TSTP Solution File: SEU819^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU819^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n089.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 13:33:13 EDT 2014
% Result : Unknown 0.88s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU819^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.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 11:33:46 CDT 2014
% % CPUTime : 0.88
% 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 0x2b876c8>, <kernel.DependentProduct object at 0x28ca1b8>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2b87d88>, <kernel.Single object at 0x28ca248>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x2b876c8>, <kernel.DependentProduct object at 0x2b2f2d8>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x2b876c8>, <kernel.DependentProduct object at 0x2b2f998>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x28ca560>, <kernel.DependentProduct object at 0x2b2f908>) 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 0x28ca200>, <kernel.DependentProduct object at 0x2b2f5a8>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x28ca518>, <kernel.DependentProduct object at 0x2b2f368>) of role type named transitiveset_type
% Using role type
% Declaring transitiveset:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) transitiveset) (fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A))))) of role definition named transitiveset
% A new definition: (((eq (fofType->Prop)) transitiveset) (fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))))
% Defined: transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A))))
% FOF formula (<kernel.Constant object at 0x28ca518>, <kernel.Sort object at 0x2617368>) of role type named setunionTransitive_type
% Using role type
% Declaring setunionTransitive:Prop
% FOF formula (((eq Prop) setunionTransitive) (forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(transitiveset Xx)))->(transitiveset (setunion X))))) of role definition named setunionTransitive
% A new definition: (((eq Prop) setunionTransitive) (forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(transitiveset Xx)))->(transitiveset (setunion X)))))
% Defined: setunionTransitive:=(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(transitiveset Xx)))->(transitiveset (setunion X))))
% FOF formula (<kernel.Constant object at 0x2b2f998>, <kernel.DependentProduct object at 0x274fdd0>) of role type named stricttotalorderedByIn_type
% Using role type
% Declaring stricttotalorderedByIn:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) stricttotalorderedByIn) (fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False)))))) of role definition named stricttotalorderedByIn
% A new definition: (((eq (fofType->Prop)) stricttotalorderedByIn) (fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False))))))
% Defined: stricttotalorderedByIn:=(fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False)))))
% FOF formula (<kernel.Constant object at 0x2b2f2d8>, <kernel.DependentProduct object at 0x274f950>) of role type named wellorderedByIn_type
% Using role type
% Declaring wellorderedByIn:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) wellorderedByIn) (fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y))))))))))))) of role definition named wellorderedByIn
% A new definition: (((eq (fofType->Prop)) wellorderedByIn) (fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y)))))))))))))
% Defined: wellorderedByIn:=(fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y))))))))))))
% FOF formula (<kernel.Constant object at 0x2b2f950>, <kernel.DependentProduct object at 0x274f950>) of role type named ordinal_type
% Using role type
% Declaring ordinal:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) ordinal) (fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx)))) of role definition named ordinal
% A new definition: (((eq (fofType->Prop)) ordinal) (fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx))))
% Defined: ordinal:=(fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx)))
% FOF formula (setunionTransitive->(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(ordinal Xx)))->(transitiveset (setunion X))))) of role conjecture named setunionOrdinalLem1
% Conjecture to prove = (setunionTransitive->(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(ordinal Xx)))->(transitiveset (setunion X))))):Prop
% We need to prove ['(setunionTransitive->(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(ordinal Xx)))->(transitiveset (setunion X)))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter powerset:(fofType->fofType).
% Parameter setunion:(fofType->fofType).
% Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop).
% Parameter subset:(fofType->(fofType->Prop)).
% Definition transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))):(fofType->Prop).
% Definition setunionTransitive:=(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(transitiveset Xx)))->(transitiveset (setunion X)))):Prop.
% Definition stricttotalorderedByIn:=(fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False))))):(fofType->Prop).
% Definition wellorderedByIn:=(fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y)))))))))))):(fofType->Prop).
% Definition ordinal:=(fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx))):(fofType->Prop).
% Trying to prove (setunionTransitive->(forall (X:fofType), ((forall (Xx:fofType), (((in Xx) X)->(ordinal Xx)))->(transitiveset (setunion X)))))
% Found x1:((in X0) (setunion X))
% Found x1 as proof of ((in X0) (setunion X))
% Found x1:((in X0) (setunion X))
% Found x1 as proof of ((in X0) (setunion X))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------