TSTP Solution File: SEU755^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU755^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n096.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 13:33:01 EDT 2014
% Result : Theorem 19.50s
% Output : Proof 19.50s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU755^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n096.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 11:23:41 CDT 2014
% % CPUTime : 19.50
% 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 0xac4878>, <kernel.DependentProduct object at 0xac4d88>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xe81488>, <kernel.DependentProduct object at 0xac43f8>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xac44d0>, <kernel.DependentProduct object at 0xac4ab8>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xac4a70>, <kernel.DependentProduct object at 0xac4878>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xac4ea8>, <kernel.Sort object at 0x98f098>) 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 0xac4f38>, <kernel.Sort object at 0x98f098>) of role type named setminusER_type
% Using role type
% Declaring setminusER:Prop
% FOF formula (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))) of role definition named setminusER
% A new definition: (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))))
% Defined: setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))
% FOF formula (<kernel.Constant object at 0xac4b48>, <kernel.Sort object at 0x98f098>) of role type named binunionTEcontra_type
% Using role type
% Declaring binunionTEcontra:Prop
% FOF formula (((eq Prop) binunionTEcontra) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False)))))))))) of role definition named binunionTEcontra
% A new definition: (((eq Prop) binunionTEcontra) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False))))))))))
% Defined: binunionTEcontra:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False)))))))))
% FOF formula (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))) of role conjecture named demorgan2b2
% Conjecture to prove = (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter binunion:(fofType->(fofType->fofType)).
% 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 setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))):Prop.
% Definition binunionTEcontra:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False))))))))):Prop.
% Trying to prove (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x6:((in Xx) ((setminus A) Y))
% Found x6 as proof of ((in Xx) ((setminus A) Y))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x2:((in X) (powerset A))
% Found x2 as proof of ((in X) (powerset A))
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binunion X) Y))
% Found x8 as proof of ((in Xx) ((binunion X) Y))
% Found x5:((in Xx) ((setminus A) X))
% Found x5 as proof of ((in Xx) ((setminus A) X))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x2:((in X) (powerset A))
% Found x2 as proof of ((in X) (powerset A))
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binunion X) Y))
% Found x8 as proof of ((in Xx) ((binunion X) Y))
% Found x5:((in Xx) ((setminus A) X))
% Found x5 as proof of ((in Xx) ((setminus A) X))
% Found x6:((in Xx) ((setminus A) Y))
% Found x6 as proof of ((in Xx) ((setminus A) Y))
% Found x2:((in X) (powerset A))
% Found x2 as proof of ((in X) (powerset A))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x5:((in Xx) ((setminus A) X))
% Found x5 as proof of ((in Xx) ((setminus A) X))
% Found x6:((in Xx) ((setminus A) Y))
% Found x6 as proof of ((in Xx) ((setminus A) Y))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x6:((in Xx) ((setminus A) Y))
% Found x6 as proof of ((in Xx) ((setminus A) Y))
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x2:((in X) (powerset A))
% Found x2 as proof of ((in X) (powerset A))
% Found x3:((in Y) (powerset A))
% Found x3 as proof of ((in Y) (powerset A))
% Found x5:((in Xx) ((setminus A) X))
% Found x5 as proof of ((in Xx) ((setminus A) X))
% Found x00000:=(x0000 x6):(((in Xx) Y)->False)
% Found (x0000 x6) as proof of (((in Xx) Y)->False)
% Found ((x000 A) x6) as proof of (((in Xx) Y)->False)
% Found (((fun (A0:fofType)=> ((x00 A0) Xx)) A) x6) as proof of (((in Xx) Y)->False)
% Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6) as proof of (((in Xx) Y)->False)
% Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6) as proof of (((in Xx) Y)->False)
% Found x00000:=(x0000 x5):(((in Xx) X)->False)
% Found (x0000 x5) as proof of (((in Xx) X)->False)
% Found ((x000 A) x5) as proof of (((in Xx) X)->False)
% Found (((fun (A0:fofType)=> ((x00 A0) Xx)) A) x5) as proof of (((in Xx) X)->False)
% Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5) as proof of (((in Xx) X)->False)
% Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5) as proof of (((in Xx) X)->False)
% Found (((((x1000 x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False
% Found ((((((x100 A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False
% Found (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> (((((((x10 A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False
% Found (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False
% Found (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))) as proof of False
% Found (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))) as proof of (((in Xx) ((binunion X) Y))->False)
% Found ((x700 x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (((x70 Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found ((((x7 ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found (fun (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))
% Found (fun (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))
% Found (fun (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))
% Found (fun (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))
% Found (fun (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))
% Found (fun (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))
% Found (fun (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))
% Found (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))
% Found (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))))
% Got proof (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))))
% Time elapsed = 19.047652s
% node=3357 cost=1466.000000 depth=27
% ::::::::::::::::::::::
% % 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:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------