TSTP Solution File: SEU631^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU631^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n111.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 0.52s
% Output : Proof 0.52s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU631^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n111.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 10:57:51 CDT 2014
% % CPUTime : 0.52
% 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 0x22cd290>, <kernel.DependentProduct object at 0x22cd098>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1fd8cb0>, <kernel.Single object at 0x22cd908>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x22cd098>, <kernel.DependentProduct object at 0x22cd170>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x22cd320>, <kernel.DependentProduct object at 0x22edb90>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x22cd908>, <kernel.DependentProduct object at 0x22edb00>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x22cd170>, <kernel.Sort object at 0x1fcf908>) 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 0x22cd4d0>, <kernel.DependentProduct object at 0x22ec128>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x22cd908>, <kernel.DependentProduct object at 0x22ec128>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))) of role definition named kpair
% A new definition: (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))
% Defined: kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))
% FOF formula (<kernel.Constant object at 0x22cd908>, <kernel.DependentProduct object at 0x22ec9e0>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) cartprod) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz)))))))))))) of role definition named cartprod
% A new definition: (((eq (fofType->(fofType->fofType))) cartprod) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz))))))))))))
% Defined: cartprod:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz)))))))))))
% FOF formula (dsetconstrER->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))) of role conjecture named cartprodmempair1
% Conjecture to prove = (dsetconstrER->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))):Prop
% We need to prove ['(dsetconstrER->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter powerset:(fofType->fofType).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Parameter binunion:(fofType->(fofType->fofType)).
% Definition kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))):(fofType->(fofType->fofType)).
% Definition cartprod:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz))))))))))):(fofType->(fofType->fofType)).
% Trying to prove (dsetconstrER->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))
% Found x00:=(x0 (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz)))))))))):(forall (Xx:fofType), (((in Xx) ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xy:fofType)=> ((ex fofType) (fun (Xy0:fofType)=> ((and ((in Xy0) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xy) ((kpair Xy0) Xz)))))))))))->((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz))))))))))
% Found (x0 (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz)))))))))) as proof of (forall (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% Found ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz)))))))))) as proof of (forall (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% Found (fun (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz))))))))))) as proof of (forall (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% Found (fun (A:fofType) (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz))))))))))) as proof of (forall (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% Found (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz))))))))))) as proof of (forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% Found (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz))))))))))) as proof of (dsetconstrER->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))
% Got proof (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz)))))))))))
% Time elapsed = 0.187133s
% node=6 cost=-179.000000 depth=5
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset (powerset ((binunion A) B)))) (fun (x3:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) x3) ((kpair Xy) Xz)))))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------