TSTP Solution File: NUM644^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM644^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n115.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 13:11:16 EST 2018
% Result : Timeout 286.71s
% 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 : NUM644^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.22 % Computer : n115.star.cs.uiowa.edu
% 0.02/0.22 % Model : x86_64 x86_64
% 0.02/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22 % Memory : 32218.625MB
% 0.02/0.22 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.22 % CPULimit : 300
% 0.02/0.22 % DateTime : Fri Jan 5 11:25:14 CST 2018
% 0.02/0.22 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 0.30/0.67 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041ea28>, <kernel.Type object at 0x2b34c041e1b8>) of role type named nat_type
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring nat:Type
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c0413368>, <kernel.Constant object at 0x2b34c041e248>) of role type named x
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring x:nat
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041e7e8>, <kernel.Constant object at 0x2b34c041e248>) of role type named y
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring y:nat
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041ea28>, <kernel.DependentProduct object at 0x2b34c041e6c8>) of role type named pl
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring pl:(nat->(nat->nat))
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041eab8>, <kernel.Type object at 0x2b34c041e7e8>) of role type named set_type
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring set:Type
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041e248>, <kernel.DependentProduct object at 0x2b34c041f680>) of role type named esti
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring esti:(nat->(set->Prop))
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041ea28>, <kernel.DependentProduct object at 0x2b34c041ff80>) of role type named setof
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring setof:((nat->Prop)->set)
% 0.30/0.67 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))) of role axiom named estie
% 0.30/0.67 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs)))
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041ea28>, <kernel.Constant object at 0x2b34c041f950>) of role type named n_1
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring n_1:nat
% 0.30/0.67 FOF formula (<kernel.Constant object at 0x2b34c041eab8>, <kernel.DependentProduct object at 0x2b34c041f050>) of role type named suc
% 0.30/0.67 Using role type
% 0.30/0.67 Declaring suc:(nat->nat)
% 0.30/0.67 FOF formula (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))) of role axiom named ax5
% 0.30/0.67 A new axiom: (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs)))))
% 0.30/0.67 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))) of role axiom named estii
% 0.30/0.67 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp))))
% 0.30/0.67 FOF formula (forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx))) of role axiom named satz4a
% 0.30/0.67 A new axiom: (forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx)))
% 0.30/0.67 FOF formula (forall (Xx:nat), (((eq nat) ((pl n_1) Xx)) (suc Xx))) of role axiom named satz4c
% 0.30/0.67 A new axiom: (forall (Xx:nat), (((eq nat) ((pl n_1) Xx)) (suc Xx)))
% 0.30/0.67 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) (suc ((pl Xx) Xy))) ((pl Xx) (suc Xy)))) of role axiom named satz4f
% 0.30/0.67 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) (suc ((pl Xx) Xy))) ((pl Xx) (suc Xy))))
% 0.30/0.67 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl (suc Xx)) Xy)) (suc ((pl Xx) Xy)))) of role axiom named satz4d
% 0.30/0.67 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl (suc Xx)) Xy)) (suc ((pl Xx) Xy))))
% 0.30/0.67 FOF formula (((eq nat) ((pl x) y)) ((pl y) x)) of role conjecture named satz6
% 0.30/0.67 Conjecture to prove = (((eq nat) ((pl x) y)) ((pl y) x)):Prop
% 0.30/0.67 Parameter set_DUMMY:set.
% 0.30/0.67 We need to prove ['(((eq nat) ((pl x) y)) ((pl y) x))']
% 0.30/0.67 Parameter nat:Type.
% 0.30/0.67 Parameter x:nat.
% 0.30/0.67 Parameter y:nat.
% 0.30/0.67 Parameter pl:(nat->(nat->nat)).
% 0.30/0.67 Parameter set:Type.
% 0.30/0.67 Parameter esti:(nat->(set->Prop)).
% 0.30/0.67 Parameter setof:((nat->Prop)->set).
% 0.30/0.67 Axiom estie:(forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))).
% 0.30/0.67 Parameter n_1:nat.
% 0.30/0.67 Parameter suc:(nat->nat).
% 0.30/0.67 Axiom ax5:(forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))).
% 0.30/0.67 Axiom estii:(forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))).
% 0.30/0.67 Axiom satz4a:(forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx))).
% 0.30/0.67 Axiom satz4c:(forall (Xx:nat), (((eq nat) ((pl n_1) Xx)) (suc Xx))).
% 0.30/0.67 Axiom satz4f:(forall (Xx:nat) (Xy:nat), (((eq nat) (suc ((pl Xx) Xy))) ((pl Xx) (suc Xy)))).
% 0.30/0.67 Axiom satz4d:(forall (Xx:nat) (Xy:nat), (((eq nat) ((pl (suc Xx)) Xy)) (suc ((pl Xx) Xy)))).
% 133.94/134.32 Trying to prove (((eq nat) ((pl x) y)) ((pl y) x))
% 133.94/134.32 Found eq_ref000:=(eq_ref00 P):((P ((pl x) y))->(P ((pl x) y)))
% 133.94/134.32 Found (eq_ref00 P) as proof of (P0 ((pl x) y))
% 133.94/134.32 Found ((eq_ref0 ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 133.94/134.32 Found (((eq_ref nat) ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 133.94/134.32 Found (((eq_ref nat) ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 133.94/134.32 Found eq_ref00:=(eq_ref0 ((pl x) y)):(((eq nat) ((pl x) y)) ((pl x) y))
% 133.94/134.32 Found (eq_ref0 ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 133.94/134.32 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl y) x))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 133.94/134.32 Found eq_ref00:=(eq_ref0 ((pl y) x)):(((eq nat) ((pl y) x)) ((pl y) x))
% 133.94/134.32 Found (eq_ref0 ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 133.94/134.32 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl x) y))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) y))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) y))
% 133.94/134.32 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) y))
% 133.94/134.32 Found x0:(P ((pl x) y))
% 133.94/134.32 Instantiate: b:=((pl x) y):nat
% 133.94/134.32 Found x0 as proof of (P0 b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 ((pl y) x)):(((eq nat) ((pl y) x)) ((pl y) x))
% 133.94/134.32 Found (eq_ref0 ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x)))))
% 133.94/134.32 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) y)) ((pl y) x))))) b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1)))))
% 133.94/134.32 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) b)
% 133.94/134.32 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) y)) ((pl y) x1))))) b)
% 133.94/134.32 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x)))))
% 190.03/190.39 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) b)
% 190.03/190.39 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) b)
% 190.03/190.39 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) b)
% 190.03/190.39 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl x) x1)) ((pl x1) x))))) b)
% 190.03/190.39 Found satz4c__eq_sym0:=(satz4c__eq_sym y):(((eq nat) (suc y)) ((pl n_1) y))
% 190.03/190.39 Found (satz4c__eq_sym y) as proof of (((eq nat) (suc y)) ((pl n_1) y))
% 190.03/190.39 Found (satz4c__eq_sym y) as proof of (((eq nat) (suc y)) ((pl n_1) y))
% 190.03/190.39 Found (satz4a__eq_sym00 (satz4c__eq_sym y)) as proof of (((eq nat) ((pl y) n_1)) ((pl n_1) y))
% 190.03/190.39 Found ((satz4a__eq_sym0 (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y)) as proof of (((eq nat) ((pl y) n_1)) ((pl n_1) y))
% 190.03/190.39 Found (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y)) as proof of (((eq nat) ((pl y) n_1)) ((pl n_1) y))
% 190.03/190.39 Found (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y)) as proof of (((eq nat) ((pl y) n_1)) ((pl n_1) y))
% 190.03/190.39 Found (estii00 (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))))
% 190.03/190.39 Found ((estii0 n_1) (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))))
% 190.03/190.39 Found (((estii (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))) n_1) (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))))
% 190.03/190.39 Found (((estii (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))) n_1) (((satz4a__eq_sym y) (fun (x1:nat)=> (((eq nat) x1) ((pl n_1) y)))) (satz4c__eq_sym y))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl y) x1)) ((pl x1) y)))))
% 190.03/190.39 Found eq_ref000:=(eq_ref00 P):((P ((pl y) (suc Xx)))->(P ((pl y) (suc Xx))))
% 190.03/190.39 Found (eq_ref00 P) as proof of (P0 ((pl y) (suc Xx)))
% 190.03/190.39 Found ((eq_ref0 ((pl y) (suc Xx))) P) as proof of (P0 ((pl y) (suc Xx)))
% 190.03/190.39 Found (((eq_ref nat) ((pl y) (suc Xx))) P) as proof of (P0 ((pl y) (suc Xx)))
% 190.03/190.39 Found (((eq_ref nat) ((pl y) (suc Xx))) P) as proof of (P0 ((pl y) (suc Xx)))
% 190.03/190.39 Found satz4c0:=(satz4c x):(((eq nat) ((pl n_1) x)) (suc x))
% 190.03/190.39 Found (satz4c x) as proof of (((eq nat) ((pl n_1) x)) (suc x))
% 190.03/190.39 Found (satz4c x) as proof of (((eq nat) ((pl n_1) x)) (suc x))
% 190.03/190.39 Found (satz4a__eq_sym00 (satz4c x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 190.03/190.39 Found ((satz4a__eq_sym0 ((eq nat) ((pl n_1) x))) (satz4c x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 190.03/190.39 Found (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 190.03/190.39 Found (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 190.03/190.39 Found (estii00 (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))))
% 190.03/190.39 Found ((estii0 n_1) (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))))
% 190.03/190.39 Found (((estii (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))) n_1) (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))))
% 190.03/190.39 Found (((estii (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))) n_1) (((satz4a__eq_sym x) ((eq nat) ((pl n_1) x))) (satz4c x))) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) ((pl x1) x)) ((pl x) x1)))))
% 190.03/190.39 Found eq_ref000:=(eq_ref00 P):((P ((pl (suc Xx)) x))->(P ((pl (suc Xx)) x)))
% 225.92/226.36 Found (eq_ref00 P) as proof of (P0 ((pl (suc Xx)) x))
% 225.92/226.36 Found ((eq_ref0 ((pl (suc Xx)) x)) P) as proof of (P0 ((pl (suc Xx)) x))
% 225.92/226.36 Found (((eq_ref nat) ((pl (suc Xx)) x)) P) as proof of (P0 ((pl (suc Xx)) x))
% 225.92/226.36 Found (((eq_ref nat) ((pl (suc Xx)) x)) P) as proof of (P0 ((pl (suc Xx)) x))
% 225.92/226.36 Found eq_ref00:=(eq_ref0 ((pl x) y)):(((eq nat) ((pl x) y)) ((pl x) y))
% 225.92/226.36 Found (eq_ref0 ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 225.92/226.36 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found eq_ref000:=(eq_ref00 P):((P ((pl x) y))->(P ((pl x) y)))
% 225.92/226.36 Found (eq_ref00 P) as proof of (P0 ((pl x) y))
% 225.92/226.36 Found ((eq_ref0 ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 225.92/226.36 Found (((eq_ref nat) ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 225.92/226.36 Found (((eq_ref nat) ((pl x) y)) P) as proof of (P0 ((pl x) y))
% 225.92/226.36 Found eq_ref00:=(eq_ref0 ((pl x) y)):(((eq nat) ((pl x) y)) ((pl x) y))
% 225.92/226.36 Found (eq_ref0 ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 225.92/226.36 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) x))
% 225.92/226.36 Found x0:(P ((pl y) x))
% 225.92/226.36 Instantiate: b:=((pl y) x):nat
% 225.92/226.36 Found x0 as proof of (P0 b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 ((pl x) y)):(((eq nat) ((pl x) y)) ((pl x) y))
% 225.92/226.36 Found (eq_ref0 ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found ((eq_ref nat) ((pl x) y)) as proof of (((eq nat) ((pl x) y)) b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 (setof (fun (x2:nat)=> (P ((pl y) x))))):(((eq set) (setof (fun (x2:nat)=> (P ((pl y) x))))) (setof (fun (x2:nat)=> (P ((pl y) x)))))
% 225.92/226.36 Found (eq_ref0 (setof (fun (x2:nat)=> (P ((pl y) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl y) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl y) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl y) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl y) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl y) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl y) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl y) x))))) b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 (setof (fun (x2:nat)=> (P ((pl x2) x))))):(((eq set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) (setof (fun (x2:nat)=> (P ((pl x2) x)))))
% 225.92/226.36 Found (eq_ref0 (setof (fun (x2:nat)=> (P ((pl x2) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) as proof of (((eq set) (setof (fun (x2:nat)=> (P ((pl x2) x))))) b)
% 225.92/226.36 Found eq_ref00:=(eq_ref0 (setof (fun (x10:nat)=> (P ((pl y) x10))))):(((eq set) (setof (fun (x10:nat)=> (P ((pl y) x10))))) (setof (fun (x10:nat)=> (P ((pl y) x10)))))
% 225.92/226.36 Found (eq_ref0 (setof (fun (x10:nat)=> (P ((pl y) x10))))) as proof of (((eq set) (setof (fun (x1:nat)=> (P ((pl y) x1))))) b)
% 225.92/226.36 Found ((eq_ref set) (setof (fun (x10:nat)=> (P ((pl y) x10))))) as proof of (((eq set) (setof (fun (x1:nat)=> (P ((pl y) x1))))) b)
% 286.71/287.10 Found ((eq_ref set) (setof (fun (x10:nat)=> (P ((pl y) x10))))) as proof of (((eq set) (setof (fun (x1:nat)=> (P ((pl y) x1))))) b)
% 286.71/287.10 Found ((eq_ref set) (setof (fun (x10:nat)=> (P ((pl y) x10))))) as proof of (((eq set) (setof (fun (x1:nat)=> (P ((pl y) x1))))) b)
% 286.71/287.10 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 286.71/287.10 Found (eq_ref0 b) as proof of (P b)
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (P b)
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (P b)
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (P b)
% 286.71/287.10 Found eq_ref00:=(eq_ref0 ((pl y) x)):(((eq nat) ((pl y) x)) ((pl y) x))
% 286.71/287.10 Found (eq_ref0 ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 286.71/287.10 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 286.71/287.10 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 286.71/287.10 Found ((eq_ref nat) ((pl y) x)) as proof of (((eq nat) ((pl y) x)) b)
% 286.71/287.10 Found eq_ref000:=(eq_ref00 P):((P ((pl x) n_1))->(P ((pl x) n_1)))
% 286.71/287.10 Found (eq_ref00 P) as proof of (P0 ((pl x) n_1))
% 286.71/287.10 Found ((eq_ref0 ((pl x) n_1)) P) as proof of (P0 ((pl x) n_1))
% 286.71/287.10 Found (((eq_ref nat) ((pl x) n_1)) P) as proof of (P0 ((pl x) n_1))
% 286.71/287.10 Found (((eq_ref nat) ((pl x) n_1)) P) as proof of (P0 ((pl x) n_1))
% 286.71/287.10 Found eq_ref000:=(eq_ref00 P):((P ((pl n_1) y))->(P ((pl n_1) y)))
% 286.71/287.10 Found (eq_ref00 P) as proof of (P0 ((pl n_1) y))
% 286.71/287.10 Found ((eq_ref0 ((pl n_1) y)) P) as proof of (P0 ((pl n_1) y))
% 286.71/287.10 Found (((eq_ref nat) ((pl n_1) y)) P) as proof of (P0 ((pl n_1) y))
% 286.71/287.10 Found (((eq_ref nat) ((pl n_1) y)) P) as proof of (P0 ((pl n_1) y))
% 286.71/287.10 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 286.71/287.10 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl (suc Xx)) y))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl (suc Xx)) y))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl (suc Xx)) y))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl (suc Xx)) y))
% 286.71/287.10 Found satz4f__eq_sym00:=(satz4f__eq_sym0 Xx):(((eq nat) ((pl y) (suc Xx))) (suc ((pl y) Xx)))
% 286.71/287.10 Found (satz4f__eq_sym0 Xx) as proof of (((eq nat) ((pl y) (suc Xx))) b)
% 286.71/287.10 Found ((satz4f__eq_sym y) Xx) as proof of (((eq nat) ((pl y) (suc Xx))) b)
% 286.71/287.10 Found ((satz4f__eq_sym y) Xx) as proof of (((eq nat) ((pl y) (suc Xx))) b)
% 286.71/287.10 Found ((satz4f__eq_sym y) Xx) as proof of (((eq nat) ((pl y) (suc Xx))) b)
% 286.71/287.10 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 286.71/287.10 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl x) (suc Xx)))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) (suc Xx)))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) (suc Xx)))
% 286.71/287.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) (suc Xx)))
% 286.71/287.10 Found satz4d00:=(satz4d0 x):(((eq nat) ((pl (suc Xx)) x)) (suc ((pl Xx) x)))
% 286.71/287.10 Found (satz4d0 x) as proof of (((eq nat) ((pl (suc Xx)) x)) b)
% 286.71/287.10 Found ((satz4d Xx) x) as proof of (((eq nat) ((pl (suc Xx)) x)) b)
% 286.71/287.10 Found ((satz4d Xx) x) as proof of (((eq nat) ((pl (suc Xx)) x)) b)
% 286.71/287.10 Found ((satz4d Xx) x) as proof of (((eq nat) ((pl (suc Xx)) x)) b)
% 286.71/287.10 Found satz4a__eq_sym0:=(satz4a__eq_sym x):(((eq nat) (suc x)) ((pl x) n_1))
% 286.71/287.10 Found (satz4a__eq_sym x) as proof of (((eq nat) (suc x)) ((pl x) n_1))
% 286.71/287.10 Found (satz4a__eq_sym x) as proof of (((eq nat) (suc x)) ((pl x) n_1))
% 286.71/287.10 Found (satz4c__eq_sym00 (satz4a__eq_sym x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 286.71/287.10 Found ((satz4c__eq_sym0 (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 286.71/287.10 Found (((satz4c__eq_sym x) (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 286.71/287.10 Found (((satz4c__eq_sym x) (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x)) as proof of (((eq nat) ((pl n_1) x)) ((pl x) n_1))
% 286.71/287.10 Found (eq_sym000 (((satz4c__eq_sym x) (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x))) as proof of (((eq nat) ((pl x) n_1)) ((pl n_1) x))
% 286.71/287.10 Found ((eq_sym00 ((pl x) n_1)) (((satz4c__eq_sym x) (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x))) as proof of (((eq nat) ((pl x) n_1)) ((pl n_1) x))
% 286.71/287.10 Found (((eq_sym0 ((pl n_1) x)) ((pl x) n_1)) (((satz4c__eq_sym x) (fun (x1:nat)=> (((eq nat) x1) ((pl x) n_1)))) (satz4a__eq_sym x))) as proof of (((eq nat) ((pl x) n_1)) ((pl n_1) x))
% 286.71/287.10 Found ((((eq_sym nat) ((pl n_1)
%------------------------------------------------------------------------------