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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU736^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n180.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 13:32:58 EDT 2014

% Result   : Theorem 1.55s
% Output   : Proof 1.55s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU736^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n180.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 11:20:36 CDT 2014
% % CPUTime  : 1.55 
% 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 0x1ef25a8>, <kernel.DependentProduct object at 0x1ef2d40>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x20d0200>, <kernel.DependentProduct object at 0x1ef25f0>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1ef2680>, <kernel.DependentProduct object at 0x1ef2878>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1ef27e8>, <kernel.DependentProduct object at 0x1ef25a8>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1ef2a28>, <kernel.Sort object at 0x1dd51b8>) of role type named setminusI_type
% Using role type
% Declaring setminusI:Prop
% FOF formula (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))) of role definition named setminusI
% A new definition: (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))))
% Defined: setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))
% FOF formula (<kernel.Constant object at 0x1ddbb90>, <kernel.Sort object at 0x1dd51b8>) of role type named contrasubsetT_type
% Using role type
% Declaring contrasubsetT:Prop
% FOF formula (((eq Prop) contrasubsetT) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((subset X) ((setminus A) Y))->(((in Xx) Y)->(((in Xx) X)->False)))))))))) of role definition named contrasubsetT
% A new definition: (((eq Prop) contrasubsetT) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((subset X) ((setminus A) Y))->(((in Xx) Y)->(((in Xx) X)->False))))))))))
% Defined: contrasubsetT:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((subset X) ((setminus A) Y))->(((in Xx) Y)->(((in Xx) X)->False)))))))))
% FOF formula (setminusI->(contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))))) of role conjecture named contraSubsetComplement
% Conjecture to prove = (setminusI->(contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(setminusI->(contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter setminus:(fofType->(fofType->fofType)).
% Definition setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))):Prop.
% Definition contrasubsetT:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((subset X) ((setminus A) Y))->(((in Xx) Y)->(((in Xx) X)->False))))))))):Prop.
% Trying to prove (setminusI->(contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x0000000000:=(x000000000 x3):(((in Xx) X)->False)
% Found (x000000000 x3) as proof of (((in Xx) X)->False)
% Found ((x00000000 x4) x3) as proof of (((in Xx) X)->False)
% Found (((x0000000 x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((x000000 x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found (((((x00000 A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> ((((((x0000 A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> (((x000 A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> (((((x00 A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3) as proof of (((in Xx) X)->False)
% Found ((x600 x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)) as proof of ((in Xx) ((setminus A) X))
% Found (((x60 Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)) as proof of ((in Xx) ((setminus A) X))
% Found ((((x6 X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)) as proof of ((in Xx) ((setminus A) X))
% Found (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)) as proof of ((in Xx) ((setminus A) X))
% Found (fun (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of ((in Xx) ((setminus A) X))
% Found (fun (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (((in Xx) Y)->((in Xx) ((setminus A) X)))
% Found (fun (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))
% Found (fun (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))
% Found (fun (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))
% Found (fun (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))
% Found (fun (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))
% Found (fun (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))
% Found (fun (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (forall (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))
% Found (fun (x0:contrasubsetT) (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))
% Found (fun (x:setminusI) (x0:contrasubsetT) (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))))
% Found (fun (x:setminusI) (x0:contrasubsetT) (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3))) as proof of (setminusI->(contrasubsetT->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))))
% Got proof (fun (x:setminusI) (x0:contrasubsetT) (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)))
% Time elapsed = 1.204652s
% node=247 cost=1045.000000 depth=25
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:setminusI) (x0:contrasubsetT) (A:fofType) (X:fofType) (x1:((in X) (powerset A))) (Y:fofType) (x2:((in Y) (powerset A))) (x3:((subset X) ((setminus A) Y))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) Y))=> (((((x A) X) Xx) x4) ((((((fun (A0:fofType) (x7:((in X) (powerset A0))) (x8:((in Y) (powerset A0))) (x9:((in Xx) A0)) (x10:((subset X) ((setminus A0) Y)))=> (((((((fun (A0:fofType) (x7:((in X) (powerset A0)))=> ((((fun (A0:fofType) (x7:((in X) (powerset A0))) (Y0:fofType) (x8:((in Y0) (powerset A0)))=> ((((((fun (A0:fofType)=> ((x0 A0) X)) A0) x7) Y0) x8) Xx)) A0) x7) Y)) A0) x7) x8) x9) x10) x5)) A) x1) x2) x4) x3)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------