TSTP Solution File: SET630^3 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET630^3 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n094.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 13:30:53 EDT 2014
% Result : Theorem 2.39s
% Output : Proof 2.39s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET630^3 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.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 10:27:06 CDT 2014
% % CPUTime : 2.39
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2624998>, <kernel.DependentProduct object at 0x26242d8>) of role type named in_decl
% Using role type
% Declaring in:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named in
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x2684098>, <kernel.DependentProduct object at 0x2624f38>) of role type named is_a_decl
% Using role type
% Declaring is_a:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named is_a
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x26808c0>, <kernel.DependentProduct object at 0x2624518>) of role type named emptyset_decl
% Using role type
% Declaring emptyset:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False)) of role definition named emptyset
% A new definition: (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False))
% Defined: emptyset:=(fun (X:fofType)=> False)
% FOF formula (<kernel.Constant object at 0x2624518>, <kernel.DependentProduct object at 0x2624b90>) of role type named unord_pair_decl
% Using role type
% Declaring unord_pair:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))) of role definition named unord_pair
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))))
% Defined: unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))
% FOF formula (<kernel.Constant object at 0x2679878>, <kernel.DependentProduct object at 0x2624f80>) of role type named singleton_decl
% Using role type
% Declaring singleton:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))) of role definition named singleton
% A new definition: (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)))
% Defined: singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))
% FOF formula (<kernel.Constant object at 0x2624f80>, <kernel.DependentProduct object at 0x26249e0>) of role type named union_decl
% Using role type
% Declaring union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% Defined: union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x26249e0>, <kernel.DependentProduct object at 0x2624128>) of role type named excl_union_decl
% Using role type
% Declaring excl_union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))) of role definition named excl_union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))))
% Defined: excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% FOF formula (<kernel.Constant object at 0x2624128>, <kernel.DependentProduct object at 0x2624f80>) of role type named intersection_decl
% Using role type
% Declaring intersection:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named intersection
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% Defined: intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x2624f80>, <kernel.DependentProduct object at 0x2624bd8>) of role type named setminus_decl
% Using role type
% Declaring setminus:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))) of role definition named setminus
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))))
% Defined: setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))
% FOF formula (<kernel.Constant object at 0x26242d8>, <kernel.DependentProduct object at 0x22485a8>) of role type named complement_decl
% Using role type
% Declaring complement:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named complement
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% Defined: complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% FOF formula (<kernel.Constant object at 0x2624518>, <kernel.DependentProduct object at 0x2248c68>) of role type named disjoint_decl
% Using role type
% Declaring disjoint:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))) of role definition named disjoint
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)))
% Defined: disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))
% FOF formula (<kernel.Constant object at 0x2624518>, <kernel.DependentProduct object at 0x2248d88>) of role type named subset_decl
% Using role type
% Declaring subset:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))) of role definition named subset
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))))
% Defined: subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))
% FOF formula (<kernel.Constant object at 0x2624518>, <kernel.DependentProduct object at 0x2248cf8>) of role type named meets_decl
% Using role type
% Declaring meets:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))) of role definition named meets
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))))
% Defined: meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))
% FOF formula (<kernel.Constant object at 0x2248cf8>, <kernel.DependentProduct object at 0x2248b00>) of role type named misses_decl
% Using role type
% Declaring misses:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))) of role definition named misses
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)))
% Defined: misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))
% FOF formula (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y))) of role conjecture named thm
% Conjecture to prove = (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y)))']
% Parameter fofType:Type.
% Definition in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition emptyset:=(fun (X:fofType)=> False):(fofType->Prop).
% Definition unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))):(fofType->(fofType->(fofType->Prop))).
% Definition singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)):(fofType->(fofType->Prop)).
% Definition union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Trying to prove (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y)))
% Found x80:=(x8 x5):False
% Found (x8 x5) as proof of False
% Found (fun (x8:((Y x0)->False))=> (x8 x5)) as proof of False
% Found (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)) as proof of (((Y x0)->False)->False)
% Found (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)) as proof of ((X x0)->(((Y x0)->False)->False))
% Found (and_rect20 (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found ((and_rect2 False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))) as proof of False
% Found (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)))) as proof of False
% Found (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5)))) as proof of (((and (X x0)) ((Y x0)->False))->False)
% Found x70:=(x7 x4):False
% Found (x7 x4) as proof of False
% Found (fun (x8:(Y x0))=> (x7 x4)) as proof of False
% Found (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)) as proof of ((Y x0)->False)
% Found (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)) as proof of (((X x0)->False)->((Y x0)->False))
% Found (and_rect20 (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))) as proof of False
% Found ((and_rect2 False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))) as proof of False
% Found (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))) as proof of False
% Found (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))) as proof of False
% Found (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))) as proof of (((and ((X x0)->False)) (Y x0))->False)
% Found ((or_ind00 (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))) as proof of False
% Found (((or_ind0 False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))) as proof of False
% Found ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))) as proof of False
% Found (fun (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))) as proof of False
% Found (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))) as proof of ((Y x0)->False)
% Found (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))) as proof of ((X x0)->((Y x0)->False))
% Found (and_rect10 (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))) as proof of False
% Found (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))) as proof of False
% Found (fun (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))) as proof of False
% Found (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))) as proof of ((((excl_union X) Y) x0)->False)
% Found (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))) as proof of ((((intersection X) Y) x0)->((((excl_union X) Y) x0)->False))
% Found (and_rect00 (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))) as proof of False
% Found ((and_rect0 False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))) as proof of False
% Found (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))) as proof of False
% Found (fun (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))) as proof of False
% Found (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))) as proof of (((and (((intersection X) Y) x0)) (((excl_union X) Y) x0))->False)
% Found (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))) as proof of (forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->False))
% Found (ex_ind00 (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))))) as proof of False
% Found ((ex_ind0 False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))))) as proof of False
% Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))))) as proof of False
% Found (fun (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))))) as proof of False
% Found (fun (Y:(fofType->Prop)) (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))))) as proof of ((misses ((intersection X) Y)) ((excl_union X) Y))
% Found (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))))) as proof of (forall (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y)))
% Found (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4)))))))))))) as proof of (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), ((misses ((intersection X) Y)) ((excl_union X) Y)))
% Got proof (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))))))
% Time elapsed = 2.009256s
% node=167 cost=803.000000 depth=33
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (x:((ex fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and (((intersection X) Y) x)) (((excl_union X) Y) x))->P)))=> (((((ex_ind fofType) (fun (U:fofType)=> ((and (((intersection X) Y) U)) (((excl_union X) Y) U)))) P) x0) x)) False) (fun (x0:fofType) (x1:((and (((intersection X) Y) x0)) (((excl_union X) Y) x0)))=> (((fun (P:Type) (x2:((((intersection X) Y) x0)->((((excl_union X) Y) x0)->P)))=> (((((and_rect (((intersection X) Y) x0)) (((excl_union X) Y) x0)) P) x2) x1)) False) (fun (x2:(((intersection X) Y) x0)) (x3:(((excl_union X) Y) x0))=> (((fun (P:Type) (x4:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x4) x2)) False) (fun (x4:(X x0)) (x5:(Y x0))=> ((((fun (P:Prop) (x6:(((and (X x0)) ((Y x0)->False))->P)) (x7:(((and ((X x0)->False)) (Y x0))->P))=> ((((((or_ind ((and (X x0)) ((Y x0)->False))) ((and ((X x0)->False)) (Y x0))) P) x6) x7) x3)) False) (fun (x6:((and (X x0)) ((Y x0)->False)))=> (((fun (P:Type) (x7:((X x0)->(((Y x0)->False)->P)))=> (((((and_rect (X x0)) ((Y x0)->False)) P) x7) x6)) False) (fun (x7:(X x0)) (x8:((Y x0)->False))=> (x8 x5))))) (fun (x6:((and ((X x0)->False)) (Y x0)))=> (((fun (P:Type) (x7:(((X x0)->False)->((Y x0)->P)))=> (((((and_rect ((X x0)->False)) (Y x0)) P) x7) x6)) False) (fun (x7:((X x0)->False)) (x8:(Y x0))=> (x7 x4))))))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------