TSTP Solution File: SEU795^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU795^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n115.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 13:33:09 EDT 2014
% Result : Theorem 1.25s
% Output : Proof 1.25s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU795^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 11:30:31 CDT 2014
% % CPUTime : 1.25
% 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 0x1f6bef0>, <kernel.DependentProduct object at 0x1f6b7e8>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f6bf38>, <kernel.DependentProduct object at 0x1f6bdd0>) of role type named exu_type
% Using role type
% Declaring exu:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))) of role definition named exu
% A new definition: (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% Defined: exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% FOF formula (<kernel.Constant object at 0x1f6bdd0>, <kernel.DependentProduct object at 0x1f6b440>) of role type named descr_type
% Using role type
% Declaring descr:((fofType->Prop)->fofType)
% FOF formula (<kernel.Constant object at 0x1f6b3f8>, <kernel.Sort object at 0x1e4b5a8>) of role type named descrp_type
% Using role type
% Declaring descrp:Prop
% FOF formula (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))) of role definition named descrp
% A new definition: (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))))
% Defined: descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))
% FOF formula (<kernel.Constant object at 0x1e4cf80>, <kernel.Sort object at 0x1e4b5a8>) of role type named in__Cong_type
% Using role type
% Declaring in__Cong:Prop
% FOF formula (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))) of role definition named in__Cong
% A new definition: (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))))
% Defined: in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))
% FOF formula (<kernel.Constant object at 0x1f6b4d0>, <kernel.Sort object at 0x1e4b5a8>) of role type named image1Ex1_type
% Using role type
% Declaring image1Ex1:Prop
% FOF formula (((eq Prop) image1Ex1) (forall (A:fofType) (Xf:(fofType->fofType)), (exu (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) of role definition named image1Ex1
% A new definition: (((eq Prop) image1Ex1) (forall (A:fofType) (Xf:(fofType->fofType)), (exu (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))))
% Defined: image1Ex1:=(forall (A:fofType) (Xf:(fofType->fofType)), (exu (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% FOF formula (<kernel.Constant object at 0x1f6bdd0>, <kernel.DependentProduct object at 0x1f6b758>) of role type named image1_type
% Using role type
% Declaring image1:(fofType->((fofType->fofType)->fofType))
% FOF formula (((eq (fofType->((fofType->fofType)->fofType))) image1) (fun (A:fofType) (Xf:(fofType->fofType))=> (descr (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) of role definition named image1
% A new definition: (((eq (fofType->((fofType->fofType)->fofType))) image1) (fun (A:fofType) (Xf:(fofType->fofType))=> (descr (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))))
% Defined: image1:=(fun (A:fofType) (Xf:(fofType->fofType))=> (descr (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% FOF formula (descrp->(in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))) of role conjecture named image1Equiv
% Conjecture to prove = (descrp->(in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(descrp->(in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Definition exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))):((fofType->Prop)->Prop).
% Parameter descr:((fofType->Prop)->fofType).
% Definition descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))):Prop.
% Definition in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))):Prop.
% Definition image1Ex1:=(forall (A:fofType) (Xf:(fofType->fofType)), (exu (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))):Prop.
% Definition image1:=(fun (A:fofType) (Xf:(fofType->fofType))=> (descr (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))):(fofType->((fofType->fofType)->fofType)).
% Trying to prove (descrp->(in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% Found x100:=(x10 Xf):(exu (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (x10 Xf) as proof of (exu (fun (Xx:fofType)=> (forall (Xx0:fofType), ((iff ((in Xx0) Xx)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx0) (Xf Xy)))))))))
% Found ((x1 A) Xf) as proof of (exu (fun (Xx:fofType)=> (forall (Xx0:fofType), ((iff ((in Xx0) Xx)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx0) (Xf Xy)))))))))
% Found ((x1 A) Xf) as proof of (exu (fun (Xx:fofType)=> (forall (Xx0:fofType), ((iff ((in Xx0) Xx)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx0) (Xf Xy)))))))))
% Found (x2 ((x1 A) Xf)) as proof of (forall (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))
% Found ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf)) as proof of (forall (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))
% Found (fun (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (forall (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))
% Found (fun (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (forall (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))
% Found (fun (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))
% Found (fun (x0:in__Cong) (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found (fun (x:descrp) (x0:in__Cong) (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (fun (x:descrp) (x0:in__Cong) (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf))) as proof of (descrp->(in__Cong->(image1Ex1->(forall (A:fofType) (Xf:(fofType->fofType)) (Xx:fofType), ((iff ((in Xx) ((image1 A) (fun (Xy:fofType)=> (Xf Xy))))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% Got proof (fun (x:descrp) (x0:in__Cong) (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf)))
% Time elapsed = 0.915760s
% node=101 cost=-98.000000 depth=10
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:descrp) (x0:in__Cong) (x1:image1Ex1) (A:fofType) (Xf:(fofType->fofType))=> ((x (fun (x3:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) x3)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) ((x1 A) Xf)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------