TSTP Solution File: SEU818^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU818^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n098.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 : Theorem 0.60s
% Output : Proof 0.60s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU818^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.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 11:33:26 CDT 2014
% % CPUTime : 0.60
% 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 0xb8a7a0>, <kernel.DependentProduct object at 0xb8aa70>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xd6d368>, <kernel.Single object at 0xb8ac68>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xb8aa70>, <kernel.DependentProduct object at 0xb8a440>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xb8ab90>, <kernel.DependentProduct object at 0xb8ad40>) 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 0xb8ad40>, <kernel.DependentProduct object at 0xb8a368>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xb8a488>, <kernel.Sort object at 0xa4fea8>) of role type named subsetI1_type
% Using role type
% Declaring subsetI1:Prop
% FOF formula (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI1
% A new definition: (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0xb8ab90>, <kernel.DependentProduct object at 0xb8add0>) 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 0xb8add0>, <kernel.DependentProduct object at 0xb8aa28>) 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 0xb8aa28>, <kernel.DependentProduct object at 0xb8a488>) 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 0xb8a488>, <kernel.DependentProduct object at 0xb8ab90>) 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 (<kernel.Constant object at 0xb8ab90>, <kernel.Sort object at 0xa4fea8>) of role type named ordinalTransSet_type
% Using role type
% Declaring ordinalTransSet:Prop
% FOF formula (((eq Prop) ordinalTransSet) (forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) of role definition named ordinalTransSet
% A new definition: (((eq Prop) ordinalTransSet) (forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))))
% Defined: ordinalTransSet:=(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))
% FOF formula (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))) of role conjecture named ordinalTransSet1
% Conjecture to prove = (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))):Prop
% We need to prove ['(subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter powerset:(fofType->fofType).
% Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop).
% Parameter subset:(fofType->(fofType->Prop)).
% Definition subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))):(fofType->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).
% Definition ordinalTransSet:=(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))):Prop.
% Trying to prove (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X)))))))
% Found x2:(transitiveset X)
% Found (fun (x3:(wellorderedByIn X))=> x2) as proof of (transitiveset X)
% Found (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2) as proof of ((wellorderedByIn X)->(transitiveset X))
% Found (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2) as proof of ((transitiveset X)->((wellorderedByIn X)->(transitiveset X)))
% Found (and_rect00 (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X)
% Found ((and_rect0 (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X)
% Found (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X)
% Found (fun (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (transitiveset X)
% Found (fun (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of ((ordinal X)->(transitiveset X))
% Found (fun (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (forall (X:fofType), ((ordinal X)->(transitiveset X)))
% Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (ordinalTransSet->(forall (X:fofType), ((ordinal X)->(transitiveset X))))
% Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(transitiveset X)))))
% Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X)))))))
% Got proof (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)))
% Time elapsed = 0.254000s
% node=42 cost=144.000000 depth=11
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------