%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : NUM741^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n031.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 13:11:35 EST 2018

% Result   : Timeout 294.99s
% 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  : NUM741^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.04  % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23  % Computer : n031.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 13:23:20 CST 2018
% 0.02/0.23  % CPUTime  : 
% 0.07/0.25  Python 2.7.13
% 8.48/8.70  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40af80>, <kernel.Type object at 0x2aef7b463fc8>) of role type named frac_type
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring frac:Type
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40a170>, <kernel.Constant object at 0x2aef7b40a560>) of role type named x
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring x:frac
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40a758>, <kernel.Constant object at 0x2aef7b4635f0>) of role type named y
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring y:frac
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40a560>, <kernel.Constant object at 0x2aef7b463b90>) of role type named z
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring z:frac
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40a758>, <kernel.Type object at 0x2aef7b463b90>) of role type named nat_type
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring nat:Type
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40af80>, <kernel.DependentProduct object at 0x2aef7b463bd8>) of role type named less
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring less:(nat->(nat->Prop))
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b40af80>, <kernel.DependentProduct object at 0x2aef7b463b48>) of role type named ts
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring ts:(nat->(nat->nat))
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b4635f0>, <kernel.DependentProduct object at 0x2aef7b4637e8>) of role type named num
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring num:(frac->nat)
% 8.48/8.70  FOF formula (<kernel.Constant object at 0x2aef7b463bd8>, <kernel.DependentProduct object at 0x2aef7b463f80>) of role type named den
% 8.48/8.70  Using role type
% 8.48/8.70  Declaring den:(frac->nat)
% 8.48/8.70  FOF formula ((less ((ts (num x)) (den y))) ((ts (num y)) (den x))) of role axiom named l
% 8.48/8.70  A new axiom: ((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 8.48/8.70  FOF formula ((less ((ts (num y)) (den z))) ((ts (num z)) (den y))) of role axiom named k
% 8.48/8.70  A new axiom: ((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 8.48/8.70  FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less ((ts Xx) Xz)) ((ts Xy) Xz))->((less Xx) Xy))) of role axiom named satz33c
% 8.48/8.70  A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less ((ts Xx) Xz)) ((ts Xy) Xz))->((less Xx) Xy)))
% 8.48/8.70  FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((less Xx) Xy)->(((less Xz) Xu)->((less ((ts Xx) Xz)) ((ts Xy) Xu))))) of role axiom named satz34a
% 8.48/8.70  A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((less Xx) Xy)->(((less Xz) Xu)->((less ((ts Xx) Xz)) ((ts Xy) Xu)))))
% 8.48/8.70  FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx))) of role axiom named satz29
% 8.48/8.70  A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx)))
% 8.48/8.70  FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((ts ((ts Xx) Xy)) Xz)) ((ts Xx) ((ts Xy) Xz)))) of role axiom named satz31
% 8.48/8.70  A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((ts ((ts Xx) Xy)) Xz)) ((ts Xx) ((ts Xy) Xz))))
% 8.48/8.70  FOF formula ((less ((ts (num x)) (den z))) ((ts (num z)) (den x))) of role conjecture named satz50
% 8.48/8.70  Conjecture to prove = ((less ((ts (num x)) (den z))) ((ts (num z)) (den x))):Prop
% 8.48/8.70  Parameter nat_DUMMY:nat.
% 8.48/8.70  We need to prove ['((less ((ts (num x)) (den z))) ((ts (num z)) (den x)))']
% 8.48/8.70  Parameter frac:Type.
% 8.48/8.70  Parameter x:frac.
% 8.48/8.70  Parameter y:frac.
% 8.48/8.70  Parameter z:frac.
% 8.48/8.70  Parameter nat:Type.
% 8.48/8.70  Parameter less:(nat->(nat->Prop)).
% 8.48/8.70  Parameter ts:(nat->(nat->nat)).
% 8.48/8.70  Parameter num:(frac->nat).
% 8.48/8.70  Parameter den:(frac->nat).
% 8.48/8.70  Axiom l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x))).
% 8.48/8.70  Axiom k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y))).
% 8.48/8.70  Axiom satz33c:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((less ((ts Xx) Xz)) ((ts Xy) Xz))->((less Xx) Xy))).
% 8.48/8.70  Axiom satz34a:(forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((less Xx) Xy)->(((less Xz) Xu)->((less ((ts Xx) Xz)) ((ts Xy) Xu))))).
% 8.48/8.70  Axiom satz29:(forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx))).
% 8.48/8.70  Axiom satz31:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((ts ((ts Xx) Xy)) Xz)) ((ts Xx) ((ts Xy) Xz)))).
% 8.48/8.70  Trying to prove ((less ((ts (num x)) (den z))) ((ts (num z)) (den x)))
% 8.48/8.70  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 33.91/34.10  Instantiate: b:=((ts (num z)) (den x)):nat
% 33.91/34.10  Found satz2900 as proof of (((eq nat) ((ts (den x)) (num z))) b)
% 33.91/34.10  Found satz29__eq_sym00:=(satz29__eq_sym0 (num z)):(((eq nat) ((ts (num z)) (den x))) ((ts (den x)) (num z)))
% 33.91/34.10  Found (satz29__eq_sym0 (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 33.91/34.10  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 33.91/34.10  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 33.91/34.10  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 33.91/34.10  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 33.91/34.10  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 33.91/34.10  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 33.91/34.10  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 33.91/34.10  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 33.91/34.10  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 33.91/34.10  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 33.91/34.10  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 33.91/34.10  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 33.91/34.10  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 48.62/48.82  Instantiate: b:=((ts (num z)) (den x)):nat
% 48.62/48.82  Found satz29__eq_sym00 as proof of (((eq nat) ((ts (den x)) (num z))) b)
% 48.62/48.82  Found satz29__eq_sym10:=(satz29__eq_sym1 (num z)):(((eq nat) ((ts (num z)) (den x))) ((ts (den x)) (num z)))
% 48.62/48.82  Found (satz29__eq_sym1 (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 48.62/48.82  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 48.62/48.82  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 48.62/48.82  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 48.62/48.82  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 48.62/48.82  Instantiate: b:=((ts (num z)) (den x)):nat
% 48.62/48.82  Found satz2900 as proof of (((eq nat) ((ts (den x)) (num z))) b)
% 48.62/48.82  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 48.62/48.82  Instantiate: b:=((ts (num z)) (den x)):nat
% 48.62/48.82  Found satz29__eq_sym00 as proof of (((eq nat) ((ts (den x)) (num z))) b)
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 48.62/48.82  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 48.62/48.82  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 48.62/48.82  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 66.92/67.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 66.92/67.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 66.92/67.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found satz29__eq_sym00:=(satz29__eq_sym0 ((ts (num z)) (den x))):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts Xz) ((ts (num z)) (den x))))
% 66.92/67.10  Found (satz29__eq_sym0 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 66.92/67.10  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 66.92/67.10  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 66.92/67.10  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 66.92/67.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 66.92/67.10  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 66.92/67.10  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 66.92/67.10  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 66.92/67.10  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 66.92/67.10  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 66.92/67.10  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 66.92/67.10  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 66.92/67.10  Instantiate: a:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 66.92/67.10  Found satz2900 as proof of (((eq nat) a) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.92/67.10  Found (eq_ref0 b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 66.92/67.10  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 66.92/67.10  Instantiate: a:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 66.92/67.10  Found satz2900 as proof of (((eq nat) a) b)
% 66.92/67.10  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.92/67.10  Found (eq_ref0 b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 66.92/67.10  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 77.56/77.78  Found satz2900:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 77.56/77.78  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 77.56/77.78  Found satz2900 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 ((ts ((ts (den x)) (num z))) Xz)):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts ((ts (den x)) (num z))) Xz))
% 77.56/77.78  Found (eq_ref0 ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 ((ts ((ts (num z)) (den x))) Xz)):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts ((ts (num z)) (den x))) Xz))
% 77.56/77.78  Found (eq_ref0 ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 ((ts ((ts (num z)) (den x))) Xz)):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts ((ts (num z)) (den x))) Xz))
% 77.56/77.78  Found (eq_ref0 ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found satz29__eq_sym00:=(satz29__eq_sym0 ((ts (den x)) (num z))):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts Xz) ((ts (den x)) (num z))))
% 77.56/77.78  Found (satz29__eq_sym0 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 77.56/77.78  Found satz31000:=(satz3100 Xz):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts (num z)) ((ts (den x)) Xz)))
% 77.56/77.78  Found (satz3100 Xz) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found ((satz310 (den x)) Xz) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found (((satz31 (num z)) (den x)) Xz) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found (((satz31 (num z)) (den x)) Xz) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found (((satz31 (num z)) (den x)) Xz) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 77.56/77.78  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 77.56/77.78  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 77.56/77.78  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 77.56/77.78  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 77.56/77.78  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 92.53/92.72  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 92.53/92.72  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 92.53/92.72  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 92.53/92.72  Found eq_ref00:=(eq_ref0 (num z)):(((eq nat) (num z)) (num z))
% 92.53/92.72  Found (eq_ref0 (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found ((eq_ref nat) (num z)) as proof of (((eq nat) (num z)) b)
% 92.53/92.72  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 92.53/92.72  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 92.53/92.72  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 92.53/92.72  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 92.53/92.72  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 92.53/92.72  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 92.53/92.72  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 92.53/92.72  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 92.53/92.72  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 92.53/92.72  Found satz2900 as proof of (((eq nat) a) Xz)
% 92.53/92.72  Found eq_ref00:=(eq_ref0 ((ts (den x)) (num z))):(((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 92.53/92.72  Found (eq_ref0 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 92.53/92.72  Found ((eq_ref nat) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 92.53/92.72  Found ((eq_ref nat) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 92.53/92.72  Found (satz29001 ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 92.53/92.72  Found ((satz2900 (fun (x1:nat)=> (((eq nat) x1) ((ts (den x)) (num z))))) ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 92.53/92.72  Found ((satz2900 (fun (x1:nat)=> (((eq nat) x1) ((ts (den x)) (num z))))) ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 92.53/92.72  Found satz31000:=(satz3100 (den x)):(((eq nat) ((ts ((ts Xz) (num z))) (den x))) ((ts Xz) ((ts (num z)) (den x))))
% 92.53/92.72  Instantiate: b:=((ts Xz) ((ts (num z)) (den x))):nat
% 103.15/103.36  Found satz31000 as proof of (((eq nat) ((ts ((ts Xz) (num z))) (den x))) b)
% 103.15/103.36  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 103.15/103.36  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 103.15/103.36  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 103.15/103.36  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 103.15/103.36  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 103.15/103.36  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 103.15/103.36  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 103.15/103.36  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 103.15/103.36  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 103.15/103.36  Found satz2900 as proof of (((eq nat) a) Xz)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 103.15/103.36  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 103.15/103.36  Found eq_ref00:=(eq_ref0 ((ts ((ts (num z)) (den x))) Xz)):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts ((ts (num z)) (den x))) Xz))
% 103.15/103.36  Found (eq_ref0 ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 124.85/125.05  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 124.85/125.05  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 124.85/125.05  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 124.85/125.05  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 124.85/125.05  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: Xz:=(den y):nat;b:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of (P b)
% 124.85/125.05  Found satz2900:=(satz290 Xz):(((eq nat) ((ts (num z)) Xz)) ((ts Xz) (num z)))
% 124.85/125.05  Found (satz290 Xz) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 124.85/125.05  Found ((satz29 (num z)) Xz) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 124.85/125.05  Found ((satz29 (num z)) Xz) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 124.85/125.05  Found ((satz29 (num z)) Xz) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: a:=((ts (num x)) (den y)):nat;Xz:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less a) Xz)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less Xz) a)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: a:=((ts (num x)) (den y)):nat;Xz:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less a) Xz)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: a:=((ts (num x)) (den y)):nat;Xz:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less a) Xz)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less Xz) a)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 124.85/125.05  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 124.85/125.05  Found l as proof of ((less Xz) a)
% 124.85/125.05  Found satz2901:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 124.85/125.05  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 124.85/125.05  Found satz2901 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 124.85/125.05  Found satz2900:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 124.85/125.05  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 124.85/125.05  Found satz2900 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 124.85/125.05  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 134.70/134.90  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 134.70/134.90  Found l as proof of ((less Xz) a)
% 134.70/134.90  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 134.70/134.90  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 134.70/134.90  Found l as proof of ((less Xz) a)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 134.70/134.90  Found (eq_ref0 b) as proof of (((eq nat) b) (den x))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 134.70/134.90  Found (eq_ref0 b) as proof of (((eq nat) b) (num z))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 134.70/134.90  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found ((eq_ref nat) a) as proof of (((eq nat) a) b)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) x)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found eq_ref00:=(eq_ref0 a):(((eq frac) a) a)
% 134.70/134.90  Found (eq_ref0 a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found ((eq_ref frac) a) as proof of (((eq frac) a) z)
% 134.70/134.90  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 134.70/134.90  Instantiate: b:=((ts (num z)) (den x)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) ((ts (den x)) (num z))) b)
% 134.70/134.90  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 134.70/134.90  Instantiate: Xz:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) Xz) b)
% 134.70/134.90  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 134.70/134.90  Instantiate: Xz:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) Xz) b)
% 134.70/134.90  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 134.70/134.90  Instantiate: Xz:=((ts (num x)) (den y)):nat;b:=((ts (num y)) (den x)):nat
% 134.70/134.90  Found l as proof of (P b)
% 134.70/134.90  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 134.70/134.90  Instantiate: Xz:=((ts (num x)) (den y)):nat;b:=((ts (num y)) (den x)):nat
% 134.70/134.90  Found l as proof of (P b)
% 134.70/134.90  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 134.70/134.90  Instantiate: a:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) a) b)
% 134.70/134.90  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 134.70/134.90  Instantiate: a:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) a) b)
% 134.70/134.90  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 134.70/134.90  Instantiate: a:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 134.70/134.90  Found satz2900 as proof of (((eq nat) a) b)
% 134.70/134.90  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 134.70/134.90  Instantiate: a:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 142.26/142.47  Found satz2900 as proof of (((eq nat) a) b)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 ((ts (num z)) (den x))):(((eq nat) ((ts (num z)) (den x))) ((ts (num z)) (den x)))
% 142.26/142.47  Found (eq_ref0 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 ((ts (num z)) (den x))):(((eq nat) ((ts (num z)) (den x))) ((ts (num z)) (den x)))
% 142.26/142.47  Found (eq_ref0 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found ((eq_ref nat) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 142.26/142.47  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) Xz)) ((ts Xz) (den x)))
% 142.26/142.47  Found (satz29__eq_sym0 (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 142.26/142.47  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 142.26/142.47  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 142.26/142.47  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 142.26/142.47  Found (eq_ref0 b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 142.26/142.47  Found (eq_ref0 b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (den x))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 142.26/142.47  Found (eq_ref0 b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 142.26/142.47  Found (eq_ref0 b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found ((eq_ref nat) b) as proof of (((eq nat) b) (num z))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 142.26/142.47  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 142.26/142.47  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 168.75/169.01  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 168.75/169.01  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 168.75/169.01  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 168.75/169.01  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 168.75/169.01  Found satz29__eq_sym00:=(satz29__eq_sym0 (num z)):(((eq nat) ((ts (num z)) (den x))) ((ts (den x)) (num z)))
% 168.75/169.01  Found (satz29__eq_sym0 (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 168.75/169.01  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 168.75/169.01  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 168.75/169.01  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 168.75/169.01  Found eq_ref00:=(eq_ref0 Xz):(((eq nat) Xz) Xz)
% 168.75/169.01  Found (eq_ref0 Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found eq_ref00:=(eq_ref0 Xz):(((eq nat) Xz) Xz)
% 168.75/169.01  Found (eq_ref0 Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 168.75/169.01  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 168.75/169.01  Instantiate: Xz:=(num z):nat;b:=((ts (num z)) (den x)):nat
% 168.75/169.01  Found satz2900 as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 168.75/169.01  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 168.75/169.01  Instantiate: Xz:=(den y):nat;b:=((ts (num y)) (den x)):nat
% 168.75/169.01  Found l as proof of (P b)
% 168.75/169.01  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 168.75/169.01  Instantiate: Xz:=(den y):nat;b:=((ts (num y)) (den x)):nat
% 168.75/169.01  Found l as proof of (P b)
% 168.75/169.01  Found eq_ref00:=(eq_ref0 ((ts (den x)) Xz)):(((eq nat) ((ts (den x)) Xz)) ((ts (den x)) Xz))
% 168.75/169.01  Found (eq_ref0 ((ts (den x)) Xz)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (den x)) Xz)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (den x)) Xz)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (den x)) Xz)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 168.75/169.01  Found satz31000:=(satz3100 (den x)):(((eq nat) ((ts ((ts Xz) (num z))) (den x))) ((ts Xz) ((ts (num z)) (den x))))
% 168.75/169.01  Instantiate: b:=((ts Xz) ((ts (num z)) (den x))):nat
% 168.75/169.01  Found satz31000 as proof of (((eq nat) ((ts ((ts Xz) (num z))) (den x))) b)
% 168.75/169.01  Found satz2901:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 168.75/169.01  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 168.75/169.01  Found satz2901 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 168.75/169.01  Found satz29__eq_sym00:=(satz29__eq_sym0 (num z)):(((eq nat) ((ts (num z)) Xz)) ((ts Xz) (num z)))
% 168.75/169.01  Found (satz29__eq_sym0 (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found eq_ref00:=(eq_ref0 ((ts (num z)) Xz)):(((eq nat) ((ts (num z)) Xz)) ((ts (num z)) Xz))
% 168.75/169.01  Found (eq_ref0 ((ts (num z)) Xz)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (num z)) Xz)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (num z)) Xz)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found ((eq_ref nat) ((ts (num z)) Xz)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 168.75/169.01  Found satz31000:=(satz3100 (den x)):(((eq nat) ((ts ((ts Xz) (num z))) (den x))) ((ts Xz) ((ts (num z)) (den x))))
% 168.75/169.01  Instantiate: b:=((ts Xz) ((ts (num z)) (den x))):nat
% 168.75/169.01  Found satz31000 as proof of (((eq nat) ((ts ((ts Xz) (num z))) (den x))) b)
% 168.75/169.01  Found satz2901:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 168.75/169.01  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 168.75/169.01  Found satz2901 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 168.75/169.01  Found satz31000:=(satz3100 (den x)):(((eq nat) ((ts ((ts Xz) (num z))) (den x))) ((ts Xz) ((ts (num z)) (den x))))
% 184.03/184.31  Instantiate: b:=((ts Xz) ((ts (num z)) (den x))):nat
% 184.03/184.31  Found satz31000 as proof of (((eq nat) ((ts ((ts Xz) (num z))) (den x))) b)
% 184.03/184.31  Found satz2900:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 184.03/184.31  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 184.03/184.31  Found satz2900 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 184.03/184.31  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 184.03/184.31  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 184.03/184.31  Found l as proof of ((less Xz) a)
% 184.03/184.31  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 184.03/184.31  Instantiate: Xz:=((ts (num x)) (den y)):nat;a:=((ts (num y)) (den x)):nat
% 184.03/184.31  Found l as proof of ((less Xz) a)
% 184.03/184.31  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 184.03/184.31  Instantiate: Xz:=((ts (num x)) (den y)):nat;b:=((ts (num y)) (den x)):nat
% 184.03/184.31  Found l as proof of (P b)
% 184.03/184.31  Found satz29__eq_sym00:=(satz29__eq_sym0 (den z)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 184.03/184.31  Instantiate: a:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 184.03/184.31  Found satz29__eq_sym00 as proof of (((eq nat) a) b)
% 184.03/184.31  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 184.03/184.31  Found (eq_ref0 b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (num z)) (den x)))
% 184.03/184.31  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 184.03/184.31  Instantiate: a:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 184.03/184.31  Found satz29__eq_sym00 as proof of (((eq nat) a) b)
% 184.03/184.31  Found satz2900:=(satz290 (den x)):(((eq nat) ((ts (num z)) (den x))) ((ts (den x)) (num z)))
% 184.03/184.31  Found (satz290 (den x)) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 184.03/184.31  Found ((satz29 (num z)) (den x)) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 184.03/184.31  Found ((satz29 (num z)) (den x)) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 184.03/184.31  Found eq_ref00:=(eq_ref0 (den x)):(((eq nat) (den x)) (den x))
% 184.03/184.31  Found (eq_ref0 (den x)) as proof of (((eq nat) (den x)) b)
% 184.03/184.31  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 184.03/184.31  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 184.03/184.31  Found ((eq_ref nat) (den x)) as proof of (((eq nat) (den x)) b)
% 184.03/184.31  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 184.03/184.31  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 184.03/184.31  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 184.03/184.31  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 184.03/184.31  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 184.03/184.31  Found satz2900:=(satz290 (den x)):(((eq nat) ((ts Xz) (den x))) ((ts (den x)) Xz))
% 184.03/184.31  Instantiate: b:=((ts (den x)) Xz):nat
% 184.03/184.31  Found satz2900 as proof of (((eq nat) ((ts Xz) (den x))) b)
% 184.03/184.31  Found k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 184.03/184.31  Instantiate: Xz:=(num y):nat;b:=((ts (num z)) (den y)):nat
% 184.03/184.31  Found k as proof of (P b)
% 184.03/184.31  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts Xz) (num z))) ((ts (num z)) Xz))
% 192.66/192.89  Instantiate: b:=((ts (num z)) Xz):nat
% 192.66/192.89  Found satz2900 as proof of (((eq nat) ((ts Xz) (num z))) b)
% 192.66/192.89  Found l:((less ((ts (num x)) (den y))) ((ts (num y)) (den x)))
% 192.66/192.89  Instantiate: Xz:=(den y):nat;b:=((ts (num y)) (den x)):nat
% 192.66/192.89  Found l as proof of (P b)
% 192.66/192.89  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (den x)) (num z))):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts Xz) ((ts (den x)) (num z))))
% 192.66/192.89  Found (satz29__eq_sym1 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 192.66/192.89  Found eq_ref00:=(eq_ref0 ((ts ((ts (num z)) (den x))) Xz)):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts ((ts (num z)) (den x))) Xz))
% 192.66/192.89  Found (eq_ref0 ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 192.66/192.89  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 192.66/192.89  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 192.66/192.89  Found ((eq_ref nat) ((ts ((ts (num z)) (den x))) Xz)) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 192.66/192.89  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) Xz)) ((ts Xz) (den x)))
% 192.66/192.89  Found (satz29__eq_sym0 (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 192.66/192.89  Found ((satz29__eq_sym Xz) (den x)) as proof of (((eq nat) ((ts (den x)) Xz)) b)
% 192.66/192.89  Found k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 192.66/192.89  Instantiate: Xz:=((ts (num y)) (den z)):nat;a:=(den y):nat
% 192.66/192.89  Found k as proof of (P ((ts (num z)) a))
% 192.66/192.89  Found k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 192.66/192.89  Instantiate: Xz:=((ts (num y)) (den z)):nat;a:=(den y):nat
% 192.66/192.89  Found k as proof of (P a)
% 192.66/192.89  Found k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 192.66/192.89  Instantiate: Xz:=((ts (num y)) (den z)):nat;a:=(den y):nat
% 192.66/192.89  Found k as proof of (P ((ts (num z)) a))
% 192.66/192.89  Found k:((less ((ts (num y)) (den z))) ((ts (num z)) (den y)))
% 192.66/192.89  Instantiate: Xz:=((ts (num y)) (den z)):nat;a:=(den y):nat
% 192.66/192.89  Found k as proof of (P a)
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 192.66/192.89  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 192.66/192.89  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) Xz)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 Xz):(((eq nat) Xz) Xz)
% 213.35/213.58  Found (eq_ref0 Xz) as proof of (((eq nat) Xz) b)
% 213.35/213.58  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 213.35/213.58  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 213.35/213.58  Found ((eq_ref nat) Xz) as proof of (((eq nat) Xz) b)
% 213.35/213.58  Found satz29__eq_sym00:=(satz29__eq_sym0 Xz):(((eq nat) ((ts Xz) (num z))) ((ts (num z)) Xz))
% 213.35/213.58  Found (satz29__eq_sym0 Xz) as proof of (((eq nat) ((ts Xz) (num z))) b)
% 213.35/213.58  Found ((satz29__eq_sym (num z)) Xz) as proof of (((eq nat) ((ts Xz) (num z))) b)
% 213.35/213.58  Found ((satz29__eq_sym (num z)) Xz) as proof of (((eq nat) ((ts Xz) (num z))) b)
% 213.35/213.58  Found ((satz29__eq_sym (num z)) Xz) as proof of (((eq nat) ((ts Xz) (num z))) b)
% 213.35/213.58  Found satz29__eq_sym00:=(satz29__eq_sym0 (num z)):(((eq nat) ((ts (num z)) (den x))) ((ts (den x)) (num z)))
% 213.35/213.58  Found (satz29__eq_sym0 (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 213.35/213.58  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 213.35/213.58  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 213.35/213.58  Found ((satz29__eq_sym (den x)) (num z)) as proof of (((eq nat) ((ts (num z)) (den x))) b)
% 213.35/213.58  Found satz29__eq_sym00:=(satz29__eq_sym0 (num z)):(((eq nat) ((ts (num z)) Xz)) ((ts Xz) (num z)))
% 213.35/213.58  Found (satz29__eq_sym0 (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 213.35/213.58  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 213.35/213.58  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 213.35/213.58  Found ((satz29__eq_sym Xz) (num z)) as proof of (((eq nat) ((ts (num z)) Xz)) b)
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 213.35/213.58  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 213.35/213.58  Found (eq_ref0 a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 213.35/213.58  Found ((eq_ref nat) a) as proof of (((eq nat) a) (num z))
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;b:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) b)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;b:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) b)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 220.92/221.19  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 220.92/221.19  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 220.92/221.19  Found satz2900 as proof of (((eq nat) a) Xz)
% 220.92/221.19  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 220.92/221.19  Found (eq_ref0 b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 220.92/221.19  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 220.92/221.19  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 220.92/221.19  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 243.98/244.22  Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 243.98/244.22  Found (eq_ref0 b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 243.98/244.22  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 243.98/244.22  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 243.98/244.22  Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 243.98/244.22  Found satz2900:=(satz290 ((ts (num z)) (den x))):(((eq nat) ((ts Xz) ((ts (num z)) (den x)))) ((ts ((ts (num z)) (den x))) Xz))
% 243.98/244.22  Instantiate: b:=((ts ((ts (num z)) (den x))) Xz):nat
% 243.98/244.22  Found satz2900 as proof of (((eq nat) ((ts Xz) ((ts (num z)) (den x)))) b)
% 243.98/244.22  Found satz2900:=(satz290 ((ts (den x)) (num z))):(((eq nat) ((ts Xz) ((ts (den x)) (num z)))) ((ts ((ts (den x)) (num z))) Xz))
% 243.98/244.22  Instantiate: b:=((ts ((ts (den x)) (num z))) Xz):nat
% 243.98/244.22  Found satz2900 as proof of (((eq nat) ((ts Xz) ((ts (den x)) (num z)))) b)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den z)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 243.98/244.22  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 243.98/244.22  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 243.98/244.22  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den z)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 243.98/244.22  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den z)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 243.98/244.22  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den z)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 243.98/244.22  Instantiate: a:=((ts (den z)) (num x)):nat;Xz:=((ts (num x)) (den z)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 243.98/244.22  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym00:=(satz29__eq_sym0 (den x)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 243.98/244.22  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x)):nat
% 243.98/244.22  Found satz29__eq_sym00 as proof of (((eq nat) a) Xz)
% 243.98/244.22  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (den x)) (num z))):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts Xz) ((ts (den x)) (num z))))
% 243.98/244.22  Found (satz29__eq_sym1 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found eq_ref00:=(eq_ref0 ((ts ((ts (den x)) (num z))) Xz)):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts ((ts (den x)) (num z))) Xz))
% 243.98/244.22  Found (eq_ref0 ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 243.98/244.22  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (num z)) (den x))):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts Xz) ((ts (num z)) (den x))))
% 253.92/254.17  Found (satz29__eq_sym1 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (num z)) (den x))):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts Xz) ((ts (num z)) (den x))))
% 253.92/254.17  Found (satz29__eq_sym1 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (den x)) (num z))):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts Xz) ((ts (den x)) (num z))))
% 253.92/254.17  Found (satz29__eq_sym1 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found satz31000:=(satz3100 Xz):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts (den x)) ((ts (num z)) Xz)))
% 253.92/254.17  Found (satz3100 Xz) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((satz310 (num z)) Xz) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found (((satz31 (den x)) (num z)) Xz) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found (((satz31 (den x)) (num z)) Xz) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found (((satz31 (den x)) (num z)) Xz) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found satz29__eq_sym10:=(satz29__eq_sym1 ((ts (num z)) (den x))):(((eq nat) ((ts ((ts (num z)) (den x))) Xz)) ((ts Xz) ((ts (num z)) (den x))))
% 253.92/254.17  Found (satz29__eq_sym1 ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found ((satz29__eq_sym Xz) ((ts (num z)) (den x))) as proof of (((eq nat) ((ts ((ts (num z)) (den x))) Xz)) b)
% 253.92/254.17  Found eq_ref00:=(eq_ref0 ((ts ((ts (den x)) (num z))) Xz)):(((eq nat) ((ts ((ts (den x)) (num z))) Xz)) ((ts ((ts (den x)) (num z))) Xz))
% 253.92/254.17  Found (eq_ref0 ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found ((eq_ref nat) ((ts ((ts (den x)) (num z))) Xz)) as proof of (((eq nat) ((ts ((ts (den x)) (num z))) Xz)) b)
% 253.92/254.17  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 253.92/254.17  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 253.92/254.17  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 253.92/254.17  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 253.92/254.17  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 253.92/254.17  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 253.92/254.17  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) (den x))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 294.99/295.28  Found (eq_ref0 a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts (num z)) (den x)))
% 294.99/295.28  Found satz2900:=(satz290 (num x)):(((eq nat) ((ts (den z)) (num x))) ((ts (num x)) (den z)))
% 294.99/295.28  Found satz2900 as proof of (((eq nat) ((ts (den z)) (num x))) b)
% 294.99/295.28  Found eq_ref00:=(eq_ref0 ((ts (den x)) (num z))):(((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 294.99/295.28  Found (eq_ref0 ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 294.99/295.28  Found ((eq_ref nat) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 294.99/295.28  Found ((eq_ref nat) ((ts (den x)) (num z))) as proof of (((eq nat) ((ts (den x)) (num z))) ((ts (den x)) (num z)))
% 294.99/295.28  Found (satz29001 ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 294.99/295.28  Found ((satz2900 (fun (x1:nat)=> (((eq nat) x1) ((ts (den x)) (num z))))) ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 294.99/295.28  Found ((satz2900 (fun (x1:nat)=> (((eq nat) x1) ((ts (den x)) (num z))))) ((eq_ref nat) ((ts (den x)) (num z)))) as proof of (((eq nat) b) ((ts (den x)) (num z)))
% 294.99/295.28  Found satz2900:=(satz290 (num z)):(((eq nat) ((ts (den x)) (num z))) ((ts (num z)) (den x)))
% 294.99/295.28  Instantiate: a:=((ts (den x)) (num z)):nat;Xz:=((ts (num z)) (den x
%------------------------------------------------------------------------------