TSTP Solution File: SEU628^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU628^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n113.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 13:32:39 EDT 2014
% Result : Theorem 0.49s
% Output : Proof 0.49s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU628^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n113.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 10:57:11 CDT 2014
% % CPUTime : 0.49
% 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 0x1ff4e18>, <kernel.DependentProduct object at 0x1ff4ef0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f9e320>, <kernel.Single object at 0x1ff4950>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x1ff4ef0>, <kernel.DependentProduct object at 0x1f808c0>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1ff4e60>, <kernel.DependentProduct object at 0x1f804d0>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1ff4710>, <kernel.DependentProduct object at 0x1f804d0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1ff4518>, <kernel.Sort object at 0x1e56c20>) of role type named powersetI1_type
% Using role type
% Declaring powersetI1:Prop
% FOF formula (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))) of role definition named powersetI1
% A new definition: (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))))
% Defined: powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))
% FOF formula (<kernel.Constant object at 0x1ff4dd0>, <kernel.DependentProduct object at 0x1f80248>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1ff4710>, <kernel.Sort object at 0x1e56c20>) of role type named ubforcartprodlem1_type
% Using role type
% Declaring ubforcartprodlem1:Prop
% FOF formula (((eq Prop) ubforcartprodlem1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))))))) of role definition named ubforcartprodlem1
% A new definition: (((eq Prop) ubforcartprodlem1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B))))))))
% Defined: ubforcartprodlem1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))))))
% FOF formula (powersetI1->(ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))))) of role conjecture named ubforcartprodlem2
% Conjecture to prove = (powersetI1->(ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))))):Prop
% We need to prove ['(powersetI1->(ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter powerset:(fofType->fofType).
% Parameter subset:(fofType->(fofType->Prop)).
% Definition powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))):Prop.
% Parameter binunion:(fofType->(fofType->fofType)).
% Definition ubforcartprodlem1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B))))))):Prop.
% Trying to prove (powersetI1->(ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))))
% Found x0000000:=(x000000 x2):((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found (x000000 x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found ((x00000 Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found (((x0000 x1) Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found ((((x000 Xx) x1) Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found (((((x00 B) Xx) x1) Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found ((((((x0 A) B) Xx) x1) Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found ((((((x0 A) B) Xx) x1) Xy) x2) as proof of ((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))
% Found (x30 ((((((x0 A) B) Xx) x1) Xy) x2)) as proof of ((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))
% Found ((x3 ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2)) as proof of ((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))
% Found (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2)) as proof of ((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))
% Found (fun (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of ((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))
% Found (fun (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))
% Found (fun (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))
% Found (fun (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))
% Found (fun (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))
% Found (fun (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (forall (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))
% Found (fun (x0:ubforcartprodlem1) (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))
% Found (fun (x:powersetI1) (x0:ubforcartprodlem1) (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))))
% Found (fun (x:powersetI1) (x0:ubforcartprodlem1) (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2))) as proof of (powersetI1->(ubforcartprodlem1->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))))
% Got proof (fun (x:powersetI1) (x0:ubforcartprodlem1) (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2)))
% Time elapsed = 0.158736s
% node=19 cost=293.000000 depth=18
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:powersetI1) (x0:ubforcartprodlem1) (A:fofType) (B:fofType) (Xx:fofType) (x1:((in Xx) A)) (Xy:fofType) (x2:((in Xy) B))=> (((x (powerset ((binunion A) B))) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((((((x0 A) B) Xx) x1) Xy) x2)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------