TSTP Solution File: SEV291^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV291^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n049.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:27:23 EDT 2015
% Result : Unknown 6.28s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV291^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.01/1.07 % Computer : n049.star.cs.uiowa.edu
% 0.01/1.07 % Model : x86_64 x86_64
% 0.01/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.01/1.07 % Memory : 32286.75MB
% 0.01/1.07 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.01/1.07 % CPULimit : 300
% 0.01/1.07 % DateTime : Thu Apr 16 12:07:32 CDT 2015
% 0.01/1.07 % CPUTime :
% 0.01/1.08 Python 2.7.5
% 0.27/1.42 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.27/1.42 FOF formula (<kernel.Constant object at 0x8f0830>, <kernel.DependentProduct object at 0x8f0368>) of role type named r_type
% 0.27/1.42 Using role type
% 0.27/1.42 Declaring r:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->Prop))
% 0.27/1.42 FOF formula (<kernel.Constant object at 0x7bedd0>, <kernel.DependentProduct object at 0x8f0878>) of role type named cNAT_type
% 0.27/1.42 Using role type
% 0.27/1.42 Declaring cNAT:(((fofType->Prop)->Prop)->Prop)
% 0.27/1.42 FOF formula (<kernel.Constant object at 0x8f0998>, <kernel.DependentProduct object at 0x8f0bd8>) of role type named cSUCC_type
% 0.27/1.42 Using role type
% 0.27/1.42 Declaring cSUCC:(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))
% 0.27/1.42 FOF formula (<kernel.Constant object at 0x8f0758>, <kernel.DependentProduct object at 0x8f0878>) of role type named cZERO_type
% 0.27/1.42 Using role type
% 0.27/1.42 Declaring cZERO:((fofType->Prop)->Prop)
% 0.27/1.42 FOF formula (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))) of role definition named cZERO_def
% 0.27/1.42 A new definition: (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)))
% 0.27/1.42 Defined: cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))
% 0.27/1.42 FOF formula (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))) of role definition named cSUCC_def
% 0.27/1.42 A new definition: (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))))
% 0.27/1.42 Defined: cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))
% 0.27/1.42 FOF formula (((eq (((fofType->Prop)->Prop)->Prop)) cNAT) (fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn))))) of role definition named cNAT_def
% 0.27/1.42 A new definition: (((eq (((fofType->Prop)->Prop)->Prop)) cNAT) (fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn)))))
% 0.27/1.42 Defined: cNAT:=(fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn))))
% 0.27/1.42 FOF formula (((and ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))->(forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r Xx) Xy)))))) of role conjecture named cTHM130_B
% 0.27/1.42 Conjecture to prove = (((and ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))->(forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r Xx) Xy)))))):Prop
% 0.27/1.42 Parameter fofType_DUMMY:fofType.
% 0.27/1.42 We need to prove ['(((and ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))->(forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r Xx) Xy))))))']
% 0.27/1.42 Parameter fofType:Type.
% 0.27/1.42 Parameter r:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->Prop)).
% 0.27/1.42 Definition cNAT:=(fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn)))):(((fofType->Prop)->Prop)->Prop).
% 0.27/1.42 Definition cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))):(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)).
% 3.47/4.69 Definition cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)):((fofType->Prop)->Prop).
% 3.47/4.69 Trying to prove (((and ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))->(forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r Xx) Xy))))))
% 3.47/4.69 Found x1:((r cZERO) cZERO)
% 3.47/4.69 Instantiate: x3:=cZERO:((fofType->Prop)->Prop)
% 3.47/4.69 Found x1 as proof of ((r cZERO) x3)
% 3.47/4.69 Found x2:((r cZERO) cZERO)
% 3.47/4.69 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 3.47/4.69 Found x2 as proof of ((r cZERO) x1)
% 3.47/4.69 Found x2:((r cZERO) cZERO)
% 3.47/4.69 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 3.47/4.69 Found x2 as proof of ((r cZERO) x1)
% 3.47/4.69 Found x2:((r cZERO) cZERO)
% 3.47/4.69 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 3.47/4.69 Found (fun (x30:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> x2) as proof of ((r cZERO) x1)
% 3.47/4.69 Found (fun (x30:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> x2) as proof of ((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((r cZERO) x1))
% 3.47/4.69 Found x20:((r cZERO) cZERO)
% 3.47/4.69 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 3.47/4.69 Found (fun (x30:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> x20) as proof of ((r cZERO) x1)
% 3.47/4.69 Found (fun (x20:((r cZERO) cZERO)) (x30:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> x20) as proof of ((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((r cZERO) x1))
% 3.47/4.69 Found (fun (x20:((r cZERO) cZERO)) (x30:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> x20) as proof of (((r cZERO) cZERO)->((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((r cZERO) x1)))
% 3.47/4.69 Found ex_intro0000:=(ex_intro000 x1):((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found (ex_intro000 x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found ((ex_intro00 cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found (((ex_intro0 (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found x200:=(x20 x5):(((r Xx0) x5)->((r (cSUCC Xx0)) (cSUCC x5)))
% 3.47/4.69 Found (x20 x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.47/4.69 Found ((x2 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.47/4.69 Found ((x2 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.47/4.69 Found ex_intro0000:=(ex_intro000 x1):((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found (ex_intro000 x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found ((ex_intro00 cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.47/4.69 Found (((ex_intro0 (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ex_intro0000:=(ex_intro000 x1):((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (ex_intro000 x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((ex_intro00 cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (((ex_intro0 (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (fun (x20:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1)) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (fun (x20:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x1)) as proof of ((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))))
% 3.97/5.13 Found x200:=(x20 x5):(((r Xx0) x5)->((r (cSUCC Xx0)) (cSUCC x5)))
% 3.97/5.13 Found (x20 x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.97/5.13 Found ((x2 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.97/5.13 Found ((x2 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 3.97/5.13 Found ex_intro0000:=(ex_intro000 x10):((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (ex_intro000 x10) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((ex_intro00 cZERO) x10) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (((ex_intro0 (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x10) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x10) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (fun (x20:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x10)) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 3.97/5.13 Found (fun (x10:((r cZERO) cZERO)) (x20:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x10)) as proof of ((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))))
% 3.97/5.13 Found (fun (x10:((r cZERO) cZERO)) (x20:(forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy)))))=> ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) x10)) as proof of (((r cZERO) cZERO)->((forall (Xx0:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx0) Xy)->((r (cSUCC Xx0)) (cSUCC Xy))))->((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))))
% 4.98/6.12 Found x2:((r cZERO) cZERO)
% 4.98/6.12 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 4.98/6.12 Found (fun (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of ((r cZERO) x1)
% 4.98/6.12 Found (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of ((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->((r cZERO) x1))
% 4.98/6.12 Found (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of (((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->((r cZERO) x1)))
% 4.98/6.12 Found (and_rect00 (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found ((and_rect0 ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found x2:((r cZERO) cZERO)
% 4.98/6.12 Instantiate: x1:=cZERO:((fofType->Prop)->Prop)
% 4.98/6.12 Found (fun (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of ((r cZERO) x1)
% 4.98/6.12 Found (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of ((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->((r cZERO) x1))
% 4.98/6.12 Found (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2) as proof of (((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->((r cZERO) x1)))
% 4.98/6.12 Found (and_rect00 (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found ((and_rect0 ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 4.98/6.12 Found (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 5.49/6.62 Found (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2)) as proof of ((r cZERO) x1)
% 5.49/6.62 Found (ex_intro000 (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) x1)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 5.49/6.62 Found ((ex_intro00 cZERO) (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) cZERO)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 5.49/6.62 Found (((ex_intro0 (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) cZERO)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 5.49/6.62 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) cZERO)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 5.49/6.62 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy))) cZERO) (((fun (P:Type) (x2:(((r cZERO) cZERO)->((forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))->P)))=> (((((and_rect ((r cZERO) cZERO)) (forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy))))) P) x2) x)) ((r cZERO) cZERO)) (fun (x2:((r cZERO) cZERO)) (x3:(forall (Xx:((fofType->Prop)->Prop)) (Xy:((fofType->Prop)->Prop)), (((r Xx) Xy)->((r (cSUCC Xx)) (cSUCC Xy)))))=> x2))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xy:((fofType->Prop)->Prop))=> ((r cZERO) Xy)))
% 5.49/6.62 Found x300:=(x30 x5):(((r Xx0) x5)->((r (cSUCC Xx0)) (cSUCC x5)))
% 5.49/6.62 Found (x30 x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 5.49/6.62 Found ((x3 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 5.49/6.62 Found ((x3 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x4))
% 6.28/7.41 Found x400:=(x40 x5):(((r Xx0) x5)->((r (cSUCC Xx0)) (cSUCC x5)))
% 6.28/7.41 Found (x40 x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 Found ((x4 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 Found ((x4 Xx0) x5) as proof of (((r Xx0) x5)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 Found x2000:=(x200 x4):(((r Xx0) x4)->((r (cSUCC Xx0)) (cSUCC x4)))
% 6.28/7.41 Found (x200 x4) as proof of (((r Xx0) x4)->((r (cSUCC Xx0)) x3))
% 6.28/7.41 Found ((x20 Xx0) x4) as proof of (((r Xx0) x4)->((r (cSUCC Xx0)) x3))
% 6.28/7.41 Found ((x20 Xx0) x4) as proof of (((r Xx0) x4)->((r (cSUCC Xx0)) x3))
% 6.28/7.41 Found x2000:=(x200 x3):(((r Xx0) x3)->((r (cSUCC Xx0)) (cSUCC x3)))
% 6.28/7.41 Found (x200 x3) as proof of (((r Xx0) x3)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 Found ((x20 Xx0) x3) as proof of (((r Xx0) x3)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 Found ((x20 Xx0) x3) as proof of (((r Xx0) x3)->((r (cSUCC Xx0)) x2))
% 6.28/7.41 % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
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