TSTP Solution File: NUM688^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM688^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n175.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 13:11:26 EST 2018
% Result : Timeout 287.60s
% 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 : NUM688^1 : TPTP v7.0.0. Released v3.7.0.
% 0.02/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n175.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 : Fri Jan 5 12:48:48 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 6.61/6.84 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c55794d0>, <kernel.Type object at 0x2ab5c55796c8>) of role type named nat_type
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring nat:Type
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c5579128>, <kernel.Constant object at 0x2ab5c5579638>) of role type named x
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring x:nat
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c5c0b128>, <kernel.Constant object at 0x2ab5c5579638>) of role type named y
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring y:nat
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c55794d0>, <kernel.Constant object at 0x2ab5c5579128>) of role type named z
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring z:nat
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c55790e0>, <kernel.Constant object at 0x2ab5c54f9bd8>) of role type named u
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring u:nat
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c5579128>, <kernel.DependentProduct object at 0x2ab5c54f9d88>) of role type named more
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring more:(nat->(nat->Prop))
% 6.61/6.84 FOF formula ((more x) y) of role axiom named m
% 6.61/6.84 A new axiom: ((more x) y)
% 6.61/6.84 FOF formula ((((more z) u)->False)->(((eq nat) z) u)) of role axiom named n
% 6.61/6.84 A new axiom: ((((more z) u)->False)->(((eq nat) z) u))
% 6.61/6.84 FOF formula (<kernel.Constant object at 0x2ab5c5579638>, <kernel.DependentProduct object at 0x2ab5c54f9b90>) of role type named pl
% 6.61/6.84 Using role type
% 6.61/6.84 Declaring pl:(nat->(nat->nat))
% 6.61/6.84 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et
% 6.61/6.84 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa))
% 6.61/6.84 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), ((((eq nat) Xx) Xy)->(((more Xz) Xu)->((more ((pl Xz) Xx)) ((pl Xu) Xy))))) of role axiom named satz19h
% 6.61/6.84 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), ((((eq nat) Xx) Xy)->(((more Xz) Xu)->((more ((pl Xz) Xx)) ((pl Xu) Xy)))))
% 6.61/6.84 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu))))) of role axiom named satz21
% 6.61/6.84 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu)))))
% 6.61/6.84 FOF formula ((more ((pl x) z)) ((pl y) u)) of role conjecture named satz22b
% 6.61/6.84 Conjecture to prove = ((more ((pl x) z)) ((pl y) u)):Prop
% 6.61/6.84 We need to prove ['((more ((pl x) z)) ((pl y) u))']
% 6.61/6.84 Parameter nat:Type.
% 6.61/6.84 Parameter x:nat.
% 6.61/6.84 Parameter y:nat.
% 6.61/6.84 Parameter z:nat.
% 6.61/6.84 Parameter u:nat.
% 6.61/6.84 Parameter more:(nat->(nat->Prop)).
% 6.61/6.84 Axiom m:((more x) y).
% 6.61/6.84 Axiom n:((((more z) u)->False)->(((eq nat) z) u)).
% 6.61/6.84 Parameter pl:(nat->(nat->nat)).
% 6.61/6.84 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)).
% 6.61/6.84 Axiom satz19h:(forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), ((((eq nat) Xx) Xy)->(((more Xz) Xu)->((more ((pl Xz) Xx)) ((pl Xu) Xy))))).
% 6.61/6.84 Axiom satz21:(forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu))))).
% 6.61/6.84 Trying to prove ((more ((pl x) z)) ((pl y) u))
% 6.61/6.84 Found m:((more x) y)
% 6.61/6.84 Found m as proof of ((more x) y)
% 6.61/6.84 Found m:((more x) y)
% 6.61/6.84 Found m as proof of ((more x) y)
% 6.61/6.84 Found x0:(P z)
% 6.61/6.84 Found x0 as proof of (P0 z)
% 6.61/6.84 Found x0:(P z)
% 6.61/6.84 Found x0 as proof of (P0 z)
% 6.61/6.84 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 6.61/6.84 Found (eq_ref00 P) as proof of (P0 z)
% 6.61/6.84 Found ((eq_ref0 z) P) as proof of (P0 z)
% 6.61/6.84 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 6.61/6.84 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 6.61/6.84 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 6.61/6.84 Found (eq_ref0 z) as proof of (P z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (P z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (P z)
% 6.61/6.84 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 6.61/6.84 Found (eq_ref00 P) as proof of (P0 z)
% 6.61/6.84 Found ((eq_ref0 z) P) as proof of (P0 z)
% 6.61/6.84 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 6.61/6.84 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 6.61/6.84 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 6.61/6.84 Found (eq_ref0 z) as proof of (P z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (P z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (P z)
% 6.61/6.84 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 6.61/6.84 Found (eq_ref0 z) as proof of (((eq nat) z) z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 6.61/6.84 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 15.00/15.23 Found (satz19h00000 ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> ((satz19h0000 x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> (((satz19h000 y) x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> ((((satz19h00 x) y) x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> (((((satz19h0 z) x) y) x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> ((((((satz19h z) z) x) y) x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found ((fun (x0:(((eq nat) z) z))=> ((((((satz19h z) z) x) y) x0) m)) ((eq_ref nat) z)) as proof of (P z)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 15.00/15.23 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 15.00/15.23 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 15.00/15.23 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 15.00/15.23 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 15.00/15.23 Found x00:=(x0 n0):False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 15.00/15.23 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 15.00/15.23 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found x00:=(x0 n0):False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 15.00/15.23 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 15.00/15.23 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 15.00/15.23 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 15.00/15.23 Found x00:=(x0 n0):False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found (fun (x0:((((eq nat) z) u)->False))=> (x0 n0)) as proof of False
% 15.00/15.23 Found (fun (x0:((((eq nat) z) u)->False))=> (x0 n0)) as proof of (((((eq nat) z) u)->False)->False)
% 15.00/15.23 Found x00:=(x0 n0):False
% 15.00/15.23 Found (x0 n0) as proof of False
% 15.00/15.23 Found (fun (x0:((((eq nat) z) u)->False))=> (x0 n0)) as proof of False
% 15.00/15.23 Found (fun (x0:((((eq nat) z) u)->False))=> (x0 n0)) as proof of (((((eq nat) z) u)->False)->False)
% 15.00/15.23 Found satz19h000000:=(satz19h00000 m):((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found (satz19h00000 m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found ((satz19h0000 y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found (((satz19h000 x) y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found ((((fun (Xz:nat) (Xu:nat)=> (((satz19h00 Xz) Xu) n0)) x) y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found ((((fun (Xz:nat) (Xu:nat)=> ((((satz19h0 u) Xz) Xu) n0)) x) y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz19h z) u) Xz) Xu) n0)) x) y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz19h z) u) Xz) Xu) n0)) x) y) m) as proof of ((more ((pl x) z)) ((pl y) u))
% 15.00/15.23 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 15.00/15.23 Found (eq_ref0 u) as proof of (((eq nat) u) u)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) u)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) u)
% 34.13/34.33 Found (satz19h00000 ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> ((satz19h0000 x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> (((satz19h000 y) x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> ((((satz19h00 x) y) x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> (((((satz19h0 u) x) y) x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> ((((((satz19h u) u) x) y) x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found ((fun (x0:(((eq nat) u) u))=> ((((((satz19h u) u) x) y) x0) m)) ((eq_ref nat) u)) as proof of (P u)
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Found x0 as proof of (P0 z)
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Found x0 as proof of (P0 z)
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Found x0 as proof of (P0 z)
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Instantiate: b:=z:nat
% 34.13/34.33 Found x0 as proof of (P0 b)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Found x0 as proof of (P0 z)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 34.13/34.33 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 34.13/34.33 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found x0:(P z)
% 34.13/34.33 Instantiate: b:=z:nat
% 34.13/34.33 Found x0 as proof of (P0 b)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 34.13/34.33 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 34.13/34.33 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 34.13/34.33 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 34.13/34.33 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 34.13/34.33 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of ((P u)->(P z))
% 34.13/34.33 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of (((eq nat) u) z)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 34.13/34.33 Found (eq_ref0 z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 34.13/34.33 Found (eq_ref0 z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 34.13/34.33 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 34.13/34.33 Found (eq_ref0 z) as proof of (P z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P z)
% 34.13/34.33 Found x00:=(x0 n0):False
% 34.13/34.33 Found (x0 n0) as proof of False
% 34.13/34.33 Found (x0 n0) as proof of False
% 34.13/34.33 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 34.13/34.33 Found (eq_ref0 z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 34.13/34.33 Found ((eq_ref nat) z) as proof of (P1 z)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 42.32/42.54 Found (eq_ref0 z) as proof of (P1 z)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (P1 z)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (P1 z)
% 42.32/42.54 Found x00:=(x0 n0):False
% 42.32/42.54 Found (x0 n0) as proof of False
% 42.32/42.54 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 42.32/42.54 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 42.32/42.54 Found x00:=(x0 n0):False
% 42.32/42.54 Found (x0 n0) as proof of False
% 42.32/42.54 Found (x0 n0) as proof of False
% 42.32/42.54 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 42.32/42.54 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 42.32/42.54 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 42.32/42.54 Found (eq_ref00 P) as proof of (P0 z)
% 42.32/42.54 Found ((eq_ref0 z) P) as proof of (P0 z)
% 42.32/42.54 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 42.32/42.54 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 42.32/42.54 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 42.32/42.54 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 42.32/42.54 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 42.32/42.54 Found (eq_ref00 P) as proof of (P0 z)
% 42.32/42.54 Found ((eq_ref0 z) P) as proof of (P0 z)
% 42.32/42.54 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 42.32/42.54 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 42.32/42.54 Found (eq_ref0 b) as proof of (P b)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (P b)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (P b)
% 42.32/42.54 Found ((eq_ref nat) b) as proof of (P b)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 42.32/42.54 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 42.32/42.54 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 42.32/42.54 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 42.32/42.54 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 42.32/42.54 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 42.32/42.54 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 42.32/42.54 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 42.32/42.54 Found x00:=(x0 n0):False
% 42.32/42.54 Found (x0 n0) as proof of False
% 42.32/42.54 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 42.32/42.54 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 42.32/42.54 Found x0:(P b)
% 42.32/42.54 Found x0 as proof of (P0 z)
% 42.32/42.54 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 42.32/42.54 Found (eq_sym010 n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 42.32/42.54 Found (eq_sym010 n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 42.32/42.54 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 42.32/42.54 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 57.22/57.46 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 57.22/57.46 Found (eq_ref00 P) as proof of (P0 z)
% 57.22/57.46 Found ((eq_ref0 z) P) as proof of (P0 z)
% 57.22/57.46 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 57.22/57.46 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 57.22/57.46 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 57.22/57.46 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 57.22/57.46 Found (eq_ref0 b) as proof of (P b)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (P b)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (P b)
% 57.22/57.46 Found ((eq_ref nat) b) as proof of (P b)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 57.22/57.46 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 57.22/57.46 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 57.22/57.46 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 57.22/57.46 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 57.22/57.46 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 57.22/57.46 Found (eq_ref00 P) as proof of (P0 z)
% 57.22/57.46 Found ((eq_ref0 z) P) as proof of (P0 z)
% 57.22/57.46 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 57.22/57.46 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 57.22/57.46 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 57.22/57.46 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of (((eq nat) u) z)
% 57.22/57.46 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 57.22/57.46 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of ((P1 u)->(P1 z))
% 57.22/57.46 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of (((eq nat) u) z)
% 57.22/57.46 Found x0:(P b)
% 57.22/57.46 Found x0 as proof of (P0 z)
% 57.22/57.46 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 57.22/57.46 Found (eq_sym010 n0) as proof of (((eq nat) u) z)
% 57.22/57.46 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) z)
% 57.22/57.46 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 57.22/57.46 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 57.22/57.46 Found x0:(P u)
% 57.22/57.46 Found x0 as proof of (P0 u)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 57.22/57.46 Found (eq_ref0 z) as proof of (((eq nat) z) b0)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 57.22/57.46 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 57.22/57.46 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 57.22/57.46 Found (eq_ref0 b0) as proof of (((eq nat) b0) u)
% 57.22/57.46 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 57.22/57.46 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 57.22/57.46 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 57.22/57.46 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 57.22/57.46 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 57.22/57.46 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 57.22/57.46 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 57.22/57.46 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 57.22/57.46 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 57.22/57.46 Found x0:(((more z) u)->False)
% 57.22/57.46 Found x0 as proof of (((more z) u)->False)
% 57.22/57.46 Found x0:(((more z) u)->False)
% 57.22/57.46 Found x0 as proof of (((more z) u)->False)
% 57.22/57.46 Found x0:(P z)
% 57.22/57.46 Found x0 as proof of (P0 z)
% 57.22/57.46 Found x0:(((more z) u)->False)
% 57.22/57.46 Found x0 as proof of (((more z) u)->False)
% 57.22/57.46 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 57.22/57.46 Found (eq_ref00 P) as proof of (P0 b)
% 57.22/57.46 Found ((eq_ref0 b) P) as proof of (P0 b)
% 57.22/57.46 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 65.20/65.38 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 65.20/65.38 Found x0:(P z)
% 65.20/65.38 Found x0 as proof of (P0 z)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 65.20/65.38 Found (eq_ref0 z) as proof of (((eq nat) z) z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 65.20/65.38 Found (n00 ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 65.20/65.38 Found ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 65.20/65.38 Found ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 65.20/65.38 Found ((eq_sym0000 ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found ((eq_sym0000 ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found (((fun (x0:(((eq nat) u) z))=> ((eq_sym000 x0) (fun (x2:nat)=> ((P z)->(P x2))))) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found (((fun (x0:(((eq nat) u) z))=> (((eq_sym00 z) x0) (fun (x2:nat)=> ((P z)->(P x2))))) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found (((fun (x0:(((eq nat) u) z))=> ((((eq_sym0 u) z) x0) (fun (x2:nat)=> ((P z)->(P x2))))) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found (((fun (x0:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x0) (fun (x2:nat)=> ((P z)->(P x2))))) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found (((fun (x0:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x0) (fun (x2:nat)=> ((P z)->(P x2))))) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) (((eq_ref nat) z) P)) as proof of ((P z)->(P u))
% 65.20/65.38 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 65.20/65.38 Found (eq_ref0 z) as proof of (P z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (P z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (P z)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 65.20/65.38 Found (eq_ref0 z) as proof of (P z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (P z)
% 65.20/65.38 Found ((eq_ref nat) z) as proof of (P z)
% 65.20/65.38 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 65.20/65.38 Found (eq_ref00 P) as proof of (P0 b)
% 65.20/65.38 Found ((eq_ref0 b) P) as proof of (P0 b)
% 65.20/65.38 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 65.20/65.38 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 65.20/65.38 Found eq_ref000:=(eq_ref00 P):((P u)->(P u))
% 65.20/65.38 Found (eq_ref00 P) as proof of (P0 u)
% 65.20/65.38 Found ((eq_ref0 u) P) as proof of (P0 u)
% 65.20/65.38 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 65.20/65.38 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 65.20/65.38 Found x0:(((more z) u)->False)
% 65.20/65.38 Found x0 as proof of (((more z) u)->False)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 65.20/65.38 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 65.20/65.38 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 65.20/65.38 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 65.20/65.38 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 65.20/65.38 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 65.20/65.38 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 65.20/65.38 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 65.20/65.38 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 70.42/70.61 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 70.42/70.61 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 70.42/70.61 Found (eq_ref0 z) as proof of (((eq nat) z) z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (((eq nat) z) z)
% 70.42/70.61 Found (n00 ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 70.42/70.61 Found ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 70.42/70.61 Found ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z)) as proof of (((eq nat) u) z)
% 70.42/70.61 Found (eq_sym0000 ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found (eq_sym0000 ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found ((fun (x0:(((eq nat) u) z))=> ((eq_sym000 x0) P)) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found ((fun (x0:(((eq nat) u) z))=> (((eq_sym00 z) x0) P)) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found ((fun (x0:(((eq nat) u) z))=> ((((eq_sym0 u) z) x0) P)) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found ((fun (x0:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x0) P)) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found ((fun (x0:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x0) P)) ((n0 (fun (x1:nat)=> (((eq nat) x1) z))) ((eq_ref nat) z))) as proof of ((P z)->(P u))
% 70.42/70.61 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 70.42/70.61 Found (eq_ref0 z) as proof of (P z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (P z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (P z)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 70.42/70.61 Found (eq_ref0 z) as proof of (P z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (P z)
% 70.42/70.61 Found ((eq_ref nat) z) as proof of (P z)
% 70.42/70.61 Found x0:(((more z) u)->False)
% 70.42/70.61 Found x0 as proof of (((more z) u)->False)
% 70.42/70.61 Found x0:(((more z) u)->False)
% 70.42/70.61 Found x0 as proof of (((more z) u)->False)
% 70.42/70.61 Found eq_ref000:=(eq_ref00 P):((P u)->(P u))
% 70.42/70.61 Found (eq_ref00 P) as proof of (P0 u)
% 70.42/70.61 Found ((eq_ref0 u) P) as proof of (P0 u)
% 70.42/70.61 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 70.42/70.61 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 70.42/70.61 Found x0:(((more z) u)->False)
% 70.42/70.61 Found x0 as proof of (((more z) u)->False)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 70.42/70.61 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 70.42/70.61 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 70.42/70.61 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 70.42/70.61 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 70.42/70.61 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 70.42/70.61 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 70.42/70.61 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 70.42/70.61 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 92.55/92.79 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 92.55/92.79 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 92.55/92.79 Found x0:(P u)
% 92.55/92.79 Instantiate: b:=u:nat
% 92.55/92.79 Found x0 as proof of (P0 b)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 92.55/92.79 Found (eq_ref00 P) as proof of (P0 z)
% 92.55/92.79 Found ((eq_ref0 z) P) as proof of (P0 z)
% 92.55/92.79 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 92.55/92.79 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 92.55/92.79 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 92.55/92.79 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 92.55/92.79 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (P z)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (P z)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (P z)
% 92.55/92.79 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 92.55/92.79 Found (eq_ref00 P) as proof of (P0 z)
% 92.55/92.79 Found ((eq_ref0 z) P) as proof of (P0 z)
% 92.55/92.79 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 92.55/92.79 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 92.55/92.79 Found x0:(P u)
% 92.55/92.79 Instantiate: b:=u:nat
% 92.55/92.79 Found x0 as proof of (P0 b)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found x0:(P1 u)
% 92.55/92.79 Found x0 as proof of (P2 u)
% 92.55/92.79 Found x0:(P1 u)
% 92.55/92.79 Found x0 as proof of (P2 u)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (P z)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (P z)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (P z)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 92.55/92.79 Found (eq_ref0 b0) as proof of (((eq nat) b0) z)
% 92.55/92.79 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 92.55/92.79 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 92.55/92.79 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 92.55/92.79 Found (eq_ref0 u) as proof of (((eq nat) u) b0)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 92.55/92.79 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 92.55/92.79 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 92.55/92.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 92.55/92.79 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 92.55/92.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 92.55/92.79 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 115.49/115.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 115.49/115.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 115.49/115.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 115.49/115.72 Found (eq_ref0 b0) as proof of (((eq nat) b0) z)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) z)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 115.49/115.72 Found (eq_ref0 u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found x00:=(x0 n0):False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found x0:((P b)->False)
% 115.49/115.72 Instantiate: b:=u:nat
% 115.49/115.72 Found x0 as proof of (((more z) u)->False)
% 115.49/115.72 Found x00:=(x0 n0):False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 115.49/115.72 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 115.49/115.72 Found x0:((P b)->False)
% 115.49/115.72 Instantiate: b:=u:nat
% 115.49/115.72 Found x0 as proof of (((more z) u)->False)
% 115.49/115.72 Found x0:((P b)->False)
% 115.49/115.72 Instantiate: b:=u:nat
% 115.49/115.72 Found x0 as proof of (((more z) u)->False)
% 115.49/115.72 Found x0:((P b)->False)
% 115.49/115.72 Instantiate: b:=u:nat
% 115.49/115.72 Found x0 as proof of (((more z) u)->False)
% 115.49/115.72 Found x00:=(x0 n0):False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 115.49/115.72 Found (eq_ref0 u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 115.49/115.72 Found (eq_ref0 b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found x0:(P b)
% 115.49/115.72 Found x0 as proof of (P0 z)
% 115.49/115.72 Found x00:=(x0 n0):False
% 115.49/115.72 Found (x0 n0) as proof of False
% 115.49/115.72 Found (fun (x0:((((eq nat) z) b)->False))=> (x0 n0)) as proof of False
% 115.49/115.72 Found (fun (x0:((((eq nat) z) b)->False))=> (x0 n0)) as proof of (((((eq nat) z) b)->False)->False)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 115.49/115.72 Found (eq_ref0 u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (((eq nat) u) b0)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 115.49/115.72 Found (eq_ref0 b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 115.49/115.72 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 115.49/115.72 Found (eq_ref0 u) as proof of (P u)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (P u)
% 115.49/115.72 Found ((eq_ref nat) u) as proof of (P u)
% 115.49/115.72 Found x0:(P z)
% 115.49/115.72 Found x0 as proof of (P0 z)
% 115.49/115.72 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 115.49/115.72 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 115.49/115.72 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 115.49/115.72 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P b))
% 115.49/115.72 Found (eq_sym0100 P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((eq_sym010 n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P b))
% 115.49/115.72 Found (eq_sym0100 P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((eq_sym010 n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 115.49/115.72 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 139.63/139.90 Found x0:(P z)
% 139.63/139.90 Found x0 as proof of (P0 z)
% 139.63/139.90 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 139.63/139.90 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 139.63/139.90 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 139.63/139.90 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 139.63/139.90 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) b) z)
% 139.63/139.90 Found (eq_sym010 n0) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_sym01 b) n0) as proof of (((eq nat) b) z)
% 139.63/139.90 Found (((eq_sym0 z) b) n0) as proof of (((eq nat) b) z)
% 139.63/139.90 Found (((eq_sym0 z) b) n0) as proof of (((eq nat) b) z)
% 139.63/139.90 Found x0:(P z)
% 139.63/139.90 Found x0 as proof of (P0 z)
% 139.63/139.90 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P b))
% 139.63/139.90 Found (eq_sym0100 P) as proof of ((P u)->(P b))
% 139.63/139.90 Found ((eq_sym010 n0) P) as proof of ((P u)->(P b))
% 139.63/139.90 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P b))
% 139.63/139.90 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 139.63/139.90 Found ((((eq_sym0 b) u) n0) P) as proof of ((P u)->(P b))
% 139.63/139.90 Found eq_sym01000:=(eq_sym0100 P):((P b)->(P z))
% 139.63/139.90 Found (eq_sym0100 P) as proof of ((P b)->(P z))
% 139.63/139.90 Found ((eq_sym010 n0) P) as proof of ((P b)->(P z))
% 139.63/139.90 Found (((eq_sym01 b) n0) P) as proof of ((P b)->(P z))
% 139.63/139.90 Found ((((eq_sym0 z) b) n0) P) as proof of ((P b)->(P z))
% 139.63/139.90 Found ((((eq_sym0 z) b) n0) P) as proof of ((P b)->(P z))
% 139.63/139.90 Found x00:=(x0 n0):False
% 139.63/139.90 Found (x0 n0) as proof of False
% 139.63/139.90 Found (x0 n0) as proof of False
% 139.63/139.90 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 139.63/139.90 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 139.63/139.90 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 139.63/139.90 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 139.63/139.90 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found eq_ref000:=(eq_ref00 P):((P u)->(P u))
% 139.63/139.90 Found (eq_ref00 P) as proof of (P0 u)
% 139.63/139.90 Found ((eq_ref0 u) P) as proof of (P0 u)
% 139.63/139.90 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 139.63/139.90 Found (((eq_ref nat) u) P) as proof of (P0 u)
% 139.63/139.90 Found x00:=(x0 n0):False
% 139.63/139.90 Found (x0 n0) as proof of False
% 139.63/139.90 Found (x0 n0) as proof of False
% 139.63/139.90 Found x00:=(x0 n0):False
% 139.63/139.90 Found (x0 n0) as proof of False
% 139.63/139.90 Found (fun (x0:((forall (P:(nat->Prop)), ((P z)->(P u)))->False))=> (x0 n0)) as proof of False
% 139.63/139.90 Found (fun (x0:((forall (P:(nat->Prop)), ((P z)->(P u)))->False))=> (x0 n0)) as proof of (((forall (P:(nat->Prop)), ((P z)->(P u)))->False)->False)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 139.63/139.90 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 139.63/139.90 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 139.63/139.90 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 139.63/139.90 Found (eq_ref0 b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) z)
% 139.63/139.90 Found x0:(P z)
% 139.63/139.90 Instantiate: b:=z:nat
% 139.63/139.90 Found x0 as proof of (P0 b)
% 139.63/139.90 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 139.63/139.90 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (fun (x0:((forall (P:(nat->Prop)), ((P z)->(P u)))->False))=> (x0 n0)) as proof of False
% 162.28/162.53 Found (fun (x0:((forall (P:(nat->Prop)), ((P z)->(P u)))->False))=> (x0 n0)) as proof of (((forall (P:(nat->Prop)), ((P z)->(P u)))->False)->False)
% 162.28/162.53 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 162.28/162.53 Found (eq_ref00 P) as proof of (P0 b)
% 162.28/162.53 Found ((eq_ref0 b) P) as proof of (P0 b)
% 162.28/162.53 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 162.28/162.53 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found x0:(P z)
% 162.28/162.53 Instantiate: b:=z:nat
% 162.28/162.53 Found x0 as proof of (P0 b)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 162.28/162.53 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found x0:(((more z) u)->False)
% 162.28/162.53 Found x0 as proof of (((more z) u)->False)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 162.28/162.53 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found x0:(((more z) u)->False)
% 162.28/162.53 Found x0 as proof of (((more z) u)->False)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 162.28/162.53 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found x0:(((more z) u)->False)
% 162.28/162.53 Found x0 as proof of (((more z) u)->False)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 162.28/162.53 Found (eq_ref0 b0) as proof of (((eq nat) b0) b)
% 162.28/162.53 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 162.28/162.53 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 162.28/162.53 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) b)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 162.28/162.53 Found (eq_ref0 z) as proof of (((eq nat) z) b0)
% 162.28/162.53 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 162.28/162.53 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 162.28/162.53 Found ((eq_ref nat) z) as proof of (((eq nat) z) b0)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 162.28/162.53 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 162.28/162.53 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 162.28/162.53 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 162.28/162.53 Found x0:(P b)
% 162.28/162.53 Found x0 as proof of (P0 z)
% 162.28/162.53 Found x00:=(x0 n0):False
% 162.28/162.53 Found (x0 n0) as proof of False
% 162.28/162.53 Found (x0 n0) as proof of False
% 203.51/203.72 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 203.51/203.72 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found x0:(P b)
% 203.51/203.72 Found x0 as proof of (P0 z)
% 203.51/203.72 Found x0:(P b)
% 203.51/203.72 Found x0 as proof of (P0 z)
% 203.51/203.72 Found x00:=(x0 n0):False
% 203.51/203.72 Found (x0 n0) as proof of False
% 203.51/203.72 Found (fun (x0:((((eq nat) b0) u)->False))=> (x0 n0)) as proof of False
% 203.51/203.72 Found (fun (x0:((((eq nat) b0) u)->False))=> (x0 n0)) as proof of (((((eq nat) b0) u)->False)->False)
% 203.51/203.72 Found x10:=(x1 n0):False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found x0:(P b)
% 203.51/203.72 Found x0 as proof of (P0 z)
% 203.51/203.72 Found x10:=(x1 n0):False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found (fun (x1:((((eq nat) b) u)->False))=> (x1 n0)) as proof of False
% 203.51/203.72 Found (fun (x1:((((eq nat) b) u)->False))=> (x1 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 203.51/203.72 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 203.51/203.72 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 203.51/203.72 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 203.51/203.72 Found (eq_trans000000 ((eq_ref nat) z)) as proof of ((P b)->(P u))
% 203.51/203.72 Found (eq_trans000000 ((eq_ref nat) z)) as proof of ((P b)->(P u))
% 203.51/203.72 Found ((fun (x0:(((eq nat) z) b))=> ((eq_trans00000 x0) P)) ((eq_ref nat) z)) as proof of ((P b)->(P u))
% 203.51/203.72 Found ((fun (x0:(((eq nat) z) b))=> (((fun (x0:(((eq nat) z) b))=> ((eq_trans0000 x0) n0)) x0) P)) ((eq_ref nat) z)) as proof of ((P b)->(P u))
% 203.51/203.72 Found ((fun (x0:(((eq nat) z) b))=> (((fun (x0:(((eq nat) z) b))=> ((eq_trans0000 x0) n0)) x0) P)) ((eq_ref nat) z)) as proof of ((P b)->(P u))
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found x10:=(x1 n0):False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found x0:(P u)
% 203.51/203.72 Instantiate: b:=u:nat
% 203.51/203.72 Found x0 as proof of (P0 b)
% 203.51/203.72 Found n0:(((eq nat) z) u)
% 203.51/203.72 Instantiate: b:=u:nat
% 203.51/203.72 Found n0 as proof of (((eq nat) z) b)
% 203.51/203.72 Found ((eq_sym0100 n0) x0) as proof of (P z)
% 203.51/203.72 Found ((eq_sym0100 n0) x0) as proof of (P z)
% 203.51/203.72 Found (((fun (x1:(((eq nat) z) b))=> ((eq_sym010 x1) P)) n0) x0) as proof of (P z)
% 203.51/203.72 Found (((fun (x1:(((eq nat) z) u))=> (((eq_sym01 u) x1) P)) n0) x0) as proof of (P z)
% 203.51/203.72 Found (((fun (x1:(((eq nat) z) u))=> ((((eq_sym0 z) u) x1) P)) n0) x0) as proof of (P z)
% 203.51/203.72 Found (((fun (x1:(((eq nat) z) u))=> ((((eq_sym0 z) u) x1) P)) n0) x0) as proof of (P z)
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found x0:(P z)
% 203.51/203.72 Found x0 as proof of (P0 z)
% 203.51/203.72 Found x10:=(x1 n0):False
% 203.51/203.72 Found (x1 n0) as proof of False
% 203.51/203.72 Found (fun (x1:((((eq nat) b) u)->False))=> (x1 n0)) as proof of False
% 203.51/203.72 Found (fun (x1:((((eq nat) b) u)->False))=> (x1 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 203.51/203.72 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 203.51/203.72 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 203.51/203.72 Found ((eq_sym0000 (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found ((eq_sym0000 (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found (((fun (x1:(((eq nat) u) b))=> ((eq_sym000 x1) P)) (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found (((fun (x1:(((eq nat) u) z))=> (((eq_sym00 z) x1) P)) (((eq_sym0 z) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found (((fun (x1:(((eq nat) u) z))=> ((((eq_sym0 u) z) x1) P)) (((eq_sym0 z) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found (((fun (x1:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x1) P)) ((((eq_sym nat) z) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found (((fun (x1:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x1) P)) ((((eq_sym nat) z) u) n0)) x0) as proof of (P u)
% 203.51/203.72 Found x0:(P z)
% 203.51/203.72 Found x0 as proof of (P0 z)
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 203.51/203.72 Found x0:(((more z) u)->False)
% 203.51/203.72 Found x0 as proof of (((more z) u)->False)
% 225.21/225.47 Found x0:(P z)
% 225.21/225.47 Found x0 as proof of (P0 z)
% 225.21/225.47 Found x00:=(x0 n0):False
% 225.21/225.47 Found (x0 n0) as proof of False
% 225.21/225.47 Found (x0 n0) as proof of False
% 225.21/225.47 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 225.21/225.47 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 225.21/225.47 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_sym0000 (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found ((eq_sym0000 (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) u) b))=> ((eq_sym000 x1) P)) (((eq_sym0 b) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) u) z))=> (((eq_sym00 z) x1) P)) (((eq_sym0 z) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) u) z))=> ((((eq_sym0 u) z) x1) P)) (((eq_sym0 z) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x1) P)) ((((eq_sym nat) z) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) u) z))=> (((((eq_sym nat) u) z) x1) P)) ((((eq_sym nat) z) u) n0)) x0) as proof of (P u)
% 225.21/225.47 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 225.21/225.47 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 225.21/225.47 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 225.21/225.47 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 225.21/225.47 Found x0:(P b)
% 225.21/225.47 Found x0 as proof of (P0 z)
% 225.21/225.47 Found ((eq_trans000000 ((eq_ref nat) z)) x0) as proof of (P u)
% 225.21/225.47 Found ((eq_trans000000 ((eq_ref nat) z)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) z) b))=> ((eq_trans00000 x1) P)) ((eq_ref nat) z)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) z) b))=> (((fun (x1:(((eq nat) z) b))=> ((eq_trans0000 x1) n0)) x1) P)) ((eq_ref nat) z)) x0) as proof of (P u)
% 225.21/225.47 Found (((fun (x1:(((eq nat) z) b))=> (((fun (x1:(((eq nat) z) b))=> ((eq_trans0000 x1) n0)) x1) P)) ((eq_ref nat) z)) x0) as proof of (P u)
% 225.21/225.47 Found x0:(P z)
% 225.21/225.47 Found x0 as proof of (P0 z)
% 225.21/225.47 Found x0:(P z)
% 225.21/225.47 Instantiate: b:=z:nat
% 225.21/225.47 Found x0 as proof of (P0 b)
% 225.21/225.47 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 225.21/225.47 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 225.21/225.47 Found x00:=(x0 n0):False
% 225.21/225.47 Found (x0 n0) as proof of False
% 225.21/225.47 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 225.21/225.47 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 225.21/225.47 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 b))
% 225.21/225.47 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 b))
% 225.21/225.47 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 b))
% 225.21/225.47 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 b))
% 225.21/225.47 Found ((((eq_sym0 b) u) n0) P1) as proof of ((P1 u)->(P1 b))
% 225.21/225.47 Found ((((eq_sym0 b) u) n0) P1) as proof of ((P1 u)->(P1 b))
% 225.21/225.47 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 225.21/225.47 Found (eq_ref0 b0) as proof of (((eq nat) b0) u)
% 225.21/225.47 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 225.21/225.47 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 225.21/225.47 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) u)
% 225.21/225.47 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 225.21/225.47 Found (eq_ref0 b) as proof of (((eq nat) b) b0)
% 225.21/225.47 Found ((eq_ref nat) b) as proof of (((eq nat) b) b0)
% 225.21/225.47 Found ((eq_ref nat) b) as proof of (((eq nat) b) b0)
% 225.21/225.47 Found ((eq_ref nat) b) as proof of (((eq nat) b) b0)
% 225.21/225.47 Found x00:=(x0 n0):False
% 225.21/225.47 Found (x0 n0) as proof of False
% 225.21/225.47 Found (x0 n0) as proof of False
% 225.21/225.47 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 225.21/225.47 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 225.21/225.47 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 225.21/225.47 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 225.21/225.47 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 225.21/225.47 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found x0:(P z)
% 259.91/260.21 Instantiate: b:=z:nat
% 259.91/260.21 Found x0 as proof of (P0 b)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 259.91/260.21 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 259.91/260.21 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 259.91/260.21 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 259.91/260.21 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 259.91/260.21 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 259.91/260.21 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found x0:(((more z) u)->False)
% 259.91/260.21 Found x0 as proof of (((more z) u)->False)
% 259.91/260.21 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 b))
% 259.91/260.21 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 b))
% 259.91/260.21 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 b))
% 259.91/260.21 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 b))
% 259.91/260.21 Found ((((eq_sym0 b) u) n0) P1) as proof of ((P1 u)->(P1 b))
% 259.91/260.21 Found ((((eq_sym0 b) u) n0) P1) as proof of ((P1 u)->(P1 b))
% 259.91/260.21 Found x00:=(x0 n0):False
% 259.91/260.21 Found (x0 n0) as proof of False
% 259.91/260.21 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 259.91/260.21 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 259.91/260.21 Found x0:(((more z) u)->False)
% 259.91/260.21 Found x0 as proof of (((more z) u)->False)
% 259.91/260.21 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 259.91/260.21 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of ((P u)->(P z))
% 259.91/260.21 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 259.91/260.21 Found x0:(((more z) u)->False)
% 259.91/260.21 Found x0 as proof of (((more z) u)->False)
% 259.91/260.21 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P z))
% 259.91/260.21 Found (eq_sym0100 P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((eq_sym010 n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found ((((eq_sym0 z) u) n0) P) as proof of ((P u)->(P z))
% 259.91/260.21 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of ((P u)->(P z))
% 259.91/260.21 Found (fun (P:(nat->Prop))=> ((((eq_sym0 z) u) n0) P)) as proof of (((eq nat) u) z)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 259.91/260.21 Found (eq_ref0 z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 259.91/260.21 Found (eq_ref0 z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found x0:(P1 u)
% 259.91/260.21 Found x0 as proof of (P2 u)
% 259.91/260.21 Found x0:(P1 u)
% 259.91/260.21 Found x0 as proof of (P2 u)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 259.91/260.21 Found (eq_ref0 z) as proof of (P z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P z)
% 259.91/260.21 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 259.91/260.21 Found (eq_ref00 P) as proof of (P0 b)
% 259.91/260.21 Found ((eq_ref0 b) P) as proof of (P0 b)
% 259.91/260.21 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 259.91/260.21 Found (((eq_ref nat) b) P) as proof of (P0 b)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 259.91/260.21 Found (eq_ref0 z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 259.91/260.21 Found (eq_ref0 z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found ((eq_ref nat) z) as proof of (P1 z)
% 259.91/260.21 Found x00:=(x0 n0):False
% 259.91/260.21 Found (x0 n0) as proof of False
% 259.91/260.21 Found (x0 n0) as proof of False
% 259.91/260.21 Found x00:=(x0 n0):False
% 259.91/260.21 Found (x0 n0) as proof of False
% 259.91/260.21 Found (x0 n0) as proof of False
% 259.91/260.21 Found x0:(P u)
% 259.91/260.21 Found x0 as proof of (P0 u)
% 259.91/260.21 Found x0:(P b)
% 259.91/260.21 Found x0 as proof of (P0 u)
% 259.91/260.21 Found eq_sym01000:=(eq_sym0100 P0):((P0 u)->(P0 b))
% 259.91/260.21 Found (eq_sym0100 P0) as proof of ((P0 u)->(P0 b))
% 259.91/260.21 Found ((eq_sym010 n0) P0) as proof of ((P0 u)->(P0 b))
% 259.91/260.21 Found (((eq_sym01 u) n0) P0) as proof of ((P0 u)->(P0 b))
% 259.91/260.21 Found ((((eq_sym0 b) u) n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found ((((eq_sym0 b) u) n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found x10:=(x1 n0):False
% 276.70/276.97 Found (x1 n0) as proof of False
% 276.70/276.97 Found (x1 n0) as proof of False
% 276.70/276.97 Found x0:(((more z) u)->False)
% 276.70/276.97 Found x0 as proof of (((more z) u)->False)
% 276.70/276.97 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) b)
% 276.70/276.97 Found (eq_sym010 n0) as proof of (((eq nat) u) b)
% 276.70/276.97 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) b)
% 276.70/276.97 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 276.70/276.97 Found (((eq_sym0 b) u) n0) as proof of (((eq nat) u) b)
% 276.70/276.97 Found x0:(P u)
% 276.70/276.97 Instantiate: b:=u:nat
% 276.70/276.97 Found x0 as proof of (P0 b)
% 276.70/276.97 Found n0:(((eq nat) z) u)
% 276.70/276.97 Instantiate: b:=u:nat
% 276.70/276.97 Found n0 as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_sym0100 n0) x0) as proof of (P z)
% 276.70/276.97 Found ((eq_sym0100 n0) x0) as proof of (P z)
% 276.70/276.97 Found (((fun (x1:(((eq nat) z) b))=> ((eq_sym010 x1) P)) n0) x0) as proof of (P z)
% 276.70/276.97 Found (((fun (x1:(((eq nat) z) u))=> (((eq_sym01 u) x1) P)) n0) x0) as proof of (P z)
% 276.70/276.97 Found (((fun (x1:(((eq nat) z) u))=> ((((eq_sym0 z) u) x1) P)) n0) x0) as proof of (P z)
% 276.70/276.97 Found (((fun (x1:(((eq nat) z) u))=> ((((eq_sym0 z) u) x1) P)) n0) x0) as proof of (P z)
% 276.70/276.97 Found x00:=(x0 n0):False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found (fun (x0:((forall (P:(nat->Prop)), ((P b)->(P u)))->False))=> (x0 n0)) as proof of False
% 276.70/276.97 Found (fun (x0:((forall (P:(nat->Prop)), ((P b)->(P u)))->False))=> (x0 n0)) as proof of (((forall (P:(nat->Prop)), ((P b)->(P u)))->False)->False)
% 276.70/276.97 Found x00:=(x0 n0):False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 276.70/276.97 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 276.70/276.97 Found x0:((P b)->False)
% 276.70/276.97 Instantiate: b:=u:nat
% 276.70/276.97 Found x0 as proof of (((more z) u)->False)
% 276.70/276.97 Found x10:=(x1 n0):False
% 276.70/276.97 Found (x1 n0) as proof of False
% 276.70/276.97 Found (fun (x1:((((eq nat) z) b)->False))=> (x1 n0)) as proof of False
% 276.70/276.97 Found (fun (x1:((((eq nat) z) b)->False))=> (x1 n0)) as proof of (((((eq nat) z) b)->False)->False)
% 276.70/276.97 Found x00:=(x0 n0):False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found x00:=(x0 n0):False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found (x0 n0) as proof of False
% 276.70/276.97 Found x0:(((more z) u)->False)
% 276.70/276.97 Found x0 as proof of (((more z) u)->False)
% 276.70/276.97 Found eq_sym01000:=(eq_sym0100 P0):((P0 u)->(P0 b))
% 276.70/276.97 Found (eq_sym0100 P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found ((eq_sym010 n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found (((eq_sym01 u) n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found ((((eq_sym0 b) u) n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found ((((eq_sym0 b) u) n0) P0) as proof of ((P0 u)->(P0 b))
% 276.70/276.97 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 276.70/276.97 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 276.70/276.97 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 276.70/276.97 Found (eq_ref00 P) as proof of (P0 z)
% 276.70/276.97 Found ((eq_ref0 z) P) as proof of (P0 z)
% 276.70/276.97 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 276.70/276.97 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 276.70/276.97 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 276.70/276.97 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 276.70/276.97 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 276.70/276.97 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 276.70/276.97 Found x10:=(x1 n0):False
% 276.70/276.97 Found (x1 n0) as proof of False
% 276.70/276.97 Found (x1 n0) as proof of False
% 276.70/276.97 Found x0:(((more z) u)->False)
% 276.70/276.97 Found x0 as proof of (((more z) u)->False)
% 276.70/276.97 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 276.70/276.97 Found (eq_ref00 P) as proof of (P0 z)
% 276.70/276.97 Found ((eq_ref0 z) P) as proof of (P0 z)
% 276.70/276.97 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 276.70/276.97 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 287.60/287.84 Found x0:(((more z) u)->False)
% 287.60/287.84 Found x0 as proof of (((more z) u)->False)
% 287.60/287.84 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 287.60/287.84 Found (eq_ref0 b) as proof of (P b)
% 287.60/287.84 Found ((eq_ref nat) b) as proof of (P b)
% 287.60/287.84 Found ((eq_ref nat) b) as proof of (P b)
% 287.60/287.84 Found ((eq_ref nat) b) as proof of (P b)
% 287.60/287.84 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 287.60/287.84 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 287.60/287.84 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 287.60/287.84 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 287.60/287.84 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 287.60/287.84 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 287.60/287.84 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 287.60/287.84 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 287.60/287.84 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 287.60/287.84 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 287.60/287.84 Found x0:((P b)->False)
% 287.60/287.84 Instantiate: b:=u:nat
% 287.60/287.84 Found x0 as proof of (((more z) u)->False)
% 287.60/287.84 Found x0:((P b)->False)
% 287.60/287.84 Instantiate: b:=u:nat
% 287.60/287.84 Found x0 as proof of (((more z) u)->False)
% 287.60/287.84 Found x00:=(x0 n0):False
% 287.60/287.84 Found (x0 n0) as proof of False
% 287.60/287.84 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of False
% 287.60/287.84 Found (fun (x0:((((eq nat) b) u)->False))=> (x0 n0)) as proof of (((((eq nat) b) u)->False)->False)
% 287.60/287.84 Found x00:=(x0 n0):False
% 287.60/287.84 Found (x0 n0) as proof of False
% 287.60/287.84 Found (fun (x0:((forall (P:(nat->Prop)), ((P b)->(P u)))->False))=> (x0 n0)) as proof of False
% 287.60/287.84 Found (fun (x0:((forall (P:(nat->Prop)), ((P b)->(P u)))->False))=> (x0 n0)) as proof of (((forall (P:(nat->Prop)), ((P b)->(P u)))->False)->False)
% 287.60/287.84 Found eq_sym01000:=(eq_sym0100 P):((P u)->(P b0))
% 287.60/287.84 Found (eq_sym0100 P) as proof of ((P u)->(P b0))
% 287.60/287.84 Found ((eq_sym010 n0) P) as proof of ((P u)->(P b0))
% 287.60/287.84 Found (((eq_sym01 u) n0) P) as proof of ((P u)->(P b0))
% 287.60/287.84 Found ((((eq_sym0 b0) u) n0) P) as proof of ((P u)->(P b0))
% 287.60/287.84 Found ((((eq_sym0 b0) u) n0) P) as proof of ((P u)->(P b0))
% 287.60/287.84 Found x0:(P b)
% 287.60/287.84 Found x0 as proof of (P0 z)
% 287.60/287.84 Found x0:((P b)->False)
% 287.60/287.84 Instantiate: b:=u:nat
% 287.60/287.84 Found x0 as proof of (((more z) u)->False)
% 287.60/287.84 Found x0:(P b)
% 287.60/287.84 Found x0 as proof of (P0 z)
% 287.60/287.84 Found x0:((P b)->False)
% 287.60/287.84 Instantiate: b:=u:nat
% 287.60/287.84 Found x0 as proof of (((more z) u)->False)
% 287.60/287.84 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 287.60/287.84 Found (eq_sym010 n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found ((eq_sym01 u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found (((eq_sym0 z) u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found (((eq_sym0 z) u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 287.60/287.84 Found (eq_sym010 n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found ((eq_sym01 u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found (((eq_sym0 z) u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found (((eq_sym0 z) u) n0) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 287.60/287.84 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 287.60/287.84 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 287.60/287.84 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 287.60/287.84 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 299.00/299.28 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 299.00/299.28 Found (eq_ref00 P) as proof of (P0 z)
% 299.00/299.28 Found ((eq_ref0 z) P) as proof of (P0 z)
% 299.00/299.28 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 299.00/299.28 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 299.00/299.28 Found (eq_ref0 z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (((eq nat) z) b)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 299.00/299.28 Found (eq_ref0 b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (((eq nat) b) u)
% 299.00/299.28 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 299.00/299.28 Found (eq_sym010 n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found eq_sym0100:=(eq_sym010 n0):(((eq nat) u) z)
% 299.00/299.28 Found (eq_sym010 n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found ((eq_sym01 u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found (((eq_sym0 z) u) n0) as proof of (((eq nat) u) z)
% 299.00/299.28 Found x10:=(x1 n0):False
% 299.00/299.28 Found (x1 n0) as proof of False
% 299.00/299.28 Found (fun (x1:((((eq nat) z) b)->False))=> (x1 n0)) as proof of False
% 299.00/299.28 Found (fun (x1:((((eq nat) z) b)->False))=> (x1 n0)) as proof of (((((eq nat) z) b)->False)->False)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 z):(((eq nat) z) z)
% 299.00/299.28 Found (eq_ref0 z) as proof of (P1 z)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (P1 z)
% 299.00/299.28 Found ((eq_ref nat) z) as proof of (P1 z)
% 299.00/299.28 Found eq_ref000:=(eq_ref00 P):((P z)->(P z))
% 299.00/299.28 Found (eq_ref00 P) as proof of (P0 z)
% 299.00/299.28 Found ((eq_ref0 z) P) as proof of (P0 z)
% 299.00/299.28 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 299.00/299.28 Found (((eq_ref nat) z) P) as proof of (P0 z)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 299.00/299.28 Found (eq_ref0 b) as proof of (P b)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (P b)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (P b)
% 299.00/299.28 Found ((eq_ref nat) b) as proof of (P b)
% 299.00/299.28 Found eq_ref00:=(eq_ref0 u):(((eq nat) u) u)
% 299.00/299.28 Found (eq_ref0 u) as proof of (((eq nat) u) b)
% 299.00/299.28 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 299.00/299.28 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 299.00/299.28 Found ((eq_ref nat) u) as proof of (((eq nat) u) b)
% 299.00/299.28 Found x0:((P b)->False)
% 299.00/299.28 Found x0 as proof of (((more z) u)->False)
% 299.00/299.28 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 299.00/299.28 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 299.00/299.28 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 299.00/299.28 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of (forall (P:(nat->Prop)), ((P u)->(P z)))
% 299.00/299.28 Found x0:((P b)->False)
% 299.00/299.28 Instantiate: b:=u:nat
% 299.00/299.28 Found x0 as proof of (((more z) u)->False)
% 299.00/299.28 Found eq_sym01000:=(eq_sym0100 P1):((P1 u)->(P1 z))
% 299.00/299.28 Found (eq_sym0100 P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((eq_sym010 n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (((eq_sym01 u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found ((((eq_sym0 z) u) n0) P1) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Prop))=> ((((eq_sym0 z) u) n0) P1)) as proof of ((P1 u)->(P1 z))
% 299.00/299.28 Found (fun (P1:(nat->Pr
%------------------------------------------------------------------------------