TSTP Solution File: NUM682^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM682^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n085.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 13:11:25 EST 2018
% Result : Theorem 24.65s
% Output : Proof 24.65s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM682^1 : 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 : n085.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 12:31:03 CST 2018
% 0.02/0.24 % CPUTime :
% 0.02/0.27 Python 2.7.13
% 1.25/1.67 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484ed908>, <kernel.Type object at 0x2ae0484ed560>) of role type named nat_type
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring nat:Type
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484f33f8>, <kernel.Constant object at 0x2ae0484edfc8>) of role type named x
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring x:nat
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484ed440>, <kernel.Constant object at 0x2ae0484edfc8>) of role type named y
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring y:nat
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484ed908>, <kernel.Constant object at 0x2ae0484edfc8>) of role type named z
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring z:nat
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484ed4d0>, <kernel.DependentProduct object at 0x2ae0484ed518>) of role type named less
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring less:(nat->(nat->Prop))
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484edb90>, <kernel.DependentProduct object at 0x2ae0484ed488>) of role type named pl
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring pl:(nat->(nat->nat))
% 1.25/1.67 FOF formula ((less ((pl x) z)) ((pl y) z)) of role axiom named l
% 1.25/1.67 A new axiom: ((less ((pl x) z)) ((pl y) z))
% 1.25/1.67 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et
% 1.25/1.67 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa))
% 1.25/1.67 FOF formula (<kernel.Constant object at 0x2ae0484ed368>, <kernel.DependentProduct object at 0x2ae0484ed830>) of role type named more
% 1.25/1.67 Using role type
% 1.25/1.67 Declaring more:(nat->(nat->Prop))
% 1.25/1.67 FOF formula (forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False)) of role axiom named satz10b
% 1.25/1.67 A new axiom: (forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False))
% 1.25/1.67 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((more Xx) Xy)->((more ((pl Xx) Xz)) ((pl Xy) Xz)))) of role axiom named satz19a
% 1.25/1.67 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((more Xx) Xy)->((more ((pl Xx) Xz)) ((pl Xy) Xz))))
% 1.25/1.67 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz)))) of role axiom named satz19b
% 1.25/1.67 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz))))
% 1.25/1.67 FOF formula (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy)))) of role axiom named satz10a
% 1.25/1.67 A new axiom: (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy))))
% 1.25/1.67 FOF formula ((less x) y) of role conjecture named satz20c
% 1.25/1.67 Conjecture to prove = ((less x) y):Prop
% 1.25/1.67 We need to prove ['((less x) y)']
% 1.25/1.67 Parameter nat:Type.
% 1.25/1.67 Parameter x:nat.
% 1.25/1.67 Parameter y:nat.
% 1.25/1.67 Parameter z:nat.
% 1.25/1.67 Parameter less:(nat->(nat->Prop)).
% 1.25/1.67 Parameter pl:(nat->(nat->nat)).
% 1.25/1.67 Axiom l:((less ((pl x) z)) ((pl y) z)).
% 1.25/1.67 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)).
% 1.25/1.67 Parameter more:(nat->(nat->Prop)).
% 1.25/1.67 Axiom satz10b:(forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False)).
% 1.25/1.67 Axiom satz19a:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((more Xx) Xy)->((more ((pl Xx) Xz)) ((pl Xy) Xz)))).
% 1.25/1.67 Axiom satz19b:(forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz)))).
% 1.25/1.67 Axiom satz10a:(forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy)))).
% 1.25/1.67 Trying to prove ((less x) y)
% 1.25/1.67 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 1.25/1.67 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 1.25/1.67 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 1.25/1.67 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 1.25/1.67 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 1.25/1.67 Found l:((less ((pl x) z)) ((pl y) z))
% 1.25/1.67 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 1.25/1.67 Found l as proof of ((less Xx) Xy)
% 11.35/11.73 Found l:((less ((pl x) z)) ((pl y) z))
% 11.35/11.73 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 11.35/11.73 Found l as proof of ((less Xx) Xy)
% 11.35/11.73 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.73 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.73 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found x0:((more x) y)
% 11.35/11.73 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.73 Found x0 as proof of ((more Xx) Xy)
% 11.35/11.73 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.73 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.73 Found x0:(((eq nat) x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.74 Found x0 as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found x0:((more x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.74 Found x0 as proof of ((more Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found x0:(((eq nat) x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.74 Found x0 as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found x2:(P Xx)
% 11.35/11.74 Instantiate: Xy:=Xx:nat
% 11.35/11.74 Found (fun (x2:(P Xx))=> x2) as proof of (P Xy)
% 11.35/11.74 Found (fun (P:(nat->Prop)) (x2:(P Xx))=> x2) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found (fun (P:(nat->Prop)) (x2:(P Xx))=> x2) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 11.35/11.74 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 11.35/11.74 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found l:((less ((pl x) z)) ((pl y) z))
% 11.35/11.74 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 11.35/11.74 Found l as proof of ((less Xx) Xy)
% 11.35/11.74 Found x0:((more x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.74 Found x0 as proof of ((more Xx) Xy)
% 11.35/11.74 Found x0:((more x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 11.35/11.74 Found x0 as proof of ((more Xx) Xy)
% 11.35/11.74 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 11.35/11.74 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 11.35/11.74 Found x0:((more x) y)
% 11.35/11.74 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of ((more Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found l:((less ((pl x) z)) ((pl y) z))
% 14.23/14.61 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 14.23/14.61 Found l as proof of ((less Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found x0:(((eq nat) x) y)
% 14.23/14.61 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found l:((less ((pl x) z)) ((pl y) z))
% 14.23/14.61 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 14.23/14.61 Found l as proof of ((less Xx) Xy)
% 14.23/14.61 Found x0:(((eq nat) x) y)
% 14.23/14.61 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found l:((less ((pl x) z)) ((pl y) z))
% 14.23/14.61 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 14.23/14.61 Found l as proof of ((less Xx) Xy)
% 14.23/14.61 Found x0:(((eq nat) x) y)
% 14.23/14.61 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found l:((less ((pl x) z)) ((pl y) z))
% 14.23/14.61 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 14.23/14.61 Found l as proof of ((less Xx) Xy)
% 14.23/14.61 Found l:((less ((pl x) z)) ((pl y) z))
% 14.23/14.61 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 14.23/14.61 Found l as proof of ((less Xx) Xy)
% 14.23/14.61 Found x0:((more x) y)
% 14.23/14.61 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of ((more Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found x0:(((eq nat) x) y)
% 14.23/14.61 Instantiate: Xx:=x:nat;Xy:=y:nat
% 14.23/14.61 Found x0 as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 14.23/14.61 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found x3:(P Xx)
% 14.23/14.61 Instantiate: Xy:=Xx:nat
% 14.23/14.61 Found (fun (x3:(P Xx))=> x3) as proof of (P Xy)
% 14.23/14.61 Found (fun (P:(nat->Prop)) (x3:(P Xx))=> x3) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop)) (x3:(P Xx))=> x3) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 14.23/14.61 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found x3:(P Xx)
% 14.23/14.61 Instantiate: Xy:=Xx:nat
% 14.23/14.61 Found (fun (x3:(P Xx))=> x3) as proof of (P Xy)
% 14.23/14.61 Found (fun (P:(nat->Prop)) (x3:(P Xx))=> x3) as proof of ((P Xx)->(P Xy))
% 14.23/14.61 Found (fun (P:(nat->Prop)) (x3:(P Xx))=> x3) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 14.23/14.61 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 14.23/14.61 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 14.23/14.61 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found x4:(P Xx)
% 20.03/20.47 Instantiate: Xy:=Xx:nat
% 20.03/20.47 Found (fun (x4:(P Xx))=> x4) as proof of (P Xy)
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x4:(P Xx))=> x4) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x4:(P Xx))=> x4) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 20.03/20.47 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 20.03/20.47 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 20.03/20.47 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found x5:(P Xx)
% 20.03/20.47 Instantiate: Xy:=Xx:nat
% 20.03/20.47 Found (fun (x5:(P Xx))=> x5) as proof of (P Xy)
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x5:(P Xx))=> x5) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x5:(P Xx))=> x5) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found x5:(P Xx)
% 20.03/20.47 Instantiate: Xy:=Xx:nat
% 20.03/20.47 Found (fun (x5:(P Xx))=> x5) as proof of (P Xy)
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x5:(P Xx))=> x5) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop)) (x5:(P Xx))=> x5) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 20.03/20.47 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy))
% 20.03/20.47 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found l:((less ((pl x) z)) ((pl y) z))
% 20.03/20.47 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 20.03/20.47 Found l as proof of ((less Xx) Xy)
% 20.03/20.47 Found l:((less ((pl x) z)) ((pl y) z))
% 20.03/20.47 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 20.03/20.47 Found l as proof of ((less Xx) Xy)
% 20.03/20.47 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 20.03/20.47 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found l:((less ((pl x) z)) ((pl y) z))
% 20.03/20.47 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 20.03/20.47 Found l as proof of ((less Xx) Xy)
% 20.03/20.47 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 20.03/20.47 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found l:((less ((pl x) z)) ((pl y) z))
% 20.03/20.47 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 20.03/20.47 Found l as proof of ((less Xx) Xy)
% 20.03/20.47 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 20.03/20.47 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 20.03/20.47 Found satz19a0000:=(satz19a000 z):((more ((pl x) z)) ((pl y) z))
% 20.03/20.47 Found (satz19a000 z) as proof of ((more Xx) Xy)
% 20.03/20.47 Found ((fun (Xz:nat)=> ((satz19a00 Xz) x0)) z) as proof of ((more Xx) Xy)
% 20.03/20.47 Found ((fun (Xz:nat)=> (((satz19a0 y) Xz) x0)) z) as proof of ((more Xx) Xy)
% 20.03/20.47 Found ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z) as proof of ((more Xx) Xy)
% 20.03/20.47 Found ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z) as proof of ((more Xx) Xy)
% 20.03/20.49 Found ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l) as proof of False
% 20.03/20.49 Found (fun (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)) as proof of False
% 20.03/20.49 Found (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)) as proof of ((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False)
% 20.03/20.49 Found (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)) as proof of ((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))
% 20.03/20.49 Found (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))) as proof of False
% 20.03/20.49 Found (fun (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))) as proof of False
% 20.03/20.49 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))) as proof of ((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False)
% 20.03/20.49 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))) as proof of (((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))
% 20.03/20.49 Found (satz10b00 (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))) as proof of False
% 20.03/20.49 Found ((satz10b0 ((pl y) z)) (fun (x1:((((eq nat) Xx) ((pl y) z))->(((more Xx) ((pl y) z))->False))) (x2:(((((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))->((((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))) (x4:(((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))) as proof of False
% 20.03/20.49 Found (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))) as proof of False
% 20.03/20.49 Found (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))))) as proof of False
% 24.34/24.71 Found (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))))) as proof of (((more x) y)->False)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 24.34/24.71 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx)
% 24.34/24.71 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Instantiate: Xx:=x:nat;Xy:=y:nat
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found x0:(((eq nat) x) y)
% 24.34/24.71 Found x0 as proof of (((eq nat) Xx) Xy)
% 24.34/24.71 Found l:((less ((pl x) z)) ((pl y) z))
% 24.34/24.71 Found l as proof of ((less Xx) Xy)
% 24.34/24.71 Found satz19b0000:=(satz19b000 z):(((eq nat) ((pl x) z)) ((pl y) z))
% 24.34/24.71 Found (satz19b000 z) as proof of (((eq nat) Xx) Xy)
% 24.34/24.75 Found ((fun (Xz:nat)=> ((satz19b00 Xz) x0)) z) as proof of (((eq nat) Xx) Xy)
% 24.34/24.75 Found ((fun (Xz:nat)=> (((satz19b0 y) Xz) x0)) z) as proof of (((eq nat) Xx) Xy)
% 24.34/24.75 Found ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z) as proof of (((eq nat) Xx) Xy)
% 24.34/24.75 Found ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z) as proof of (((eq nat) Xx) Xy)
% 24.34/24.75 Found ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)) as proof of False
% 24.34/24.75 Found (fun (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))) as proof of False
% 24.34/24.75 Found (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))) as proof of ((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False)
% 24.34/24.75 Found (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))) as proof of ((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))
% 24.34/24.75 Found (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))) as proof of False
% 24.34/24.75 Found (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))) as proof of False
% 24.34/24.75 Found (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))) as proof of ((False->False)->False)
% 24.34/24.75 Found (et0 (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))) as proof of False
% 24.34/24.75 Found ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))) as proof of False
% 24.34/24.75 Found (fun (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))))) as proof of False
% 24.34/24.75 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))))) as proof of ((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False)
% 24.34/24.75 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))))) as proof of (((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))
% 24.34/24.75 Found (satz10b00 (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x5:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))) as proof of False
% 24.34/24.75 Found ((satz10b0 ((pl y) z)) (fun (x1:((((eq nat) Xx) ((pl y) z))->(((more Xx) ((pl y) z))->False))) (x2:(((((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))->((((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))) (x5:(((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))) as proof of False
% 24.42/24.81 Found (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))) as proof of False
% 24.42/24.81 Found (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))))))) as proof of False
% 24.42/24.81 Found (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z))))))))) as proof of (not (((eq nat) x) y))
% 24.42/24.81 Found ((satz10a00 (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))))) as proof of ((less x) y)
% 24.42/24.81 Found (((satz10a0 y) (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))))) as proof of ((less x) y)
% 24.42/24.81 Found ((((satz10a x) y) (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))))) as proof of ((less x) y)
% 24.42/24.81 Found ((((satz10a x) y) (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l))))))) as proof of ((less x) y)
% 24.42/24.81 Got proof ((((satz10a x) y) (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))))))
% 24.65/25.03 Time elapsed = 24.078703s
% 24.65/25.03 node=4477 cost=1101.000000 depth=25
% 24.65/25.03::::::::::::::::::::::
% 24.65/25.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.65/25.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.65/25.03 ((((satz10a x) y) (fun (x0:(((eq nat) x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> ((et False) (fun (x3:(False->False))=> (x2 (fun (x4:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x5:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x5 l) ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x0)) z)))))))))) (fun (x0:((more x) y))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 ((fun (Xz:nat)=> ((((satz19a x) y) Xz) x0)) z)) l)))))))
% 24.65/25.03 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------