TSTP Solution File: NUM691^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM691^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n058.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 13:11:27 EST 2018
% Result : Theorem 53.42s
% Output : Proof 53.42s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM691^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n058.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 12:54:03 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.26 Python 2.7.13
% 5.34/5.73 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fac20>, <kernel.Type object at 0x2b95d56fa7e8>) of role type named nat_type
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring nat:Type
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d540f200>, <kernel.Constant object at 0x2b95d56fa560>) of role type named x
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring x:nat
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fa440>, <kernel.Constant object at 0x2b95d56fa560>) of role type named y
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring y:nat
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fac20>, <kernel.Constant object at 0x2b95d56fa560>) of role type named z
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring z:nat
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fad40>, <kernel.Constant object at 0x2b95d56fa560>) of role type named u
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring u:nat
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fa440>, <kernel.DependentProduct object at 0x2b95d56fa320>) of role type named more
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring more:(nat->(nat->Prop))
% 5.34/5.73 FOF formula ((((more x) y)->False)->(((eq nat) x) y)) of role axiom named m
% 5.34/5.73 A new axiom: ((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 FOF formula ((((more z) u)->False)->(((eq nat) z) u)) of role axiom named n
% 5.34/5.73 A new axiom: ((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 FOF formula (<kernel.Constant object at 0x2b95d56fa1b8>, <kernel.DependentProduct object at 0x2b95d56fa2d8>) of role type named pl
% 5.34/5.73 Using role type
% 5.34/5.73 Declaring pl:(nat->(nat->nat))
% 5.34/5.73 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et
% 5.34/5.73 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa))
% 5.34/5.73 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((((more Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu))))) of role axiom named satz22a
% 5.34/5.73 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((((more Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu)))))
% 5.34/5.73 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((((more Xz) Xu)->False)->(((eq nat) Xz) Xu))->((more ((pl Xx) Xz)) ((pl Xy) Xu))))) of role axiom named satz22b
% 5.34/5.73 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((((more Xz) Xu)->False)->(((eq nat) Xz) Xu))->((more ((pl Xx) Xz)) ((pl Xy) Xu)))))
% 5.34/5.73 FOF formula ((((more ((pl x) z)) ((pl y) u))->False)->(((eq nat) ((pl x) z)) ((pl y) u))) of role conjecture named satz23
% 5.34/5.73 Conjecture to prove = ((((more ((pl x) z)) ((pl y) u))->False)->(((eq nat) ((pl x) z)) ((pl y) u))):Prop
% 5.34/5.73 We need to prove ['((((more ((pl x) z)) ((pl y) u))->False)->(((eq nat) ((pl x) z)) ((pl y) u)))']
% 5.34/5.73 Parameter nat:Type.
% 5.34/5.73 Parameter x:nat.
% 5.34/5.73 Parameter y:nat.
% 5.34/5.73 Parameter z:nat.
% 5.34/5.73 Parameter u:nat.
% 5.34/5.73 Parameter more:(nat->(nat->Prop)).
% 5.34/5.73 Axiom m:((((more x) y)->False)->(((eq nat) x) y)).
% 5.34/5.73 Axiom n:((((more z) u)->False)->(((eq nat) z) u)).
% 5.34/5.73 Parameter pl:(nat->(nat->nat)).
% 5.34/5.73 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)).
% 5.34/5.73 Axiom satz22a:(forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((((more Xx) Xy)->False)->(((eq nat) Xx) Xy))->(((more Xz) Xu)->((more ((pl Xx) Xz)) ((pl Xy) Xu))))).
% 5.34/5.73 Axiom satz22b:(forall (Xx:nat) (Xy:nat) (Xz:nat) (Xu:nat), (((more Xx) Xy)->(((((more Xz) Xu)->False)->(((eq nat) Xz) Xu))->((more ((pl Xx) Xz)) ((pl Xy) Xu))))).
% 5.34/5.73 Trying to prove ((((more ((pl x) z)) ((pl y) u))->False)->(((eq nat) ((pl x) z)) ((pl y) u)))
% 5.34/5.73 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 5.34/5.73 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 5.34/5.73 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found eq_ref000:=(eq_ref00 P):((P ((pl x) z))->(P ((pl x) z)))
% 33.93/34.30 Found (eq_ref00 P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found ((eq_ref0 ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found (((eq_ref nat) ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found (((eq_ref nat) ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found eq_ref000:=(eq_ref00 P):((P ((pl x) z))->(P ((pl x) z)))
% 33.93/34.30 Found (eq_ref00 P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found ((eq_ref0 ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found (((eq_ref nat) ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found (((eq_ref nat) ((pl x) z)) P) as proof of (P0 ((pl x) z))
% 33.93/34.30 Found eq_ref00:=(eq_ref0 ((pl x) z)):(((eq nat) ((pl x) z)) ((pl x) z))
% 33.93/34.30 Found (eq_ref0 ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 33.93/34.30 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found eq_ref00:=(eq_ref0 ((pl x) z)):(((eq nat) ((pl x) z)) ((pl x) z))
% 33.93/34.30 Found (eq_ref0 ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found ((eq_ref nat) ((pl x) z)) as proof of (((eq nat) ((pl x) z)) b)
% 33.93/34.30 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 33.93/34.30 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl y) u))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 33.93/34.30 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 33.93/34.30 Found x00:False
% 33.93/34.30 Found (fun (x01:((((eq nat) ((pl x) z)) ((pl y) u))->False))=> x00) as proof of False
% 33.93/34.30 Found (fun (x01:((((eq nat) ((pl x) z)) ((pl y) u))->False))=> x00) as proof of (((((eq nat) ((pl x) z)) ((pl y) u))->False)->False)
% 49.13/49.56 Found eq_ref00:=(eq_ref0 ((pl y) u)):(((eq nat) ((pl y) u)) ((pl y) u))
% 49.13/49.56 Found (eq_ref0 ((pl y) u)) as proof of (((eq nat) ((pl y) u)) b)
% 49.13/49.56 Found ((eq_ref nat) ((pl y) u)) as proof of (((eq nat) ((pl y) u)) b)
% 49.13/49.56 Found ((eq_ref nat) ((pl y) u)) as proof of (((eq nat) ((pl y) u)) b)
% 49.13/49.56 Found ((eq_ref nat) ((pl y) u)) as proof of (((eq nat) ((pl y) u)) b)
% 49.13/49.56 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 49.13/49.56 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl x) z))
% 49.13/49.56 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) z))
% 49.13/49.56 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) z))
% 49.13/49.56 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl x) z))
% 49.13/49.56 Found x00:False
% 49.13/49.56 Found (fun (x01:(((P ((pl x) z))->(P ((pl y) u)))->False))=> x00) as proof of False
% 49.13/49.56 Found (fun (x01:(((P ((pl x) z))->(P ((pl y) u)))->False))=> x00) as proof of ((((P ((pl x) z))->(P ((pl y) u)))->False)->False)
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found x01:False
% 49.13/49.56 Found (fun (x1:((P ((pl y) u))->False))=> x01) as proof of False
% 49.13/49.56 Found (fun (x1:((P ((pl y) u))->False))=> x01) as proof of (((P ((pl y) u))->False)->False)
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found satz22b000000:=(satz22b00000 n):((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found (satz22b00000 n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((satz22b0000 u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found (((satz22b000 z) u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> (((satz22b00 Xz) Xu) x1)) z) u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> ((((satz22b0 y) Xz) Xu) x1)) z) u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)) as proof of False
% 49.13/49.56 Found (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n))) as proof of False
% 49.13/49.56 Found (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n))) as proof of (((more x) y)->False)
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 49.13/49.56 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 49.13/49.56 Found satz22a000000:=(satz22a00000 x1):((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found (satz22a00000 x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((satz22a0000 u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found (((satz22a000 z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> (((satz22a00 Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 49.13/49.56 Found ((((fun (Xz:nat) (Xu:nat)=> ((((satz22a0 y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)) as proof of False
% 52.72/53.12 Found (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))) as proof of False
% 52.72/53.12 Found (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))) as proof of (((more z) u)->False)
% 52.72/53.12 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found m:((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found m as proof of ((((more x) y)->False)->(((eq nat) x) y))
% 52.72/53.12 Found n:((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found n as proof of ((((more z) u)->False)->(((eq nat) z) u))
% 52.72/53.12 Found satz22a000000:=(satz22a00000 x1):((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found (satz22a00000 x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((satz22a0000 u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found (((satz22a000 z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> (((satz22a00 Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> ((((satz22a0 y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1) as proof of ((more ((pl x) z)) ((pl y) u))
% 52.72/53.12 Found (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)) as proof of False
% 52.72/53.12 Found (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))) as proof of False
% 52.72/53.12 Found (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))) as proof of (((more z) u)->False)
% 52.72/53.12 Found (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))) as proof of (((eq nat) z) u)
% 52.72/53.12 Found (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))) as proof of (((eq nat) z) u)
% 52.72/53.12 Found (eq_substitution00000 (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 52.72/53.12 Found ((eq_substitution0000 (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 52.72/53.12 Found (((eq_substitution000 u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 52.72/53.12 Found ((((eq_substitution00 z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 52.72/53.12 Found (((((eq_substitution0 nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 52.72/53.12 Found ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 53.42/53.85 Found ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))) as proof of (P x)
% 53.42/53.85 Found ((m0 (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))))) as proof of (((eq nat) ((pl x) z)) ((pl y) u))
% 53.42/53.85 Found ((m0 (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))))) as proof of (((eq nat) ((pl x) z)) ((pl y) u))
% 53.42/53.85 Found (((fun (x00:(((more x) y)->False))=> ((m x00) (fun (x1:nat)=> (((eq nat) ((pl x) z)) ((pl x1) u))))) (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))))) as proof of (((eq nat) ((pl x) z)) ((pl y) u))
% 53.42/53.85 Found (fun (x0:(((more ((pl x) z)) ((pl y) u))->False))=> (((fun (x00:(((more x) y)->False))=> ((m x00) (fun (x1:nat)=> (((eq nat) ((pl x) z)) ((pl x1) u))))) (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))))) as proof of (((eq nat) ((pl x) z)) ((pl y) u))
% 53.42/53.85 Found (fun (x0:(((more ((pl x) z)) ((pl y) u))->False))=> (((fun (x00:(((more x) y)->False))=> ((m x00) (fun (x1:nat)=> (((eq nat) ((pl x) z)) ((pl x1) u))))) (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1))))))) as proof of ((((more ((pl x) z)) ((pl y) u))->False)->(((eq nat) ((pl x) z)) ((pl y) u)))
% 53.42/53.85 Got proof (fun (x0:(((more ((pl x) z)) ((pl y) u))->False))=> (((fun (x00:(((more x) y)->False))=> ((m x00) (fun (x1:nat)=> (((eq nat) ((pl x) z)) ((pl x1) u))))) (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))))))
% 53.42/53.85 Time elapsed = 52.565277s
% 53.42/53.85 node=12258 cost=671.000000 depth=23
% 53.42/53.85::::::::::::::::::::::
% 53.42/53.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.42/53.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.42/53.85 (fun (x0:(((more ((pl x) z)) ((pl y) u))->False))=> (((fun (x00:(((more x) y)->False))=> ((m x00) (fun (x1:nat)=> (((eq nat) ((pl x) z)) ((pl x1) u))))) (fun (x1:((more x) y))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22b x) y) Xz) Xu) x1)) z) u) n)))) ((((((eq_substitution nat) nat) z) u) (pl x)) (n (fun (x1:((more z) u))=> (x0 ((((fun (Xz:nat) (Xu:nat)=> (((((satz22a x) y) Xz) Xu) m)) z) u) x1)))))))
% 53.42/53.85 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------