TSTP Solution File: SEU770^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU770^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n107.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 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:04 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU770^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.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 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:26:01 CDT 2014
% % CPUTime : 300.03
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x969710>, <kernel.DependentProduct object at 0xd44ef0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xd9af38>, <kernel.Single object at 0xd44c68>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xda3c68>, <kernel.DependentProduct object at 0xd44bd8>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xda3c68>, <kernel.DependentProduct object at 0xd44b48>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0xd44ef0>, <kernel.Sort object at 0xbfcea8>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xd44d88>, <kernel.Sort object at 0xbfcea8>) of role type named dsetconstrEL_type
% Using role type
% Declaring dsetconstrEL:Prop
% FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL
% A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))))
% Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0xd44cb0>, <kernel.Sort object at 0xbfcea8>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0xd44b90>, <kernel.DependentProduct object at 0xd44e60>) of role type named nonempty_type
% Using role type
% Declaring nonempty:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) of role definition named nonempty
% A new definition: (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))))
% Defined: nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))
% FOF formula (<kernel.Constant object at 0xd44e60>, <kernel.Sort object at 0xbfcea8>) of role type named nonemptyI_type
% Using role type
% Declaring nonemptyI:Prop
% FOF formula (((eq Prop) nonemptyI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named nonemptyI
% A new definition: (((eq Prop) nonemptyI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: nonemptyI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xd446c8>, <kernel.Sort object at 0xbfcea8>) of role type named powersetI_type
% Using role type
% Declaring powersetI:Prop
% FOF formula (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))) of role definition named powersetI
% A new definition: (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A)))))
% Defined: powersetI:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))
% FOF formula (<kernel.Constant object at 0xd441b8>, <kernel.DependentProduct object at 0xd448c0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xd44908>, <kernel.DependentProduct object at 0xd44368>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xd446c8>, <kernel.DependentProduct object at 0xd444d0>) of role type named ex1_type
% Using role type
% Declaring ex1:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0xd444d0>, <kernel.Sort object at 0xbfcea8>) of role type named ex1I_type
% Using role type
% Declaring ex1I:Prop
% FOF formula (((eq Prop) ex1I) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named ex1I
% A new definition: (((eq Prop) ex1I) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: ex1I:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xd44908>, <kernel.DependentProduct object at 0xd44560>) of role type named breln1Set_type
% Using role type
% Declaring breln1Set:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xd44710>, <kernel.DependentProduct object at 0xd448c0>) of role type named transitive_type
% Using role type
% Declaring transitive:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xd444d0>, <kernel.DependentProduct object at 0xd44908>) of role type named antisymmetric_type
% Using role type
% Declaring antisymmetric:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) antisymmetric) (fun (A:fofType) (R:fofType)=> (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((and ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R))->(((eq fofType) Xx) Xy)))))))) of role definition named antisymmetric
% A new definition: (((eq (fofType->(fofType->Prop))) antisymmetric) (fun (A:fofType) (R:fofType)=> (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((and ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R))->(((eq fofType) Xx) Xy))))))))
% Defined: antisymmetric:=(fun (A:fofType) (R:fofType)=> (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((and ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R))->(((eq fofType) Xx) Xy)))))))
% FOF formula (<kernel.Constant object at 0xd44908>, <kernel.DependentProduct object at 0xd44560>) of role type named reflexive_type
% Using role type
% Declaring reflexive:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xd448c0>, <kernel.DependentProduct object at 0xd44290>) of role type named refllinearorder_type
% Using role type
% Declaring refllinearorder:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) refllinearorder) (fun (A:fofType) (R:fofType)=> ((and ((and ((and ((reflexive A) R)) ((transitive A) R))) ((antisymmetric A) R))) (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R))))))))) of role definition named refllinearorder
% A new definition: (((eq (fofType->(fofType->Prop))) refllinearorder) (fun (A:fofType) (R:fofType)=> ((and ((and ((and ((reflexive A) R)) ((transitive A) R))) ((antisymmetric A) R))) (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R)))))))))
% Defined: refllinearorder:=(fun (A:fofType) (R:fofType)=> ((and ((and ((and ((reflexive A) R)) ((transitive A) R))) ((antisymmetric A) R))) (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xy) Xx)) R))))))))
% FOF formula (<kernel.Constant object at 0xd46560>, <kernel.DependentProduct object at 0xd44dd0>) of role type named reflwellordering_type
% Using role type
% Declaring reflwellordering:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) reflwellordering) (fun (A:fofType) (R:fofType)=> ((and ((refllinearorder A) R)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Xy:fofType), (((in Xy) X)->((in ((kpair Xx) Xy)) R)))))))))))) of role definition named reflwellordering
% A new definition: (((eq (fofType->(fofType->Prop))) reflwellordering) (fun (A:fofType) (R:fofType)=> ((and ((refllinearorder A) R)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Xy:fofType), (((in Xy) X)->((in ((kpair Xx) Xy)) R))))))))))))
% Defined: reflwellordering:=(fun (A:fofType) (R:fofType)=> ((and ((refllinearorder A) R)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Xy:fofType), (((in Xy) X)->((in ((kpair Xx) Xy)) R)))))))))))
% FOF formula (dsetconstrI->(dsetconstrEL->(dsetconstrER->(nonemptyI->(powersetI->(ex1I->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))), ((forall (Xx:fofType), (((in Xx) A)->((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) ((Xphi Xx) Xy))))))->(forall (R:fofType), (((in R) (breln1Set B))->(((reflwellordering B) R)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((and ((Xphi Xx) Xy)) (forall (Xz:fofType), (((in Xz) B)->(((Xphi Xx) Xz)->((in ((kpair Xy) Xz)) R))))))))))))))))))))) of role conjecture named choice2fnsingleton
% Conjecture to prove = (dsetconstrI->(dsetconstrEL->(dsetconstrER->(nonemptyI->(powersetI->(ex1I->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))), ((forall (Xx:fofType), (((in Xx) A)->((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) ((Xphi Xx) Xy))))))->(forall (R:fofType), (((in R) (breln1Set B))->(((reflwellordering B) R)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((and ((Xphi Xx) Xy)) (forall (Xz:fofType), (((in Xz) B)->(((Xphi Xx) Xz)->((in ((kpair Xy) Xz)) R))))))))))))))))))))):Prop
% We need to prove ['(dsetconstrI->(dsetconstrEL->(dsetconstrER->(nonemptyI->(powersetI->(ex1I->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))), ((forall (Xx:fofType), (((in Xx) A)->((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) ((Xphi Xx) Xy))))))->(forall (R:fofType), (((in R) (breln1Set B))->(((reflwellordering B) R)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((and ((Xphi Xx) Xy)) (forall (Xz:fofType), (((in Xz) B)->(((Xphi Xx) Xz)->((in ((kpair Xy) Xz)) R))))))))
% EOF
%------------------------------------------------------------------------------