%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET580^3 : TPTP v6.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n100.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:30:45 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET580^3 : TPTP v6.1.0. Released v3.6.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n100.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 10:11:36 CDT 2014
% % CPUTime  : 300.09 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x29ae908>, <kernel.DependentProduct object at 0x29ae050>) of role type named in_decl
% Using role type
% Declaring in:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named in
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x29ae908>, <kernel.DependentProduct object at 0x29ae3b0>) of role type named is_a_decl
% Using role type
% Declaring is_a:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named is_a
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x29ae3b0>, <kernel.DependentProduct object at 0x29ae1b8>) of role type named emptyset_decl
% Using role type
% Declaring emptyset:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False)) of role definition named emptyset
% A new definition: (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False))
% Defined: emptyset:=(fun (X:fofType)=> False)
% FOF formula (<kernel.Constant object at 0x29ae368>, <kernel.DependentProduct object at 0x29ae1b8>) of role type named unord_pair_decl
% Using role type
% Declaring unord_pair:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))) of role definition named unord_pair
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))))
% Defined: unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))
% FOF formula (<kernel.Constant object at 0x29ae908>, <kernel.DependentProduct object at 0x29cd680>) of role type named singleton_decl
% Using role type
% Declaring singleton:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))) of role definition named singleton
% A new definition: (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)))
% Defined: singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))
% FOF formula (<kernel.Constant object at 0x29ae1b8>, <kernel.DependentProduct object at 0x29cd6c8>) of role type named union_decl
% Using role type
% Declaring union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% Defined: union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x29ae1b8>, <kernel.DependentProduct object at 0x29cd368>) of role type named excl_union_decl
% Using role type
% Declaring excl_union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))) of role definition named excl_union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))))
% Defined: excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% FOF formula (<kernel.Constant object at 0x29ae368>, <kernel.DependentProduct object at 0x29cdc20>) of role type named intersection_decl
% Using role type
% Declaring intersection:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named intersection
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% Defined: intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x29cdc20>, <kernel.DependentProduct object at 0x29cd368>) of role type named setminus_decl
% Using role type
% Declaring setminus:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))) of role definition named setminus
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))))
% Defined: setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))
% FOF formula (<kernel.Constant object at 0x29cd368>, <kernel.DependentProduct object at 0x29cda28>) of role type named complement_decl
% Using role type
% Declaring complement:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named complement
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% Defined: complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% FOF formula (<kernel.Constant object at 0x29cda28>, <kernel.DependentProduct object at 0x29cdd88>) of role type named disjoint_decl
% Using role type
% Declaring disjoint:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))) of role definition named disjoint
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)))
% Defined: disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))
% FOF formula (<kernel.Constant object at 0x29cdd88>, <kernel.DependentProduct object at 0x29cd6c8>) of role type named subset_decl
% Using role type
% Declaring subset:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))) of role definition named subset
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))))
% Defined: subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))
% FOF formula (<kernel.Constant object at 0x29cd6c8>, <kernel.DependentProduct object at 0x29cda28>) of role type named meets_decl
% Using role type
% Declaring meets:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))) of role definition named meets
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))))
% Defined: meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))
% FOF formula (<kernel.Constant object at 0x29cda28>, <kernel.DependentProduct object at 0x29cd440>) of role type named misses_decl
% Using role type
% Declaring misses:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))) of role definition named misses
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)))
% Defined: misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))
% FOF formula (forall (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType), ((iff (((excl_union X) Y) U)) ((iff (X U)) ((Y U)->False)))) of role conjecture named thm
% Conjecture to prove = (forall (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType), ((iff (((excl_union X) Y) U)) ((iff (X U)) ((Y U)->False)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType), ((iff (((excl_union X) Y) U)) ((iff (X U)) ((Y U)->False))))']
% Parameter fofType:Type.
% Definition in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition emptyset:=(fun (X:fofType)=> False):(fofType->Prop).
% Definition unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))):(fofType->(fofType->(fofType->Prop))).
% Definition singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)):(fofType->(fofType->Prop)).
% Definition union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Trying to prove (forall (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType), ((iff (((excl_union X) Y) U)) ((iff (X U)) ((Y U)->False))))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x1:(X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (((Y U)->False)->(X U))
% Found x2:((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((X U)->((Y U)->False))
% Found ((conj10 (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of (((Y U)->False)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff (X U)) ((Y U)->False)))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:(Y U))=> (x1 x3)) as proof of False
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((Y U)->False)
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((X U)->((Y U)->False))
% Found False_rect00:=(False_rect0 (X U)):(X U)
% Found (False_rect0 (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) x30)) (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (((Y U)->False)->(X U))
% Found ((conj10 (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((Y U)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of (((X U)->False)->((Y U)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of (((and ((X U)->False)) (Y U))->((iff (X U)) ((Y U)->False)))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((or_ind0 ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((((excl_union X) Y) U)->((iff (X U)) ((Y U)->False)))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((Y U)->False)
% Found (fun (x3:((is_a U) X))=> x2) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X))=> x2) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found x1:(X U)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found ((conj10 (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of (((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:((is_a U) Y))=> (x1 x3)) as proof of False
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found False_rect00:=(False_rect0 ((is_a U) X)):((is_a U) X)
% Found (False_rect0 ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found ((conj10 (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of (((X U)->False)->((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of (((and ((X U)->False)) (Y U))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((or_ind0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((((excl_union X) Y) U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((X U)->((Y U)->False))
% Found x1:(X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (((Y U)->False)->(X U))
% Found ((conj10 (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of (((Y U)->False)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff (X U)) ((Y U)->False)))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:(Y U))=> (x1 x3)) as proof of False
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((Y U)->False)
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((X U)->((Y U)->False))
% Found False_rect00:=(False_rect0 (X U)):(X U)
% Found (False_rect0 (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) x30)) (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (((Y U)->False)->(X U))
% Found ((conj10 (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((Y U)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of (((X U)->False)->((Y U)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of (((and ((X U)->False)) (Y U))->((iff (X U)) ((Y U)->False)))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((or_ind0 ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((((excl_union X) Y) U)->((iff (X U)) ((Y U)->False)))
% Found x2:((Y U)->False)
% Found (fun (x3:((is_a U) X))=> x2) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X))=> x2) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found x1:(X U)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found ((conj10 (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of (((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:((is_a U) Y))=> (x1 x3)) as proof of False
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found False_rect00:=(False_rect0 ((is_a U) X)):((is_a U) X)
% Found (False_rect0 ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found ((conj10 (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of (((X U)->False)->((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of (((and ((X U)->False)) (Y U))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((or_ind0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((((excl_union X) Y) U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((not ((is_a U) Y))->((is_a U) X))->((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((excl_union X) Y) U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of (((excl_union X) Y) U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of (((not ((is_a U) Y))->((is_a U) X))->((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((not ((is_a U) Y))->((is_a U) X))->((and (X U)) ((Y U)->False)))
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x20:(X U)
% Found x20 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((not ((is_a U) Y))->((is_a U) X))->((and (X U)) ((Y U)->False)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((excl_union X) Y) U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of (((excl_union X) Y) U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of (((not ((is_a U) Y))->((is_a U) X))->((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x20:((is_a U) X)
% Found x20 as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of (((not ((is_a U) Y))->((is_a U) X))->((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((not ((is_a U) Y))->((is_a U) X))->((and (X U)) ((Y U)->False)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_intror00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found ((or_intror0 ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of ((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False)))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> (((or_intror ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00))) as proof of (((not ((is_a U) Y))->((is_a U) X))->((or ((and ((X U)->False)) (Y U))) ((and (X U)) ((Y U)->False))))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x20:(X U)
% Found x20 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x1:(X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> x1) as proof of (((Y U)->False)->(X U))
% Found x2:((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((Y U)->False)
% Found (fun (x3:(X U))=> x2) as proof of ((X U)->((Y U)->False))
% Found ((conj10 (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of (((Y U)->False)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff (X U)) ((Y U)->False)))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:(Y U))=> (x1 x3)) as proof of False
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((Y U)->False)
% Found (fun (x3:(X U)) (x4:(Y U))=> (x1 x3)) as proof of ((X U)->((Y U)->False))
% Found False_rect00:=(False_rect0 (X U)):(X U)
% Found (False_rect0 (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) x30)) (X U)) as proof of (X U)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (X U)
% Found (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))) as proof of (((Y U)->False)->(X U))
% Found ((conj10 (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((conj1 (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of ((Y U)->((iff (X U)) ((Y U)->False)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))) as proof of (((X U)->False)->((Y U)->((iff (X U)) ((Y U)->False))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((and_rect0 ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))) as proof of (((and ((X U)->False)) (Y U))->((iff (X U)) ((Y U)->False)))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (((or_ind0 ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U)))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((iff (X U)) ((Y U)->False))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff (X U)) ((Y U)->False))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U))=> x2)) (fun (x3:((Y U)->False))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff (X U)) ((Y U)->False))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj ((X U)->((Y U)->False))) (((Y U)->False)->(X U))) (fun (x3:(X U)) (x4:(Y U))=> (x1 x3))) (fun (x3:((Y U)->False))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) (X U))))))))) as proof of ((((excl_union X) Y) U)->((iff (X U)) ((Y U)->False)))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x20:((is_a U) X)
% Found x20 as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x20:(X U)
% Found x20 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x1:(X U)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> x1) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found x2:((Y U)->False)
% Found (fun (x3:((is_a U) X))=> x2) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X))=> x2) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found ((conj10 (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of (((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))) as proof of ((X U)->(((Y U)->False)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1))))) as proof of (((and (X U)) ((Y U)->False))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x3):False
% Found (x1 x3) as proof of False
% Found (fun (x4:((is_a U) Y))=> (x1 x3)) as proof of False
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (not ((is_a U) Y))
% Found (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3)) as proof of (((is_a U) X)->(not ((is_a U) Y)))
% Found False_rect00:=(False_rect0 ((is_a U) X)):((is_a U) X)
% Found (False_rect0 ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((is_a U) X)) as proof of ((is_a U) X)
% Found ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((is_a U) X)
% Found (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))) as proof of ((not ((is_a U) Y))->((is_a U) X))
% Found ((conj10 (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((conj1 ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of ((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))) as proof of (((X U)->False)->((Y U)->((iff ((is_a U) X)) (not ((is_a U) Y)))))
% Found (and_rect00 (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((and_rect0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))) as proof of (((and ((X U)->False)) (Y U))->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found ((or_ind00 (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (((or_ind0 ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X)))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((iff ((is_a U) X)) (not ((is_a U) Y)))
% Found (fun (x:(((excl_union X) Y) U))=> ((((fun (P:Prop) (x0:(((and (X U)) ((Y U)->False))->P)) (x1:(((and ((X U)->False)) (Y U))->P))=> ((((((or_ind ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) P) x0) x1) x)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x0:((and (X U)) ((Y U)->False)))=> (((fun (P:Type) (x1:((X U)->(((Y U)->False)->P)))=> (((((and_rect (X U)) ((Y U)->False)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:(X U)) (x2:((Y U)->False))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X))=> x2)) (fun (x3:(not ((is_a U) Y)))=> x1)))))) (fun (x0:((and ((X U)->False)) (Y U)))=> (((fun (P:Type) (x1:(((X U)->False)->((Y U)->P)))=> (((((and_rect ((X U)->False)) (Y U)) P) x1) x0)) ((iff ((is_a U) X)) (not ((is_a U) Y)))) (fun (x1:((X U)->False)) (x2:(Y U))=> ((((conj (((is_a U) X)->(not ((is_a U) Y)))) ((not ((is_a U) Y))->((is_a U) X))) (fun (x3:((is_a U) X)) (x4:((is_a U) Y))=> (x1 x3))) (fun (x3:(not ((is_a U) Y)))=> ((fun (P:Type)=> ((False_rect P) (x3 x2))) ((is_a U) X))))))))) as proof of ((((excl_union X) Y) U)->((iff ((is_a U) X)) (not ((is_a U) Y))))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x20:((is_a U) X)
% Found x20 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x20:(X U)
% Found x20 as proof of (X U)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x22:(X U)
% Found x22 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x20:((is_a U) X)
% Found x20 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x22:((is_a U) X)
% Found x22 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x21):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found (x1 x20) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found (x1 x20) as proof of (not ((is_a U) Y))
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x22:(X U)
% Found x22 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x22:(X U)
% Found x22 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of ((is_a U) Y)
% Found x22:((is_a U) X)
% Found x22 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x21):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x0):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x10:=(x1 x20):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x22:((is_a U) X)
% Found x22 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x21):((Y U)->False)
% Found x10 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x12):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x0):((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found (x1 x0) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x12):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x20):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x0:(Y U)
% Found x0 as proof of (Y U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found (x1 x0) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x10:=(x1 x21):((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found (x1 x21) as proof of ((Y U)->False)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found (x0 x11) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x02:(not ((is_a U) Y))
% Found x02 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x2:(Y U)
% Found x2 as proof of (Y U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x0:(X U)
% Found x0 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x02:(not ((is_a U) Y))
% Found x02 as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((and (X U)) ((Y U)->False))
% Found (fun (x1:((not ((is_a U) Y))->((is_a U) X)))=> ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of (((not ((is_a U) Y))->((is_a U) X))->((and (X U)) ((Y U)->False)))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x0:(Y U)
% Found x0 as proof of ((is_a U) Y)
% Found x0:(X U)
% Found x0 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x2:(X U)
% Found x2 as proof of (X U)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x01):((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found (x1 x01) as proof of ((is_a U) X)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x11:((is_a U) X)
% Found x11 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x10:(X U)
% Found x10 as proof of (X U)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x22):((Y U)->False)
% Found (x1 x22) as proof of ((Y U)->False)
% Found (x1 x22) as proof of ((Y U)->False)
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x12:(X U)
% Found x12 as proof of (X U)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x2:((is_a U) Y)
% Found x2 as proof of ((is_a U) Y)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x02:(not ((is_a U) Y))
% Found x02 as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found (x0 x2) as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of (X U)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x01:(not ((is_a U) Y))
% Found x01 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found (x0 x11) as proof of (not ((is_a U) Y))
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x11:((is_a U) X)
% Found x11 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x12):((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found (x0 x12) as proof of ((Y U)->False)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:((is_a U) X)
% Found x10 as proof of ((is_a U) X)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x2):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x12:((is_a U) X)
% Found x12 as proof of ((is_a U) X)
% Found x10:=(x1 x02):((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found (x1 x02) as proof of ((is_a U) X)
% Found x00:=(x0 x2):((Y U)->False)
% Found x00 as proof of ((Y U)->False)
% Found x00:=(x0 x12):(not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found (x0 x12) as proof of (not ((is_a U) Y))
% Found x10:=(x1 x0):(not ((is_a U) Y))
% Found x10 as proof of (not ((is_a U) Y))
% Found x00:=(x0 x11):(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found (x1 x00) as proof of ((is_a U) X)
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found (x0 x10) as proof of (not ((is_a U) Y))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x00:(not ((is_a U) Y))
% Found x00 as proof of (not ((is_a U) Y))
% Found x10:=(x1 x00):((is_a U) X)
% Found (x1 x00) as proof of (X U)
% Found (x1 x00) as proof of (X U)
% Found ((conj10 (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) (x1 x00)) x00)) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x2:(X U)
% Found x2 as proof of ((is_a U) X)
% Found x10:=(x1 x21):(not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found (x1 x21) as proof of (not ((is_a U) Y))
% Found x00:=(x0 x10):(not ((is_a U) Y))
% Found (x0 x10) as proof of ((Y U)->False)
% Found (x0 x10) as proof of ((Y U)->False)
% Found ((conj10 x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (((conj1 ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found ((((conj (X U)) ((Y U)->False)) x10) (x0 x10)) as proof of ((and (X U)) ((Y U)->False))
% Found (or_introl00 ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found ((or_introl0 ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found (((or_introl ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))) ((((conj (X U)) ((Y U)->False)) x10) (x0 x10))) as proof of ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))
% Found x00:=(x0 x2):((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found (x0 x2) as proof of ((Y U)->False)
% Found x00:=(x0 x12):(
% EOF
%------------------------------------------------------------------------------