TSTP Solution File: NUM768^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM768^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n030.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 13:11:41 EST 2018
% Result : Timeout 300.05s
% 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 : NUM768^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n030.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 14:03:03 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.25 Python 2.7.13
% 0.07/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882200>, <kernel.Type object at 0x2b46088823b0>) of role type named frac_type
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring frac:Type
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608527560>, <kernel.Constant object at 0x2b4608882998>) of role type named x
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring x:frac
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882488>, <kernel.Constant object at 0x2b4608882998>) of role type named y
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring y:frac
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882200>, <kernel.Type object at 0x2b4608882fc8>) of role type named nat_type
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring nat:Type
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882cf8>, <kernel.DependentProduct object at 0x2b4608524998>) of role type named some
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring some:((nat->Prop)->Prop)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b46088823b0>, <kernel.DependentProduct object at 0x2b4608fa1638>) of role type named ts
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ts:(nat->(nat->nat))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608524998>, <kernel.DependentProduct object at 0x2b4608882c68>) of role type named num
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring num:(frac->nat)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608524998>, <kernel.DependentProduct object at 0x2b4608882488>) of role type named den
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring den:(frac->nat)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b46088823b0>, <kernel.DependentProduct object at 0x2b4608882488>) of role type named pl
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring pl:(nat->(nat->nat))
% 0.07/0.51 FOF formula (some (fun (Xu:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xu)))) of role axiom named m
% 0.07/0.51 A new axiom: (some (fun (Xu:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xu))))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608fa1638>, <kernel.DependentProduct object at 0x2b4608882cf8>) of role type named eq
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring _TPTP_eq:(frac->(frac->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608fa1638>, <kernel.DependentProduct object at 0x2b46088823b0>) of role type named pf
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring pf:(frac->(frac->frac))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b46088823f8>, <kernel.DependentProduct object at 0x2b4608882200>) of role type named fr
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring fr:(nat->(nat->frac))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882b00>, <kernel.DependentProduct object at 0x2b4608fa5518>) of role type named ind
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ind:((nat->Prop)->nat)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b4608882200>, <kernel.DependentProduct object at 0x2b4608fa54d0>) of role type named amone
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring amone:((nat->Prop)->Prop)
% 0.07/0.51 FOF formula (forall (Xx:nat) (Xy:nat), (amone (fun (Xz:nat)=> (((eq nat) Xx) ((pl Xy) Xz))))) of role axiom named satz8b
% 0.07/0.51 A new axiom: (forall (Xx:nat) (Xy:nat), (amone (fun (Xz:nat)=> (((eq nat) Xx) ((pl Xy) Xz)))))
% 0.07/0.51 FOF formula (forall (Xx:frac) (Xy:frac) (Xz:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xy) Xz)->((_TPTP_eq Xx) Xz)))) of role axiom named satz39
% 0.07/0.51 A new axiom: (forall (Xx:frac) (Xy:frac) (Xz:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xy) Xz)->((_TPTP_eq Xx) Xz))))
% 0.07/0.51 FOF formula (forall (Xx:frac) (Xy:frac) (Xz:frac) (Xu:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xz) Xu)->((_TPTP_eq ((pf Xx) Xz)) ((pf Xy) Xu))))) of role axiom named satz56
% 0.07/0.51 A new axiom: (forall (Xx:frac) (Xy:frac) (Xz:frac) (Xu:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xz) Xu)->((_TPTP_eq ((pf Xx) Xz)) ((pf Xy) Xu)))))
% 0.07/0.51 FOF formula (forall (Xx:frac) (Xn:nat), ((_TPTP_eq Xx) ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn)))) of role axiom named satz40
% 0.07/0.51 A new axiom: (forall (Xx:frac) (Xn:nat), ((_TPTP_eq Xx) ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn))))
% 0.07/0.51 FOF formula (forall (Xx:frac), ((_TPTP_eq Xx) Xx)) of role axiom named satz37
% 0.07/0.51 A new axiom: (forall (Xx:frac), ((_TPTP_eq Xx) Xx))
% 0.07/0.51 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx))) of role axiom named satz29
% 0.07/0.51 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx)))
% 2.81/3.01 FOF formula (forall (Xx1:nat) (Xx2:nat) (Xn:nat), ((_TPTP_eq ((pf ((fr Xx1) Xn)) ((fr Xx2) Xn))) ((fr ((pl Xx1) Xx2)) Xn))) of role axiom named satz57
% 2.81/3.01 A new axiom: (forall (Xx1:nat) (Xx2:nat) (Xn:nat), ((_TPTP_eq ((pf ((fr Xx1) Xn)) ((fr Xx2) Xn))) ((fr ((pl Xx1) Xx2)) Xn)))
% 2.81/3.01 FOF formula (forall (Xp:(nat->Prop)), ((((amone Xp)->((some Xp)->False))->False)->(Xp (ind Xp)))) of role axiom named oneax
% 2.81/3.01 A new axiom: (forall (Xp:(nat->Prop)), ((((amone Xp)->((some Xp)->False))->False)->(Xp (ind Xp))))
% 2.81/3.01 FOF formula (forall (Xx:frac) (Xn:nat), ((_TPTP_eq ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn))) Xx)) of role axiom named satz40a
% 2.81/3.01 A new axiom: (forall (Xx:frac) (Xn:nat), ((_TPTP_eq ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn))) Xx))
% 2.81/3.01 FOF formula ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) x) of role conjecture named satz67c
% 2.81/3.01 Conjecture to prove = ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) x):Prop
% 2.81/3.01 Parameter nat_DUMMY:nat.
% 2.81/3.01 We need to prove ['((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) x)']
% 2.81/3.01 Parameter frac:Type.
% 2.81/3.01 Parameter x:frac.
% 2.81/3.01 Parameter y:frac.
% 2.81/3.01 Parameter nat:Type.
% 2.81/3.01 Parameter some:((nat->Prop)->Prop).
% 2.81/3.01 Parameter ts:(nat->(nat->nat)).
% 2.81/3.01 Parameter num:(frac->nat).
% 2.81/3.01 Parameter den:(frac->nat).
% 2.81/3.01 Parameter pl:(nat->(nat->nat)).
% 2.81/3.01 Axiom m:(some (fun (Xu:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xu)))).
% 2.81/3.01 Parameter _TPTP_eq:(frac->(frac->Prop)).
% 2.81/3.01 Parameter pf:(frac->(frac->frac)).
% 2.81/3.01 Parameter fr:(nat->(nat->frac)).
% 2.81/3.01 Parameter ind:((nat->Prop)->nat).
% 2.81/3.01 Parameter amone:((nat->Prop)->Prop).
% 2.81/3.01 Axiom satz8b:(forall (Xx:nat) (Xy:nat), (amone (fun (Xz:nat)=> (((eq nat) Xx) ((pl Xy) Xz))))).
% 2.81/3.01 Axiom satz39:(forall (Xx:frac) (Xy:frac) (Xz:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xy) Xz)->((_TPTP_eq Xx) Xz)))).
% 2.81/3.01 Axiom satz56:(forall (Xx:frac) (Xy:frac) (Xz:frac) (Xu:frac), (((_TPTP_eq Xx) Xy)->(((_TPTP_eq Xz) Xu)->((_TPTP_eq ((pf Xx) Xz)) ((pf Xy) Xu))))).
% 2.81/3.01 Axiom satz40:(forall (Xx:frac) (Xn:nat), ((_TPTP_eq Xx) ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn)))).
% 2.81/3.01 Axiom satz37:(forall (Xx:frac), ((_TPTP_eq Xx) Xx)).
% 2.81/3.01 Axiom satz29:(forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) Xy)) ((ts Xy) Xx))).
% 2.81/3.01 Axiom satz57:(forall (Xx1:nat) (Xx2:nat) (Xn:nat), ((_TPTP_eq ((pf ((fr Xx1) Xn)) ((fr Xx2) Xn))) ((fr ((pl Xx1) Xx2)) Xn))).
% 2.81/3.01 Axiom oneax:(forall (Xp:(nat->Prop)), ((((amone Xp)->((some Xp)->False))->False)->(Xp (ind Xp)))).
% 2.81/3.01 Axiom satz40a:(forall (Xx:frac) (Xn:nat), ((_TPTP_eq ((fr ((ts (num Xx)) Xn)) ((ts (den Xx)) Xn))) Xx)).
% 2.81/3.01 Trying to prove ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) x)
% 2.81/3.01 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 2.81/3.01 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 2.81/3.01 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 2.81/3.01 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 2.81/3.01 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y)))))
% 2.81/3.01 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 2.81/3.01 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 21.59/21.80 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y)))))
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 21.59/21.80 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x)))))
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 21.59/21.80 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 21.59/21.80 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 21.59/21.80 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 21.59/21.80 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 21.59/21.80 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 21.59/21.80 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 21.59/21.80 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 21.59/21.80 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x)))))
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x)))))
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 27.21/27.43 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x)))))
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 27.21/27.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 97.22/97.43 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 97.22/97.43 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 97.22/97.43 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x)))))
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x)))))
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.22/97.43 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.22/97.43 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y)))))
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 97.59/97.79 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x)))))
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 97.59/97.79 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 97.59/97.79 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y)))))
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 97.59/97.79 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 283.49/283.73 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 283.49/283.73 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x)))))
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den y)) (den x))))) Xy)
% 283.49/283.73 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 283.49/283.73 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 283.49/283.73 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found eq_ref00:=(eq_ref0 x):(((eq frac) x) x)
% 283.49/283.73 Found (eq_ref0 x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found ((eq_ref frac) x) as proof of (((eq frac) x) b)
% 283.49/283.73 Found satz370:=(satz37 Xy0):((_TPTP_eq Xy0) Xy0)
% 283.49/283.73 Found (satz37 Xy0) as proof of ((_TPTP_eq Xy0) x)
% 283.49/283.73 Found (satz37 Xy0) as proof of ((_TPTP_eq Xy0) x)
% 283.49/283.73 Found (satz37 Xy0) as proof of ((_TPTP_eq Xy0) x)
% 283.49/283.73 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y)))))
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy0)
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy0)
% 283.49/283.73 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (num x)) (den y))) ((pl ((ts (num y)) (den x))) Xt))))) ((ts (den x)) (den y))))) Xy0)
% 283.49/283.73 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 283.49/283.73 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y)))))
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y)))))
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found satz370:=(satz37 Xy):((_TPTP_eq Xy) Xy)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found (satz37 Xy) as proof of ((_TPTP_eq Xy) x)
% 284.51/284.77 Found satz370:=(satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))):((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y)))))
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) Xy)
% 284.51/284.77 Found (satz37 ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl ((ts (den x)) (num y))) Xt))))) ((ts (den x)) (den y))))) as proof of ((_TPTP_eq ((pf y) ((fr (ind (fun (Xt:nat)=> (((eq nat) ((ts (den y)) (num x))) ((pl (
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