TSTP Solution File: GRA030^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : GRA030^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n089.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 13:22:13 EDT 2014
% Result : Timeout 300.00s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRA030^1 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.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 07:38:16 CDT 2014
% % CPUTime : 300.00
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((G Xx1) Xx0)->False))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xx3:(Prop->Prop)) (Xx4:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (Xp2:((Prop->Prop)->Prop)) (Xp3:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp0 Xx3)->False))) ((Xp0 Xx4)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))) ((G Xx3) Xx0))) ((G Xx3) Xx1))) ((G Xx3) Xx2))) ((G Xx4) Xx0))) ((G Xx4) Xx1))) ((G Xx4) Xx2))) ((G Xx4) Xx3))))))) of role conjecture named ramsey_l_2_5_4
% Conjecture to prove = ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((G Xx1) Xx0)->False))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xx3:(Prop->Prop)) (Xx4:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (Xp2:((Prop->Prop)->Prop)) (Xp3:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp0 Xx3)->False))) ((Xp0 Xx4)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))) ((G Xx3) Xx0))) ((G Xx3) Xx1))) ((G Xx3) Xx2))) ((G Xx4) Xx0))) ((G Xx4) Xx1))) ((G Xx4) Xx2))) ((G Xx4) Xx3))))))):Prop
% We need to prove ['((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((G Xx1) Xx0)->False))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xx3:(Prop->Prop)) (Xx4:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (Xp2:((Prop->Prop)->Prop)) (Xp3:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp0 Xx3)->False))) ((Xp0 Xx4)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))) ((G Xx3) Xx0))) ((G Xx3) Xx1))) ((G Xx3) Xx2))) ((G Xx4) Xx0))) ((G Xx4) Xx1))) ((G Xx4) Xx2))) ((G Xx4) Xx3)))))))']
% Trying to prove ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((G Xx1) Xx0)->False))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xx3:(Prop->Prop)) (Xx4:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (Xp2:((Prop->Prop)->Prop)) (Xp3:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp0 Xx3)->False))) ((Xp0 Xx4)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))) ((G Xx3) Xx0))) ((G Xx3) Xx1))) ((G Xx3) Xx2))) ((G Xx4) Xx0))) ((G Xx4) Xx1))) ((G Xx4) Xx2))) ((G Xx4) Xx3)))))))
% Found x0000:=(x000 x0):False
% Found (x000 x0) as proof of False
% Found ((x00 Xp0) x0) as proof of False
% Found ((x00 Xp0) x0) as proof of False
% Found (fun (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of False
% Found (fun (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (((x Xx1) Xx0)->False)
% Found (fun (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((x Xx1) Xx0)->False))
% Found (fun (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((x Xx1) Xx0)->False)))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((x Xx1) Xx0)->False)))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((x Xx1) Xx0)->False)))
% Found x01:((Xp0 Xx1)->False)
% Instantiate: x:=(fun (x2:(Prop->Prop)) (x10:(Prop->Prop))=> (Xp0 x2)):((Prop->Prop)->((Prop->Prop)->Prop))
% Found (fun (x01:((Xp0 Xx1)->False))=> x01) as proof of (not ((x Xx1) Xx0))
% Found (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01) as proof of (((Xp0 Xx1)->False)->(not ((x Xx1) Xx0)))
% Found (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01) as proof of ((Xp0 Xx0)->(((Xp0 Xx1)->False)->(not ((x Xx1) Xx0))))
% Found (and_rect00 (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01)) as proof of (not ((x Xx1) Xx0))
% Found ((and_rect0 (not ((x Xx1) Xx0))) (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01)) as proof of (not ((x Xx1) Xx0))
% Found (((fun (P:Type) (x1:((Xp0 Xx0)->(((Xp0 Xx1)->False)->P)))=> (((((and_rect (Xp0 Xx0)) ((Xp0 Xx1)->False)) P) x1) x0)) (not ((x Xx1) Xx0))) (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01)) as proof of (not ((x Xx1) Xx0))
% Found (fun (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False)))=> (((fun (P:Type) (x1:((Xp0 Xx0)->(((Xp0 Xx1)->False)->P)))=> (((((and_rect (Xp0 Xx0)) ((Xp0 Xx1)->False)) P) x1) x0)) (not ((x Xx1) Xx0))) (fun (x00:(Xp0 Xx0)) (x01:((Xp0 Xx1)->False))=> x01))) as proof of (not ((x Xx1) Xx0))
% Found x0000:=(x000 x0):False
% Found (x000 x0) as proof of False
% Found ((x00 Xp0) x0) as proof of False
% Found ((x00 Xp0) x0) as proof of False
% Found (fun (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of False
% Found (fun (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (not ((x Xx1) Xx0))
% Found (fun (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(not ((x Xx1) Xx0)))
% Found (fun (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(not ((x Xx1) Xx0))))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(not ((x Xx1) Xx0))))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (x0:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x00:((x Xx1) Xx0))=> ((x00 Xp0) x0)) as proof of (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)), (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(not ((x Xx1) Xx0))))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))):((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found (((or_comm_i ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found (((or_comm_i ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))):((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found (((or_comm_i ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found (((or_comm_i ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found False_rect00:=(False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))):((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (or_intror00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((or_intror0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))):((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found False_rect00:=(False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))):((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (or_intror00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((or_intror0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))):((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found False_rect00:=(False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))):((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (False_rect0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (or_intror00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((or_intror0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (((or_intror ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))):((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (False_rect0 ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))) as proof of ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found (((or_comm_i ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx2)) ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))
% Found False_rect00:=(False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))):((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (False_rect0 ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))) as proof of ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2)))
% Found (or_comm_i00 ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found ((or_comm_i0 ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((x Xx4) Xx3))
% Found (((or_comm_i ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))) ((fun (P:Type)=> ((False_rect P) x010)) ((or ((x Xx4) Xx3)) ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) ((x Xx3) Xx0))) ((x Xx3) Xx1))) ((x Xx3) Xx2))) ((x Xx4) Xx0))) ((x Xx4) Xx1))) ((x Xx4) Xx2))))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((x Xx1) Xx0)) ((x Xx
% EOF
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