TSTP Solution File: NUM667^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM667^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n069.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:22 EST 2018
% Result : Theorem 55.72s
% Output : Proof 55.72s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM667^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.24 % Computer : n069.star.cs.uiowa.edu
% 0.02/0.24 % Model : x86_64 x86_64
% 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24 % Memory : 32218.625MB
% 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24 % CPULimit : 300
% 0.02/0.24 % DateTime : Fri Jan 5 12:13:22 CST 2018
% 0.02/0.24 % CPUTime :
% 0.08/0.31 Python 2.7.13
% 9.02/9.66 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 9.02/9.66 FOF formula (<kernel.Constant object at 0x2b097f34bf80>, <kernel.Type object at 0x2b097f34bea8>) of role type named nat_type
% 9.02/9.66 Using role type
% 9.02/9.66 Declaring nat:Type
% 9.02/9.66 FOF formula (<kernel.Constant object at 0x2b097f3cc680>, <kernel.Constant object at 0x2b097f34be60>) of role type named x
% 9.02/9.66 Using role type
% 9.02/9.66 Declaring x:nat
% 9.02/9.66 FOF formula (<kernel.Constant object at 0x2b097f34bd88>, <kernel.Constant object at 0x2b097f34be60>) of role type named y
% 9.02/9.66 Using role type
% 9.02/9.66 Declaring y:nat
% 9.02/9.66 FOF formula (<kernel.Constant object at 0x2b097f34bf80>, <kernel.Constant object at 0x2b097f34be60>) of role type named z
% 9.02/9.66 Using role type
% 9.02/9.66 Declaring z:nat
% 9.02/9.66 FOF formula (<kernel.Constant object at 0x2b097f34b320>, <kernel.DependentProduct object at 0x2b097f34b3f8>) of role type named less
% 9.02/9.66 Using role type
% 9.02/9.66 Declaring less:(nat->(nat->Prop))
% 9.02/9.66 FOF formula ((((less x) y)->False)->(((eq nat) x) y)) of role axiom named l
% 9.02/9.66 A new axiom: ((((less x) y)->False)->(((eq nat) x) y))
% 9.02/9.66 FOF formula ((((less y) z)->False)->(((eq nat) y) z)) of role axiom named k
% 9.02/9.66 A new axiom: ((((less y) z)->False)->(((eq nat) y) z))
% 9.02/9.66 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et
% 9.02/9.66 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa))
% 9.02/9.66 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((((less Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((less Xy) Xz)->((less Xx) Xz)))) of role axiom named satz16a
% 9.02/9.66 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((((less Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((less Xy) Xz)->((less Xx) Xz))))
% 9.02/9.66 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->(((((less Xy) Xz)->False)->(((eq nat) Xy) Xz))->((less Xx) Xz)))) of role axiom named satz16b
% 9.02/9.66 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->(((((less Xy) Xz)->False)->(((eq nat) Xy) Xz))->((less Xx) Xz))))
% 9.02/9.66 FOF formula ((((less x) z)->False)->(((eq nat) x) z)) of role conjecture named satz17
% 9.02/9.66 Conjecture to prove = ((((less x) z)->False)->(((eq nat) x) z)):Prop
% 9.02/9.66 We need to prove ['((((less x) z)->False)->(((eq nat) x) z))']
% 9.02/9.66 Parameter nat:Type.
% 9.02/9.66 Parameter x:nat.
% 9.02/9.66 Parameter y:nat.
% 9.02/9.66 Parameter z:nat.
% 9.02/9.66 Parameter less:(nat->(nat->Prop)).
% 9.02/9.66 Axiom l:((((less x) y)->False)->(((eq nat) x) y)).
% 9.02/9.66 Axiom k:((((less y) z)->False)->(((eq nat) y) z)).
% 9.02/9.66 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)).
% 9.02/9.66 Axiom satz16a:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((((less Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((less Xy) Xz)->((less Xx) Xz)))).
% 9.02/9.66 Axiom satz16b:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->(((((less Xy) Xz)->False)->(((eq nat) Xy) Xz))->((less Xx) Xz)))).
% 9.02/9.66 Trying to prove ((((less x) z)->False)->(((eq nat) x) z))
% 9.02/9.66 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 9.02/9.66 Found (eq_ref00 P) as proof of (P0 x)
% 9.02/9.66 Found ((eq_ref0 x) P) as proof of (P0 x)
% 9.02/9.66 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 9.02/9.66 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 9.02/9.66 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 9.02/9.66 Found (eq_ref00 P) as proof of (P0 x)
% 9.02/9.66 Found ((eq_ref0 x) P) as proof of (P0 x)
% 9.02/9.66 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 9.02/9.66 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 9.02/9.66 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 9.02/9.66 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 9.02/9.66 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 9.02/9.66 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 9.02/9.66 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 9.02/9.66 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 9.02/9.66 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 30.41/31.09 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.41/31.09 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.41/31.09 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.50/31.13 Found x00:False
% 30.50/31.13 Found (fun (x01:((((eq nat) x) z)->False))=> x00) as proof of False
% 30.50/31.13 Found (fun (x01:((((eq nat) x) z)->False))=> x00) as proof of (((((eq nat) x) z)->False)->False)
% 30.50/31.13 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 30.50/31.13 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 30.50/31.13 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found x00:False
% 30.50/31.13 Found (fun (x01:(((P x)->(P z))->False))=> x00) as proof of False
% 30.50/31.13 Found (fun (x01:(((P x)->(P z))->False))=> x00) as proof of ((((P x)->(P z))->False)->False)
% 30.50/31.13 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found x01:False
% 30.50/31.13 Found (fun (x1:((P z)->False))=> x01) as proof of False
% 30.50/31.13 Found (fun (x1:((P z)->False))=> x01) as proof of (((P z)->False)->False)
% 30.50/31.13 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 30.50/31.13 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 30.50/31.13 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 30.50/31.13 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 30.50/31.13 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 30.50/31.13 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.50/31.13 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.50/31.13 Found x00:False
% 30.50/31.13 Found (fun (x01:((((eq nat) x) z)->False))=> x00) as proof of False
% 30.50/31.13 Found (fun (x01:((((eq nat) x) z)->False))=> x00) as proof of (((((eq nat) x) z)->False)->False)
% 30.50/31.13 Found (et0 (fun (x01:((((eq nat) x) z)->False))=> x00)) as proof of (((eq nat) x) z)
% 30.50/31.13 Found ((et (((eq nat) x) z)) (fun (x01:((((eq nat) x) z)->False))=> x00)) as proof of (((eq nat) x) z)
% 30.50/31.13 Found ((et (((eq nat) x) z)) (fun (x01:((((eq nat) x) z)->False))=> x00)) as proof of (((eq nat) x) z)
% 30.50/31.13 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 30.50/31.13 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 30.50/31.13 Found x00:False
% 30.50/31.13 Found (fun (x01:(((P x)->(P z))->False))=> x00) as proof of False
% 30.50/31.13 Found (fun (x01:(((P x)->(P z))->False))=> x00) as proof of ((((P x)->(P z))->False)->False)
% 30.50/31.13 Found (et0 (fun (x01:(((P x)->(P z))->False))=> x00)) as proof of ((P x)->(P z))
% 30.50/31.13 Found ((et ((P x)->(P z))) (fun (x01:(((P x)->(P z))->False))=> x00)) as proof of ((P x)->(P z))
% 30.50/31.13 Found ((et ((P x)->(P z))) (fun (x01:(((P x)->(P z))->False))=> x00)) as proof of ((P x)->(P z))
% 30.50/31.13 Found x01:False
% 30.50/31.13 Found (fun (x1:((P z)->False))=> x01) as proof of False
% 55.21/55.80 Found (fun (x1:((P z)->False))=> x01) as proof of (((P z)->False)->False)
% 55.21/55.80 Found (et0 (fun (x1:((P z)->False))=> x01)) as proof of (P z)
% 55.21/55.80 Found ((et (P z)) (fun (x1:((P z)->False))=> x01)) as proof of (P z)
% 55.21/55.80 Found ((et (P z)) (fun (x1:((P z)->False))=> x01)) as proof of (P z)
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found x00:False
% 55.21/55.80 Found (fun (x01:((((eq nat) z) x)->False))=> x00) as proof of False
% 55.21/55.80 Found (fun (x01:((((eq nat) z) x)->False))=> x00) as proof of (((((eq nat) z) x)->False)->False)
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found x00:False
% 55.21/55.80 Found (fun (x01:(((P z)->(P x))->False))=> x00) as proof of False
% 55.21/55.80 Found (fun (x01:(((P z)->(P x))->False))=> x00) as proof of ((((P z)->(P x))->False)->False)
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found x01:False
% 55.21/55.80 Found (fun (x02:((P x)->False))=> x01) as proof of False
% 55.21/55.80 Found (fun (x02:((P x)->False))=> x01) as proof of (((P x)->False)->False)
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l0:(((eq nat) x) y)
% 55.21/55.80 Found l0 as proof of (P y)
% 55.21/55.80 Found x00:False
% 55.21/55.80 Found (fun (x1:((less y) z))=> x00) as proof of False
% 55.21/55.80 Found (fun (x1:((less y) z))=> x00) as proof of (((less y) z)->False)
% 55.21/55.80 Found l:((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found l as proof of ((((less x) y)->False)->(((eq nat) x) y))
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k:((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found k as proof of ((((less y) z)->False)->(((eq nat) y) z))
% 55.21/55.80 Found satz16a00000:=(satz16a0000 x1):((less x) z)
% 55.21/55.80 Found (satz16a0000 x1) as proof of ((less x) z)
% 55.21/55.80 Found ((satz16a000 l) x1) as proof of ((less x) z)
% 55.21/55.80 Found (((satz16a00 y) l) x1) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> ((satz16a0 Xy) z)) y) l) x1) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1) as proof of ((less x) z)
% 55.21/55.80 Found (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)) as proof of False
% 55.21/55.80 Found (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1))) as proof of False
% 55.21/55.80 Found (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1))) as proof of (((less y) z)->False)
% 55.21/55.80 Found satz16b00000:=(satz16b0000 k):((less x) z)
% 55.21/55.80 Found (satz16b0000 k) as proof of ((less x) z)
% 55.21/55.80 Found ((satz16b000 x1) k) as proof of ((less x) z)
% 55.21/55.80 Found (((satz16b00 y) x1) k) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> ((satz16b0 Xy) z)) y) x1) k) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k) as proof of ((less x) z)
% 55.21/55.80 Found ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k) as proof of ((less x) z)
% 55.21/55.80 Found (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k)) as proof of False
% 55.21/55.80 Found (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))) as proof of False
% 55.21/55.80 Found (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))) as proof of (((less x) y)->False)
% 55.21/55.80 Found (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k)))) as proof of (P y)
% 55.21/55.80 Found (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k)))) as proof of (P y)
% 55.21/55.80 Found ((k0 (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))))) as proof of (((eq nat) x) z)
% 55.72/56.32 Found ((k0 (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))))) as proof of (((eq nat) x) z)
% 55.72/56.32 Found (((fun (x1:(((less y) z)->False))=> ((k x1) ((eq nat) x))) (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))))) as proof of (((eq nat) x) z)
% 55.72/56.32 Found (fun (x0:(((less x) z)->False))=> (((fun (x1:(((less y) z)->False))=> ((k x1) ((eq nat) x))) (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k)))))) as proof of (((eq nat) x) z)
% 55.72/56.32 Found (fun (x0:(((less x) z)->False))=> (((fun (x1:(((less y) z)->False))=> ((k x1) ((eq nat) x))) (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k)))))) as proof of ((((less x) z)->False)->(((eq nat) x) z))
% 55.72/56.32 Got proof (fun (x0:(((less x) z)->False))=> (((fun (x1:(((less y) z)->False))=> ((k x1) ((eq nat) x))) (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))))))
% 55.72/56.32 Time elapsed = 54.847651s
% 55.72/56.32 node=15340 cost=613.000000 depth=15
% 55.72/56.32::::::::::::::::::::::
% 55.72/56.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.72/56.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.72/56.32 (fun (x0:(((less x) z)->False))=> (((fun (x1:(((less y) z)->False))=> ((k x1) ((eq nat) x))) (fun (x1:((less y) z))=> (x0 ((((fun (Xy:nat)=> (((satz16a x) Xy) z)) y) l) x1)))) (l (fun (x1:((less x) y))=> (x0 ((((fun (Xy:nat)=> (((satz16b x) Xy) z)) y) x1) k))))))
% 55.72/56.32 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------