%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU604^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n189.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 13:32:35 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU604^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.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 10:52:06 CDT 2014
% % CPUTime  : 300.01 
% 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 0x9a8bd8>, <kernel.DependentProduct object at 0x9a8ea8>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xda0368>, <kernel.Single object at 0x9a8b90>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x9a8ea8>, <kernel.DependentProduct object at 0x9a89e0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x9a8a28>, <kernel.Sort object at 0x88dab8>) of role type named subsetI2_type
% Using role type
% Declaring subsetI2:Prop
% FOF formula (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI2
% A new definition: (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0x9a8908>, <kernel.Sort object at 0x88dab8>) of role type named subsetE_type
% Using role type
% Declaring subsetE:Prop
% FOF formula (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) of role definition named subsetE
% A new definition: (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))))
% Defined: subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))
% FOF formula (<kernel.Constant object at 0x9a8ea8>, <kernel.Sort object at 0x88dab8>) of role type named subsetemptysetimpeq_type
% Using role type
% Declaring subsetemptysetimpeq:Prop
% FOF formula (((eq Prop) subsetemptysetimpeq) (forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset)))) of role definition named subsetemptysetimpeq
% A new definition: (((eq Prop) subsetemptysetimpeq) (forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset))))
% Defined: subsetemptysetimpeq:=(forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset)))
% FOF formula (<kernel.Constant object at 0x9a8488>, <kernel.DependentProduct object at 0x9a8998>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x9a84d0>, <kernel.Sort object at 0x88dab8>) of role type named setminusEL_type
% Using role type
% Declaring setminusEL:Prop
% FOF formula (((eq Prop) setminusEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A)))) of role definition named setminusEL
% A new definition: (((eq Prop) setminusEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A))))
% Defined: setminusEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0x9a8ea8>, <kernel.Sort object at 0x88dab8>) 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 (subsetI2->(subsetE->(subsetemptysetimpeq->(setminusEL->(setminusER->(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset)))))))) of role conjecture named setminusSubset2
% Conjecture to prove = (subsetI2->(subsetE->(subsetemptysetimpeq->(setminusEL->(setminusER->(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset)))))))):Prop
% We need to prove ['(subsetI2->(subsetE->(subsetemptysetimpeq->(setminusEL->(setminusER->(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter subset:(fofType->(fofType->Prop)).
% Definition subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))):Prop.
% Definition subsetemptysetimpeq:=(forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset))):Prop.
% Parameter setminus:(fofType->(fofType->fofType)).
% Definition setminusEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A))):Prop.
% Definition setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))):Prop.
% Trying to prove (subsetI2->(subsetE->(subsetemptysetimpeq->(setminusEL->(setminusER->(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset))))))))
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P ((setminus A) B))
% Instantiate: A0:=((setminus A) B):fofType
% Found x5 as proof of (P0 A0)
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found x5:(P ((setminus A) B))
% Instantiate: b:=((setminus A) B):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P0 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P ((setminus A) B))
% Instantiate: A0:=((setminus A) B):fofType
% Found x5 as proof of (P0 A0)
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found x5:(P ((setminus A) B))
% Instantiate: b:=((setminus A) B):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P0 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P ((setminus A) B))
% Instantiate: a:=((setminus A) B):fofType
% Found x5 as proof of (P0 a)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found x5:(P2 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P2 A0))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of ((P2 A0)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of (P1 A0)
% Found x5:(P2 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P2 A0))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of ((P2 A0)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of (P1 A0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P2 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P2 b))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of ((P2 b)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P2 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P2 b))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of ((P2 b)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of (P1 b)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x60:(P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P emptyset)
% Instantiate: a:=emptyset:fofType
% Found x5 as proof of (P0 a)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found x60:(P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P2 ((setminus A) B))
% Found x60:(P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x5:(P b)
% Found x5 as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=emptyset:fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 emptyset)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 emptyset))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x50:(P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found x5:(P emptyset)
% Found x5 as proof of (P0 emptyset)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) A0)
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found x5:(P0 ((setminus A) B))
% Found (fun (x5:(P0 ((setminus A) B)))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 ((setminus A) B)))=> x5) as proof of ((P0 ((setminus A) B))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 ((setminus A) B)))=> x5) as proof of (P ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b00)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b00)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b00)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x50:(P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x6:((in Xx) A0)
% Found x6 as proof of ((in Xx) A0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 emptyset)
% Found (fun (x5:(P0 emptyset))=> x5) as proof of (P0 emptyset)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 emptyset))=> x5) as proof of ((P0 emptyset)->(P0 emptyset))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 emptyset))=> x5) as proof of (P emptyset)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) emptyset)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) emptyset)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) emptyset)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found x6:((in Xx) b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found x50:(P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P0 b0)
% Found x5:(P ((setminus A) B))
% Instantiate: a:=((setminus A) B):fofType
% Found x5 as proof of (P0 a)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of (P ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x5:(P ((setminus A) B))
% Instantiate: A0:=((setminus A) B):fofType
% Found x5 as proof of (P0 A0)
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x5:(P2 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P2 A0))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of ((P2 A0)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of (P1 A0)
% Found x5:(P2 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P2 A0))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of ((P2 A0)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 A0))=> x5) as proof of (P1 A0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P2 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P2 b))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of ((P2 b)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P2 b)
% Instantiate: b:=((setminus A) B):fofType
% Found (fun (x5:(P2 b))=> x5) as proof of (P2 ((setminus A) B))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of ((P2 b)->(P2 ((setminus A) B)))
% Found (fun (P2:(fofType->Prop)) (x5:(P2 b))=> x5) as proof of (P1 b)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x7:((in Xx) ((setminus A) B))
% Found x7 as proof of ((in Xx) ((setminus A) B))
% Found x7:((in Xx) b)
% Found x7 as proof of ((in Xx) b)
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x5:(P ((setminus A) B))
% Instantiate: b0:=((setminus A) B):fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found x7:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x7:((in Xx) A0))=> x7) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x7:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x60 (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found ((x6 emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x7:((in Xx) A0))=> x7)) as proof of ((subset A0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x60:(P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P2 emptyset)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P ((setminus A) B))
% Found x5 as proof of (P0 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found x5:(P emptyset)
% Instantiate: a:=emptyset:fofType
% Found x5 as proof of (P0 a)
% Found x5:(P emptyset)
% Instantiate: a:=emptyset:fofType
% Found x5 as proof of (P0 a)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found x60:(P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P2 ((setminus A) B))
% Found x60:(P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P2 ((setminus A) B))
% Found x50:(P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P0 b0)
% Found x60:(P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P2 b)
% Found x60:(P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x50:(P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found (fun (x50:(P1 ((setminus A) B)))=> x50) as proof of (P2 ((setminus A) B))
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found x5:(P1 emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found x5:(P0 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x5:(P0 A0))=> x5) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of ((P0 A0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 A0))=> x5) as proof of (P A0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found x200:=(x20 B):(forall (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A)))
% Found (x20 B) as proof of (forall (Xx:fofType), (((in Xx) b)->((in Xx) b0)))
% Found ((x2 A) B) as proof of (forall (Xx:fofType), (((in Xx) b)->((in Xx) b0)))
% Found ((x2 A) B) as proof of (forall (Xx:fofType), (((in Xx) b)->((in Xx) b0)))
% Found ((x2 A) B) as proof of (forall (Xx:fofType), (((in Xx) b)->((in Xx) b0)))
% Found (x50 ((x2 A) B)) as proof of (P b0)
% Found ((x5 b0) ((x2 A) B)) as proof of (P b0)
% Found (((x b) b0) ((x2 A) B)) as proof of (P b0)
% Found (((x b) b0) ((x2 A) B)) as proof of (P b0)
% Found x60:((in Xx) b)
% Found (fun (x60:((in Xx) b))=> x60) as proof of ((in Xx) b)
% Found (fun (x60:((in Xx) b))=> x60) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x6:((in Xx) A0)
% Instantiate: A0:=emptyset:fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found (((x A0) emptyset) (fun (Xx:fofType) (x6:((in Xx) A0))=> x6)) as proof of ((subset A0) emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b0)
% Instantiate: b0:=emptyset:fofType
% Found (fun (x6:((in Xx) b0))=> x6) as proof of ((in Xx) emptyset)
% Found (fun (Xx:fofType) (x6:((in Xx) b0))=> x6) as proof of (((in Xx) b0)->((in Xx) emptyset))
% Found (fun (Xx:fofType) (x6:((in Xx) b0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) b0)->((in Xx) emptyset)))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) b0))=> x6)) as proof of (P b0)
% Found ((x5 emptyset) (fun (Xx:fofType) (x6:((in Xx) b0))=> x6)) as proof of (P b0)
% Found (((x b0) emptyset) (fun (Xx:fofType) (x6:((in Xx) b0))=> x6)) as proof of (P b0)
% Found (((x b0) emptyset) (fun (Xx:fofType) (x6:((in Xx) b0))=> x6)) as proof of (P b0)
% Found x60:(P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P1 emptyset)
% Found (fun (x60:(P1 emptyset))=> x60) as proof of (P2 emptyset)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of (P ((setminus A) B))
% Found x50:(P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P b0)
% Found (fun (x50:(P b0))=> x50) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found x5:(P0 ((setminus A) B))
% Found (fun (x5:(P0 ((setminus A) B)))=> x5) as proof of (P0 ((setminus A) B))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 ((setminus A) B)))=> x5) as proof of ((P0 ((setminus A) B))->(P0 ((setminus A) B)))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 ((setminus A) B)))=> x5) as proof of (P ((setminus A) B))
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found x5:(P b)
% Instantiate: A0:=b:fofType
% Found x5 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found ((eq_ref fofType) ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b1)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P1 b)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x50:(P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P1 emptyset)
% Found (fun (x50:(P1 emptyset))=> x50) as proof of (P2 emptyset)
% Found x60:(P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P1 ((setminus A) B))
% Found (fun (x60:(P1 ((setminus A) B)))=> x60) as proof of (P2 ((setminus A) B))
% Found x60:(P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P1 b)
% Found (fun (x60:(P1 b))=> x60) as proof of (P2 b)
% Found x6:((in Xx) ((setminus A) B))
% Found x6 as proof of ((in Xx) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found x50:(P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P0 b)
% Found (fun (x50:(P0 b))=> x50) as proof of (P1 b)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=emptyset:fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 emptyset)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 emptyset))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P0 b0)
% Instantiate: b0:=emptyset:fofType
% Found (fun (x5:(P0 b0))=> x5) as proof of (P0 emptyset)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of ((P0 b0)->(P0 emptyset))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b0))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x5:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b0)
% Found x7:((in Xx) A0)
% Instantiate: A1:=A0:fofType
% Found x7 as proof of (P1 A1)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x5:(P emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x6:((in Xx) ((setminus A) B))
% Found (fun (x6:((in Xx) ((setminus A) B)))=> x6) as proof of ((in Xx) ((setminus A) B))
% Found (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6) as proof of (((in Xx) ((setminus A) B))->((in Xx) ((setminus A) B)))
% Found (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6) as proof of (forall (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) ((setminus A) B))))
% Found (x50 (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6)) as proof of (P ((setminus A) B))
% Found ((x5 ((setminus A) B)) (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6)) as proof of (P ((setminus A) B))
% Found (((x ((setminus A) B)) ((setminus A) B)) (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6)) as proof of (P ((setminus A) B))
% Found (((x ((setminus A) B)) ((setminus A) B)) (fun (Xx:fofType) (x6:((in Xx) ((setminus A) B)))=> x6)) as proof of (P ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P b)
% Found (fun (x50:(P b))=> x50) as proof of (P b)
% Found (fun (x50:(P b))=> x50) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x50:(P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P emptyset)
% Found (fun (x50:(P emptyset))=> x50) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x50:(P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P ((setminus A) B))
% Found (fun (x50:(P ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found x5:(P emptyset)
% Found x5 as proof of (P0 emptyset)
% Found x50:(P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found x50:(P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found x5:(P emptyset)
% Found x5 as proof of (P0 emptyset)
% Found x6:((in Xx) b)
% Found x6 as proof of ((in Xx) b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) B))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x50:(P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P1 b)
% Found (fun (x50:(P1 b))=> x50) as proof of (P2 b)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x50:(P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P0 ((setminus A) B))
% Found (fun (x50:(P0 ((setminus A) B)))=> x50) as proof of (P1 ((setminus A) B))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b1)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) A0)
% Found x6:(P2 A0)
% Instantiate: A0:=((setminus A) B):fofType
% Found (fun (x6:(P2 A0))=> x6) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x6:(P2 A0))=> x6) as proof of ((P2 A0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x6:(P2 A0))=> x6) as proof of (P1 A0)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found x6:(P2 b0)
% Instantiate: b0:=((setminus A) B):fofType
% Found (fun (x6:(P2 b0))=> x6) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x6:(P2 b0))=> x6) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x6:(P2 b0))=> x6) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((setminus A) B)):(((eq fofType) ((setminus A) B)) ((setminus A) B))
% Found (eq_ref0 ((setminus A) B)) as proof of (((eq fofType) ((setminus A) B)) b0)
% Found ((eq_ref fofType) ((
% EOF
%------------------------------------------------------------------------------