TSTP Solution File: NUM636^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM636^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n156.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 13:11:14 EST 2018
% Result : Theorem 6.58s
% Output : Proof 6.58s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^1 : 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 : n156.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 11:14:30 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.26 Python 2.7.13
% 6.44/6.86 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad012345a8>, <kernel.Type object at 0x2aad01234b90>) of role type named nat_type
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring nat:Type
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad01234128>, <kernel.Constant object at 0x2aad0115b3b0>) of role type named x
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring x:nat
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad0115b1b8>, <kernel.DependentProduct object at 0x2aad01154a70>) of role type named suc
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring suc:(nat->nat)
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad01234560>, <kernel.Type object at 0x2aad01154a70>) of role type named set_type
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring set:Type
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad012345a8>, <kernel.DependentProduct object at 0x2aad011544d0>) of role type named esti
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring esti:(nat->(set->Prop))
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad01234560>, <kernel.DependentProduct object at 0x2aad01154098>) of role type named setof
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring setof:((nat->Prop)->set)
% 6.44/6.86 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))) of role axiom named estie
% 6.44/6.86 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs)))
% 6.44/6.86 FOF formula (<kernel.Constant object at 0x2aad01234560>, <kernel.Constant object at 0x2aad011547a0>) of role type named n_1
% 6.44/6.86 Using role type
% 6.44/6.86 Declaring n_1:nat
% 6.44/6.86 FOF formula (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))) of role axiom named ax5
% 6.44/6.86 A new axiom: (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs)))))
% 6.44/6.86 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))) of role axiom named estii
% 6.44/6.86 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp))))
% 6.44/6.86 FOF formula (forall (Xx:nat), (not (((eq nat) (suc Xx)) n_1))) of role axiom named ax3
% 6.44/6.86 A new axiom: (forall (Xx:nat), (not (((eq nat) (suc Xx)) n_1)))
% 6.44/6.86 FOF formula (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->(not (((eq nat) (suc Xx)) (suc Xy))))) of role axiom named satz1
% 6.44/6.86 A new axiom: (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->(not (((eq nat) (suc Xx)) (suc Xy)))))
% 6.44/6.86 FOF formula (not (((eq nat) (suc x)) x)) of role conjecture named satz2
% 6.44/6.86 Conjecture to prove = (not (((eq nat) (suc x)) x)):Prop
% 6.44/6.86 Parameter set_DUMMY:set.
% 6.44/6.86 We need to prove ['(not (((eq nat) (suc x)) x))']
% 6.44/6.86 Parameter nat:Type.
% 6.44/6.86 Parameter x:nat.
% 6.44/6.86 Parameter suc:(nat->nat).
% 6.44/6.86 Parameter set:Type.
% 6.44/6.86 Parameter esti:(nat->(set->Prop)).
% 6.44/6.86 Parameter setof:((nat->Prop)->set).
% 6.44/6.86 Axiom estie:(forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))).
% 6.44/6.86 Parameter n_1:nat.
% 6.44/6.86 Axiom ax5:(forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))).
% 6.44/6.86 Axiom estii:(forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))).
% 6.44/6.86 Axiom ax3:(forall (Xx:nat), (not (((eq nat) (suc Xx)) n_1))).
% 6.44/6.86 Axiom satz1:(forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->(not (((eq nat) (suc Xx)) (suc Xy))))).
% 6.44/6.86 Trying to prove (not (((eq nat) (suc x)) x))
% 6.44/6.86 Found ax30:=(ax3 n_1):(not (((eq nat) (suc n_1)) n_1))
% 6.44/6.86 Found (ax3 n_1) as proof of (not (((eq nat) (suc n_1)) n_1))
% 6.44/6.86 Found (ax3 n_1) as proof of (not (((eq nat) (suc n_1)) n_1))
% 6.44/6.86 Found (estii00 (ax3 n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.86 Found ((estii0 n_1) (ax3 n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.86 Found (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.86 Found (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.86 Found estie100:=(estie10 x0):(not (((eq nat) (suc Xx)) Xx))
% 6.44/6.86 Found (estie10 x0) as proof of (not (((eq nat) (suc Xx)) Xx))
% 6.44/6.87 Found ((estie1 (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0) as proof of (not (((eq nat) (suc Xx)) Xx))
% 6.44/6.87 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0) as proof of (not (((eq nat) (suc Xx)) Xx))
% 6.44/6.87 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0) as proof of (not (((eq nat) (suc Xx)) Xx))
% 6.44/6.87 Found (satz100 (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)) as proof of (not (((eq nat) (suc (suc Xx))) (suc Xx)))
% 6.44/6.87 Found ((satz10 Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)) as proof of (not (((eq nat) (suc (suc Xx))) (suc Xx)))
% 6.44/6.87 Found (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)) as proof of (not (((eq nat) (suc (suc Xx))) (suc Xx)))
% 6.44/6.87 Found (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)) as proof of (not (((eq nat) (suc (suc Xx))) (suc Xx)))
% 6.44/6.87 Found (estii00 (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.87 Found ((estii0 (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.87 Found (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.87 Found (fun (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.87 Found (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))) as proof of (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))
% 6.44/6.87 Found (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))) as proof of (forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))))
% 6.44/6.87 Found ((ax500 (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))) as proof of ((esti x) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.44/6.87 Found (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> (((ax50 x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))) as proof of ((esti x) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.53/6.90 Found (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))) as proof of ((esti x) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.53/6.90 Found (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))) as proof of ((esti x) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))
% 6.53/6.90 Found (estie00 (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))))) as proof of (not (((eq nat) (suc x)) x))
% 6.53/6.90 Found ((estie0 (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))))) as proof of (not (((eq nat) (suc x)) x))
% 6.53/6.90 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) x)) (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))))) as proof of (not (((eq nat) (suc x)) x))
% 6.53/6.90 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) x)) (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0)))))) as proof of (not (((eq nat) (suc x)) x))
% 6.58/6.97 Got proof (((fun (Xp:(nat->Prop))=> ((estie Xp) x)) (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))))
% 6.58/6.97 Time elapsed = 6.193355s
% 6.58/6.97 node=1273 cost=568.000000 depth=21
% 6.58/6.97::::::::::::::::::::::
% 6.58/6.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.58/6.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.58/6.97 (((fun (Xp:(nat->Prop))=> ((estie Xp) x)) (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (((fun (x0:((esti n_1) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))) (x1:(forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))))=> ((((ax5 (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))) x0) x1) x)) (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) n_1) (ax3 n_1))) (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1))))))=> (((estii (fun (x1:nat)=> (not (((eq nat) (suc x1)) x1)))) (suc Xx)) (((satz1 (suc Xx)) Xx) (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x2:nat)=> (not (((eq nat) (suc x2)) x2)))) x0))))))
% 6.58/6.97 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------