253.22/253.53 Found (fun (x6:((prime X)->False))=> (x6 x4)) as proof of False
% 253.22/253.53 Found (fun (x6:((prime X)->False))=> (x6 x4)) as proof of (((prime X)->False)->False)
% 253.22/253.53 Found x4:(prime a)
% 253.22/253.53 Instantiate: X:=a:fofType
% 253.22/253.53 Found x4 as proof of (prime X)
% 253.22/253.53 Found (x6 x4) as proof of False
% 253.22/253.53 Found (fun (x6:((prime X)->False))=> (x6 x4)) as proof of False
% 253.22/253.53 Found (fun (x6:((prime X)->False))=> (x6 x4)) as proof of (((prime X)->False)->False)
% 253.22/253.53 Found x50:False
% 253.22/253.53 Found (fun (x6:((less (factorial_plus_one a)) X0))=> x50) as proof of False
% 253.22/253.53 Found (fun (x6:((less (factorial_plus_one a)) X0))=> x50) as proof of (((less (factorial_plus_one a)) X0)->False)
% 253.22/253.53 Found x50:False
% 253.22/253.53 Found (fun (x6:((or ((prime X0)->False)) (((less a) X0)->False)))=> x50) as proof of False
% 253.22/253.53 Found (fun (x6:((or ((prime X0)->False)) (((less a) X0)->False)))=> x50) as proof of (((or ((prime X0)->False)) (((less a) X0)->False))->False)
% 253.22/253.53 Found x4:(not (prime X0))
% 253.22/253.53 Instantiate: X0:=a:fofType
% 253.22/253.53 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 253.22/253.53 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 253.22/253.53 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 253.22/253.53 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 253.25/253.54 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 253.25/253.54 Found (fun (x4:(not (prime X0)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 255.04/255.34 Found (fun (x4:(not (prime X0)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of ((not (prime X0))->False)
% 255.04/255.34 Found x4:(not (prime X0))
% 255.04/255.34 Instantiate: X0:=a:fofType
% 255.04/255.34 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 255.04/255.34 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 255.04/255.34 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 255.04/255.34 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 255.04/255.34 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 255.04/255.35 Found (fun (x4:(not (prime X0)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 258.03/258.37 Found (fun (x4:(not (prime X0)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of ((not (prime X0))->False)
% 258.03/258.37 Found x90:False
% 258.03/258.37 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of False
% 258.03/258.37 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 278.83/279.20 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x90) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 278.83/279.20 Found x50:False
% 278.83/279.20 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of False
% 278.83/279.20 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 278.83/279.20 Found x50:False
% 278.83/279.20 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of False
% 278.83/279.20 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 278.83/279.20 Found x4:(prime a)
% 278.83/279.20 Instantiate: X:=a:fofType
% 278.83/279.20 Found x4 as proof of (prime X)
% 278.83/279.20 Found (x12 x4) as proof of False
% 278.83/279.20 Found (fun (x12:(not (prime X)))=> (x12 x4)) as proof of False
% 278.83/279.20 Found (fun (x12:(not (prime X)))=> (x12 x4)) as proof of ((not (prime X))->False)
% 278.83/279.20 Found x4:(prime a)
% 278.83/279.20 Instantiate: X:=a:fofType
% 278.83/279.20 Found x4 as proof of (prime X)
% 278.83/279.20 Found (x7 x4) as proof of False
% 278.83/279.20 Found (fun (x7:(not (prime X)))=> (x7 x4)) as proof of False
% 278.83/279.20 Found (fun (x7:(not (prime X)))=> (x7 x4)) as proof of ((not (prime X))->False)
% 278.83/279.20 Found x50:False
% 278.83/279.20 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of False
% 278.83/279.20 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 278.83/279.20 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 283.18/283.50 Found x4:(not (prime X))
% 283.18/283.50 Instantiate: X:=a:fofType
% 283.18/283.50 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 283.18/283.50 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 283.18/283.50 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 283.18/283.51 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 283.18/283.51 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 283.18/283.51 Found (fun (x4:(not (prime X)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 283.18/283.51 Found (fun (x4:(not (prime X)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of ((not (prime X))->False)
% 284.20/284.51 Found x4:(not (prime X))
% 284.20/284.51 Instantiate: X:=a:fofType
% 284.20/284.51 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of ((prime a)->False)
% 284.20/284.51 Found (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->False))
% 284.20/284.51 Found (and_rect10 (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 284.20/284.51 Found ((and_rect1 False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 284.20/284.51 Found (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4)) as proof of False
% 284.20/284.51 Found (fun (x4:(not (prime X)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of False
% 284.20/284.51 Found (fun (x4:(not (prime X)))=> (((fun (P:Type) (x5:(((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))->((prime a)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X))))) (prime a)) P) x5) x0)) False) (fun (x5:((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))) (forall (X:fofType), ((or (prime X)) (prime (prime_divisor X)))))) (forall (X:fofType), ((or (prime X)) ((less (prime_divisor X)) X)))))=> x4))) as proof of ((not (prime X))->False)
% 294.09/294.40 Found x3:(prime a)
% 294.09/294.40 Instantiate: X0:=a:fofType
% 294.09/294.40 Found x3 as proof of (prime X0)
% 294.09/294.40 Found (x8 x3) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of (((prime X0)->False)->False)
% 294.09/294.40 Found x3:(prime a)
% 294.09/294.40 Instantiate: X0:=a:fofType
% 294.09/294.40 Found x3 as proof of (prime X0)
% 294.09/294.40 Found (x8 x3) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of (((prime X0)->False)->False)
% 294.09/294.40 Found x3:(prime a)
% 294.09/294.40 Instantiate: X0:=a:fofType
% 294.09/294.40 Found x3 as proof of (prime X0)
% 294.09/294.40 Found (x8 x3) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of (((prime X0)->False)->False)
% 294.09/294.40 Found x3:(prime a)
% 294.09/294.40 Instantiate: X0:=a:fofType
% 294.09/294.40 Found x3 as proof of (prime X0)
% 294.09/294.40 Found (x8 x3) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of False
% 294.09/294.40 Found (fun (x8:((prime X0)->False))=> (x8 x3)) as proof of (((prime X0)->False)->False)
% 294.09/294.40 Found x50:False
% 294.09/294.40 Found (fun (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of False
% 294.09/294.40 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of ((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False)
% 294.09/294.40 Found (fun (x11:((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))) (x12:(forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X))))=> x50) as proof of (((and ((and ((and ((and ((and ((and (forall (X:fofType), (((less X) X)->False))) (forall (X:fofType) (Y:fofType), ((or (((less X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((divides X) X)))) (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((divides X) Y)->False)) (((divides Y) Z)->False))) ((divides X) Z))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) Y)->False)) (((less Y) X)->False))))) (forall (X:fofType), ((less X) (factorial_plus_one X))))) (forall (X:fofType) (Y:fofType), ((or (((divides X) (factorial_plus_one Y))->False)) ((less Y) X))))->((forall (X:fofType), ((or (prime X)) ((divides (prime_divisor X)) X)))->False))
% 294.09/294.40 Found x3
%------------------------------------------------------------------------------