TSTP Solution File: SEU731^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU731^2 : 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 13:32:57 EDT 2014
% Result : Theorem 9.01s
% Output : Proof 9.01s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU731^2 : 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 11:20:06 CDT 2014
% % CPUTime : 9.01
% 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 0x27ef8c0>, <kernel.DependentProduct object at 0x27efb90>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x29cc3b0>, <kernel.DependentProduct object at 0x27ef908>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x27ef638>, <kernel.DependentProduct object at 0x27efb00>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x27efa28>, <kernel.Sort object at 0x26cf128>) of role type named complementT_lem_type
% Using role type
% Declaring complementT_lem:Prop
% FOF formula (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))) of role definition named complementT_lem
% A new definition: (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))))
% Defined: complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))
% FOF formula (<kernel.Constant object at 0x27ef9e0>, <kernel.Sort object at 0x26cf128>) of role type named setextT_type
% Using role type
% Declaring setextT:Prop
% FOF formula (((eq Prop) setextT) (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)->((in Xx) Y))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y)))))))) of role definition named setextT
% A new definition: (((eq Prop) setextT) (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)->((in Xx) Y))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y))))))))
% Defined: setextT:=(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)->((in Xx) Y))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y)))))))
% FOF formula (<kernel.Constant object at 0x27ef950>, <kernel.Sort object at 0x26cf128>) of role type named doubleComplementI1_type
% Using role type
% Declaring doubleComplementI1:Prop
% FOF formula (((eq Prop) doubleComplementI1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))))) of role definition named doubleComplementI1
% A new definition: (((eq Prop) doubleComplementI1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X)))))))))
% Defined: doubleComplementI1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))))
% FOF formula (<kernel.Constant object at 0x27ef908>, <kernel.Sort object at 0x26cf128>) of role type named doubleComplementE1_type
% Using role type
% Declaring doubleComplementE1:Prop
% FOF formula (((eq Prop) doubleComplementE1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))))) of role definition named doubleComplementE1
% A new definition: (((eq Prop) doubleComplementE1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X)))))))
% Defined: doubleComplementE1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))))
% FOF formula (complementT_lem->(setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X))))))))) of role conjecture named doubleComplementEq
% Conjecture to prove = (complementT_lem->(setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(complementT_lem->(setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter setminus:(fofType->(fofType->fofType)).
% Definition complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))):Prop.
% Definition setextT:=(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)->((in Xx) Y))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y))))))):Prop.
% Definition doubleComplementI1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X)))))))):Prop.
% Definition doubleComplementE1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X)))))):Prop.
% Trying to prove (complementT_lem->(setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))))))
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((setminus A) X))):(((eq fofType) ((setminus A) ((setminus A) X))) ((setminus A) ((setminus A) X)))
% Found (eq_ref0 ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found x4:(P X)
% Instantiate: b:=X:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((setminus A) X))):(((eq fofType) ((setminus A) ((setminus A) X))) ((setminus A) ((setminus A) X)))
% Found (eq_ref0 ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((setminus A) X))):(((eq fofType) ((setminus A) ((setminus A) X))) ((setminus A) ((setminus A) X)))
% Found (eq_ref0 ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found ((eq_ref fofType) ((setminus A) ((setminus A) X))) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) b)
% Found x4:(P0 b)
% Instantiate: b:=X:fofType
% Found (fun (x4:(P0 b))=> x4) as proof of (P0 X)
% Found (fun (P0:(fofType->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 X))
% Found (fun (P0:(fofType->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% Found x4:(P ((setminus A) ((setminus A) X)))
% Instantiate: b:=((setminus A) ((setminus A) X)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x3:((in X) (powerset A))
% Instantiate: A0:=A:fofType
% Found x3 as proof of ((in X) (powerset A0))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((setminus A) X)))
% Found x40:(P X)
% Found (fun (x40:(P X))=> x40) as proof of (P X)
% Found (fun (x40:(P X))=> x40) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((setminus A) X)))
% Found x1000:=(x100 x3):(forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))
% Found (x100 x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))
% Found ((x10 X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))
% Found (((x1 A) X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))
% Found (((x1 A) X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) ((setminus A) ((setminus A) X))))))
% Found x2000:=(x200 x3):(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))
% Found (x200 x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))
% Found ((x20 X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))
% Found (((x2 A) X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))
% Found (((x2 A) X) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((setminus A) X)))->((in Xx) X))))
% Found x410:=(x41 x3):((in ((setminus A) X)) (powerset A))
% Found (x41 x3) as proof of ((in ((setminus A) X)) (powerset A))
% Found ((x4 X) x3) as proof of ((in ((setminus A) X)) (powerset A))
% Found ((x4 X) x3) as proof of ((in ((setminus A) X)) (powerset A))
% Found (x40 ((x4 X) x3)) as proof of ((in ((setminus A) ((setminus A) X))) (powerset A))
% Found ((x4 ((setminus A) X)) ((x4 X) x3)) as proof of ((in ((setminus A) ((setminus A) X))) (powerset A))
% Found (((x A) ((setminus A) X)) (((x A) X) x3)) as proof of ((in ((setminus A) ((setminus A) X))) (powerset A))
% Found (((x A) ((setminus A) X)) (((x A) X) x3)) as proof of ((in ((setminus A) ((setminus A) X))) (powerset A))
% Found ((((x0000 (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) X)
% Found (((((x000 A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) X)
% Found ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> (((x00 A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) X)
% Found ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) X)
% Found ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)) as proof of (((eq fofType) ((setminus A) ((setminus A) X))) X)
% Found (eq_sym000 ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))) as proof of (((eq fofType) X) ((setminus A) ((setminus A) X)))
% Found ((eq_sym00 X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))) as proof of (((eq fofType) X) ((setminus A) ((setminus A) X)))
% Found (((eq_sym0 ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))) as proof of (((eq fofType) X) ((setminus A) ((setminus A) X)))
% Found ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))) as proof of (((eq fofType) X) ((setminus A) ((setminus A) X)))
% Found (fun (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (((eq fofType) X) ((setminus A) ((setminus A) X)))
% Found (fun (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X))))
% Found (fun (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (forall (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))
% Found (fun (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))
% Found (fun (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X))))))
% Found (fun (x0:setextT) (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))))
% Found (fun (x:complementT_lem) (x0:setextT) (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X))))))))
% Found (fun (x:complementT_lem) (x0:setextT) (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3)))) as proof of (complementT_lem->(setextT->(doubleComplementI1->(doubleComplementE1->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(((eq fofType) X) ((setminus A) ((setminus A) X)))))))))
% Got proof (fun (x:complementT_lem) (x0:setextT) (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))))
% Time elapsed = 8.604980s
% node=1462 cost=1164.000000 depth=23
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:complementT_lem) (x0:setextT) (x1:doubleComplementI1) (x2:doubleComplementE1) (A:fofType) (X:fofType) (x3:((in X) (powerset A)))=> ((((eq_sym fofType) ((setminus A) ((setminus A) X))) X) ((((((fun (A0:fofType) (x4:((in ((setminus A) ((setminus A) X))) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) ((setminus A) ((setminus A) X)))) A0) x4) X)) A) (((x A) ((setminus A) X)) (((x A) X) x3))) x3) (((x2 A) X) x3)) (((x1 A) X) x3))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------