TSTP Solution File: GRA057^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : GRA057^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n118.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 13:22:16 EDT 2014
% Result : Timeout 300.05s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRA057^1 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n118.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 08:01:01 CDT 2014
% % CPUTime : 300.05
% 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->(Prop->(Prop->Prop)))->Prop))) (fun (G:((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop)))=> ((and ((and (forall (Xx:(Prop->(Prop->(Prop->Prop)))) (Xy:(Prop->(Prop->(Prop->Prop)))), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False))) (((G Xx3) Xx0)->False))) (((G Xx3) Xx1)->False))) (((G Xx3) Xx2)->False))) (((G Xx4) Xx0)->False))) (((G Xx4) Xx1)->False))) (((G Xx4) Xx2)->False))) (((G Xx4) Xx3)->False))) (((G Xx5) Xx0)->False))) (((G Xx5) Xx1)->False))) (((G Xx5) Xx2)->False))) (((G Xx5) Xx3)->False))) (((G Xx5) Xx4)->False)))))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xx6:(Prop->(Prop->(Prop->Prop)))) (Xx7:(Prop->(Prop->(Prop->Prop)))) (Xx8:(Prop->(Prop->(Prop->Prop)))) (Xx9:(Prop->(Prop->(Prop->Prop)))) (Xx10:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp5:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp6:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp7:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp8:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp9:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp0 Xx6)->False))) ((Xp0 Xx7)->False))) ((Xp0 Xx8)->False))) ((Xp0 Xx9)->False))) ((Xp0 Xx10)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp1 Xx6)->False))) ((Xp1 Xx7)->False))) ((Xp1 Xx8)->False))) ((Xp1 Xx9)->False))) ((Xp1 Xx10)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp2 Xx6)->False))) ((Xp2 Xx7)->False))) ((Xp2 Xx8)->False))) ((Xp2 Xx9)->False))) ((Xp2 Xx10)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp3 Xx6)->False))) ((Xp3 Xx7)->False))) ((Xp3 Xx8)->False))) ((Xp3 Xx9)->False))) ((Xp3 Xx10)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))) ((Xp4 Xx6)->False))) ((Xp4 Xx7)->False))) ((Xp4 Xx8)->False))) ((Xp4 Xx9)->False))) ((Xp4 Xx10)->False))) ((Xp5 Xx0)->False))) ((Xp5 Xx1)->False))) ((Xp5 Xx2)->False))) ((Xp5 Xx3)->False))) ((Xp5 Xx4)->False))) (Xp5 Xx5))) ((Xp5 Xx6)->False))) ((Xp5 Xx7)->False))) ((Xp5 Xx8)->False))) ((Xp5 Xx9)->False))) ((Xp5 Xx10)->False))) ((Xp6 Xx0)->False))) ((Xp6 Xx1)->False))) ((Xp6 Xx2)->False))) ((Xp6 Xx3)->False))) ((Xp6 Xx4)->False))) ((Xp6 Xx5)->False))) (Xp6 Xx6))) ((Xp6 Xx7)->False))) ((Xp6 Xx8)->False))) ((Xp6 Xx9)->False))) ((Xp6 Xx10)->False))) ((Xp7 Xx0)->False))) ((Xp7 Xx1)->False))) ((Xp7 Xx2)->False))) ((Xp7 Xx3)->False))) ((Xp7 Xx4)->False))) ((Xp7 Xx5)->False))) ((Xp7 Xx6)->False))) (Xp7 Xx7))) ((Xp7 Xx8)->False))) ((Xp7 Xx9)->False))) ((Xp7 Xx10)->False))) ((Xp8 Xx0)->False))) ((Xp8 Xx1)->False))) ((Xp8 Xx2)->False))) ((Xp8 Xx3)->False))) ((Xp8 Xx4)->False))) ((Xp8 Xx5)->False))) ((Xp8 Xx6)->False))) ((Xp8 Xx7)->False))) (Xp8 Xx8))) ((Xp8 Xx9)->False))) ((Xp8 Xx10)->False))) ((Xp9 Xx0)->False))) ((Xp9 Xx1)->False))) ((Xp9 Xx2)->False))) ((Xp9 Xx3)->False))) ((Xp9 Xx4)->False))) ((Xp9 Xx5)->False))) ((Xp9 Xx6)->False))) ((Xp9 Xx7)->False))) ((Xp9 Xx8)->False))) (Xp9 Xx9))) ((Xp9 Xx10)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((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))) ((G Xx5) Xx0))) ((G Xx5) Xx1))) ((G Xx5) Xx2))) ((G Xx5) Xx3))) ((G Xx5) Xx4))) ((G Xx6) Xx0))) ((G Xx6) Xx1))) ((G Xx6) Xx2))) ((G Xx6) Xx3))) ((G Xx6) Xx4))) ((G Xx6) Xx5))) ((G Xx7) Xx0))) ((G Xx7) Xx1))) ((G Xx7) Xx2))) ((G Xx7) Xx3))) ((G Xx7) Xx4))) ((G Xx7) Xx5))) ((G Xx7) Xx6))) ((G Xx8) Xx0))) ((G Xx8) Xx1))) ((G Xx8) Xx2))) ((G Xx8) Xx3))) ((G Xx8) Xx4))) ((G Xx8) Xx5))) ((G Xx8) Xx6))) ((G Xx8) Xx7))) ((G Xx9) Xx0))) ((G Xx9) Xx1))) ((G Xx9) Xx2))) ((G Xx9) Xx3))) ((G Xx9) Xx4))) ((G Xx9) Xx5))) ((G Xx9) Xx6))) ((G Xx9) Xx7))) ((G Xx9) Xx8))) ((G Xx10) Xx0))) ((G Xx10) Xx1))) ((G Xx10) Xx2))) ((G Xx10) Xx3))) ((G Xx10) Xx4))) ((G Xx10) Xx5))) ((G Xx10) Xx6))) ((G Xx10) Xx7))) ((G Xx10) Xx8))) ((G Xx10) Xx9))))))) of role conjecture named ramsey_l_6_11_256
% Conjecture to prove = ((ex ((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop))) (fun (G:((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop)))=> ((and ((and (forall (Xx:(Prop->(Prop->(Prop->Prop)))) (Xy:(Prop->(Prop->(Prop->Prop)))), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False))) (((G Xx3) Xx0)->False))) (((G Xx3) Xx1)->False))) (((G Xx3) Xx2)->False))) (((G Xx4) Xx0)->False))) (((G Xx4) Xx1)->False))) (((G Xx4) Xx2)->False))) (((G Xx4) Xx3)->False))) (((G Xx5) Xx0)->False))) (((G Xx5) Xx1)->False))) (((G Xx5) Xx2)->False))) (((G Xx5) Xx3)->False))) (((G Xx5) Xx4)->False)))))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xx6:(Prop->(Prop->(Prop->Prop)))) (Xx7:(Prop->(Prop->(Prop->Prop)))) (Xx8:(Prop->(Prop->(Prop->Prop)))) (Xx9:(Prop->(Prop->(Prop->Prop)))) (Xx10:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp5:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp6:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp7:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp8:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp9:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp0 Xx6)->False))) ((Xp0 Xx7)->False))) ((Xp0 Xx8)->False))) ((Xp0 Xx9)->False))) ((Xp0 Xx10)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp1 Xx6)->False))) ((Xp1 Xx7)->False))) ((Xp1 Xx8)->False))) ((Xp1 Xx9)->False))) ((Xp1 Xx10)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp2 Xx6)->False))) ((Xp2 Xx7)->False))) ((Xp2 Xx8)->False))) ((Xp2 Xx9)->False))) ((Xp2 Xx10)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp3 Xx6)->False))) ((Xp3 Xx7)->False))) ((Xp3 Xx8)->False))) ((Xp3 Xx9)->False))) ((Xp3 Xx10)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))) ((Xp4 Xx6)->False))) ((Xp4 Xx7)->False))) ((Xp4 Xx8)->False))) ((Xp4 Xx9)->False))) ((Xp4 Xx10)->False))) ((Xp5 Xx0)->False))) ((Xp5 Xx1)->False))) ((Xp5 Xx2)->False))) ((Xp5 Xx3)->False))) ((Xp5 Xx4)->False))) (Xp5 Xx5))) ((Xp5 Xx6)->False))) ((Xp5 Xx7)->False))) ((Xp5 Xx8)->False))) ((Xp5 Xx9)->False))) ((Xp5 Xx10)->False))) ((Xp6 Xx0)->False))) ((Xp6 Xx1)->False))) ((Xp6 Xx2)->False))) ((Xp6 Xx3)->False))) ((Xp6 Xx4)->False))) ((Xp6 Xx5)->False))) (Xp6 Xx6))) ((Xp6 Xx7)->False))) ((Xp6 Xx8)->False))) ((Xp6 Xx9)->False))) ((Xp6 Xx10)->False))) ((Xp7 Xx0)->False))) ((Xp7 Xx1)->False))) ((Xp7 Xx2)->False))) ((Xp7 Xx3)->False))) ((Xp7 Xx4)->False))) ((Xp7 Xx5)->False))) ((Xp7 Xx6)->False))) (Xp7 Xx7))) ((Xp7 Xx8)->False))) ((Xp7 Xx9)->False))) ((Xp7 Xx10)->False))) ((Xp8 Xx0)->False))) ((Xp8 Xx1)->False))) ((Xp8 Xx2)->False))) ((Xp8 Xx3)->False))) ((Xp8 Xx4)->False))) ((Xp8 Xx5)->False))) ((Xp8 Xx6)->False))) ((Xp8 Xx7)->False))) (Xp8 Xx8))) ((Xp8 Xx9)->False))) ((Xp8 Xx10)->False))) ((Xp9 Xx0)->False))) ((Xp9 Xx1)->False))) ((Xp9 Xx2)->False))) ((Xp9 Xx3)->False))) ((Xp9 Xx4)->False))) ((Xp9 Xx5)->False))) ((Xp9 Xx6)->False))) ((Xp9 Xx7)->False))) ((Xp9 Xx8)->False))) (Xp9 Xx9))) ((Xp9 Xx10)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((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))) ((G Xx5) Xx0))) ((G Xx5) Xx1))) ((G Xx5) Xx2))) ((G Xx5) Xx3))) ((G Xx5) Xx4))) ((G Xx6) Xx0))) ((G Xx6) Xx1))) ((G Xx6) Xx2))) ((G Xx6) Xx3))) ((G Xx6) Xx4))) ((G Xx6) Xx5))) ((G Xx7) Xx0))) ((G Xx7) Xx1))) ((G Xx7) Xx2))) ((G Xx7) Xx3))) ((G Xx7) Xx4))) ((G Xx7) Xx5))) ((G Xx7) Xx6))) ((G Xx8) Xx0))) ((G Xx8) Xx1))) ((G Xx8) Xx2))) ((G Xx8) Xx3))) ((G Xx8) Xx4))) ((G Xx8) Xx5))) ((G Xx8) Xx6))) ((G Xx8) Xx7))) ((G Xx9) Xx0))) ((G Xx9) Xx1))) ((G Xx9) Xx2))) ((G Xx9) Xx3))) ((G Xx9) Xx4))) ((G Xx9) Xx5))) ((G Xx9) Xx6))) ((G Xx9) Xx7))) ((G Xx9) Xx8))) ((G Xx10) Xx0))) ((G Xx10) Xx1))) ((G Xx10) Xx2))) ((G Xx10) Xx3))) ((G Xx10) Xx4))) ((G Xx10) Xx5))) ((G Xx10) Xx6))) ((G Xx10) Xx7))) ((G Xx10) Xx8))) ((G Xx10) Xx9))))))):Prop
% We need to prove ['((ex ((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop))) (fun (G:((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop)))=> ((and ((and (forall (Xx:(Prop->(Prop->(Prop->Prop)))) (Xy:(Prop->(Prop->(Prop->Prop)))), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False))) (((G Xx3) Xx0)->False))) (((G Xx3) Xx1)->False))) (((G Xx3) Xx2)->False))) (((G Xx4) Xx0)->False))) (((G Xx4) Xx1)->False))) (((G Xx4) Xx2)->False))) (((G Xx4) Xx3)->False))) (((G Xx5) Xx0)->False))) (((G Xx5) Xx1)->False))) (((G Xx5) Xx2)->False))) (((G Xx5) Xx3)->False))) (((G Xx5) Xx4)->False)))))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xx6:(Prop->(Prop->(Prop->Prop)))) (Xx7:(Prop->(Prop->(Prop->Prop)))) (Xx8:(Prop->(Prop->(Prop->Prop)))) (Xx9:(Prop->(Prop->(Prop->Prop)))) (Xx10:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp5:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp6:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp7:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp8:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp9:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp0 Xx6)->False))) ((Xp0 Xx7)->False))) ((Xp0 Xx8)->False))) ((Xp0 Xx9)->False))) ((Xp0 Xx10)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp1 Xx6)->False))) ((Xp1 Xx7)->False))) ((Xp1 Xx8)->False))) ((Xp1 Xx9)->False))) ((Xp1 Xx10)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp2 Xx6)->False))) ((Xp2 Xx7)->False))) ((Xp2 Xx8)->False))) ((Xp2 Xx9)->False))) ((Xp2 Xx10)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp3 Xx6)->False))) ((Xp3 Xx7)->False))) ((Xp3 Xx8)->False))) ((Xp3 Xx9)->False))) ((Xp3 Xx10)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))) ((Xp4 Xx6)->False))) ((Xp4 Xx7)->False))) ((Xp4 Xx8)->False))) ((Xp4 Xx9)->False))) ((Xp4 Xx10)->False))) ((Xp5 Xx0)->False))) ((Xp5 Xx1)->False))) ((Xp5 Xx2)->False))) ((Xp5 Xx3)->False))) ((Xp5 Xx4)->False))) (Xp5 Xx5))) ((Xp5 Xx6)->False))) ((Xp5 Xx7)->False))) ((Xp5 Xx8)->False))) ((Xp5 Xx9)->False))) ((Xp5 Xx10)->False))) ((Xp6 Xx0)->False))) ((Xp6 Xx1)->False))) ((Xp6 Xx2)->False))) ((Xp6 Xx3)->False))) ((Xp6 Xx4)->False))) ((Xp6 Xx5)->False))) (Xp6 Xx6))) ((Xp6 Xx7)->False))) ((Xp6 Xx8)->False))) ((Xp6 Xx9)->False))) ((Xp6 Xx10)->False))) ((Xp7 Xx0)->False))) ((Xp7 Xx1)->False))) ((Xp7 Xx2)->False))) ((Xp7 Xx3)->False))) ((Xp7 Xx4)->False))) ((Xp7 Xx5)->False))) ((Xp7 Xx6)->False))) (Xp7 Xx7))) ((Xp7 Xx8)->False))) ((Xp7 Xx9)->False))) ((Xp7 Xx10)->False))) ((Xp8 Xx0)->False))) ((Xp8 Xx1)->False))) ((Xp8 Xx2)->False))) ((Xp8 Xx3)->False))) ((Xp8 Xx4)->False))) ((Xp8 Xx5)->False))) ((Xp8 Xx6)->False))) ((Xp8 Xx7)->False))) (Xp8 Xx8))) ((Xp8 Xx9)->False))) ((Xp8 Xx10)->False))) ((Xp9 Xx0)->False))) ((Xp9 Xx1)->False))) ((Xp9 Xx2)->False))) ((Xp9 Xx3)->False))) ((Xp9 Xx4)->False))) ((Xp9 Xx5)->False))) ((Xp9 Xx6)->False))) ((Xp9 Xx7)->False))) ((Xp9 Xx8)->False))) (Xp9 Xx9))) ((Xp9 Xx10)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((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))) ((G Xx5) Xx0))) ((G Xx5) Xx1))) ((G Xx5) Xx2))) ((G Xx5) Xx3))) ((G Xx5) Xx4))) ((G Xx6) Xx0))) ((G Xx6) Xx1))) ((G Xx6) Xx2))) ((G Xx6) Xx3))) ((G Xx6) Xx4))) ((G Xx6) Xx5))) ((G Xx7) Xx0))) ((G Xx7) Xx1))) ((G Xx7) Xx2))) ((G Xx7) Xx3))) ((G Xx7) Xx4))) ((G Xx7) Xx5))) ((G Xx7) Xx6))) ((G Xx8) Xx0))) ((G Xx8) Xx1))) ((G Xx8) Xx2))) ((G Xx8) Xx3))) ((G Xx8) Xx4))) ((G Xx8) Xx5))) ((G Xx8) Xx6))) ((G Xx8) Xx7))) ((G Xx9) Xx0))) ((G Xx9) Xx1))) ((G Xx9) Xx2))) ((G Xx9) Xx3))) ((G Xx9) Xx4))) ((G Xx9) Xx5))) ((G Xx9) Xx6))) ((G Xx9) Xx7))) ((G Xx9) Xx8))) ((G Xx10) Xx0))) ((G Xx10) Xx1))) ((G Xx10) Xx2))) ((G Xx10) Xx3))) ((G Xx10) Xx4))) ((G Xx10) Xx5))) ((G Xx10) Xx6))) ((G Xx10) Xx7))) ((G Xx10) Xx8))) ((G Xx10) Xx9)))))))']
% Trying to prove ((ex ((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop))) (fun (G:((Prop->(Prop->(Prop->Prop)))->((Prop->(Prop->(Prop->Prop)))->Prop)))=> ((and ((and (forall (Xx:(Prop->(Prop->(Prop->Prop)))) (Xy:(Prop->(Prop->(Prop->Prop)))), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False))) (((G Xx3) Xx0)->False))) (((G Xx3) Xx1)->False))) (((G Xx3) Xx2)->False))) (((G Xx4) Xx0)->False))) (((G Xx4) Xx1)->False))) (((G Xx4) Xx2)->False))) (((G Xx4) Xx3)->False))) (((G Xx5) Xx0)->False))) (((G Xx5) Xx1)->False))) (((G Xx5) Xx2)->False))) (((G Xx5) Xx3)->False))) (((G Xx5) Xx4)->False)))))) (forall (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xx6:(Prop->(Prop->(Prop->Prop)))) (Xx7:(Prop->(Prop->(Prop->Prop)))) (Xx8:(Prop->(Prop->(Prop->Prop)))) (Xx9:(Prop->(Prop->(Prop->Prop)))) (Xx10:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp5:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp6:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp7:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp8:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp9:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp0 Xx6)->False))) ((Xp0 Xx7)->False))) ((Xp0 Xx8)->False))) ((Xp0 Xx9)->False))) ((Xp0 Xx10)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp1 Xx6)->False))) ((Xp1 Xx7)->False))) ((Xp1 Xx8)->False))) ((Xp1 Xx9)->False))) ((Xp1 Xx10)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp2 Xx6)->False))) ((Xp2 Xx7)->False))) ((Xp2 Xx8)->False))) ((Xp2 Xx9)->False))) ((Xp2 Xx10)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp3 Xx6)->False))) ((Xp3 Xx7)->False))) ((Xp3 Xx8)->False))) ((Xp3 Xx9)->False))) ((Xp3 Xx10)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))) ((Xp4 Xx6)->False))) ((Xp4 Xx7)->False))) ((Xp4 Xx8)->False))) ((Xp4 Xx9)->False))) ((Xp4 Xx10)->False))) ((Xp5 Xx0)->False))) ((Xp5 Xx1)->False))) ((Xp5 Xx2)->False))) ((Xp5 Xx3)->False))) ((Xp5 Xx4)->False))) (Xp5 Xx5))) ((Xp5 Xx6)->False))) ((Xp5 Xx7)->False))) ((Xp5 Xx8)->False))) ((Xp5 Xx9)->False))) ((Xp5 Xx10)->False))) ((Xp6 Xx0)->False))) ((Xp6 Xx1)->False))) ((Xp6 Xx2)->False))) ((Xp6 Xx3)->False))) ((Xp6 Xx4)->False))) ((Xp6 Xx5)->False))) (Xp6 Xx6))) ((Xp6 Xx7)->False))) ((Xp6 Xx8)->False))) ((Xp6 Xx9)->False))) ((Xp6 Xx10)->False))) ((Xp7 Xx0)->False))) ((Xp7 Xx1)->False))) ((Xp7 Xx2)->False))) ((Xp7 Xx3)->False))) ((Xp7 Xx4)->False))) ((Xp7 Xx5)->False))) ((Xp7 Xx6)->False))) (Xp7 Xx7))) ((Xp7 Xx8)->False))) ((Xp7 Xx9)->False))) ((Xp7 Xx10)->False))) ((Xp8 Xx0)->False))) ((Xp8 Xx1)->False))) ((Xp8 Xx2)->False))) ((Xp8 Xx3)->False))) ((Xp8 Xx4)->False))) ((Xp8 Xx5)->False))) ((Xp8 Xx6)->False))) ((Xp8 Xx7)->False))) (Xp8 Xx8))) ((Xp8 Xx9)->False))) ((Xp8 Xx10)->False))) ((Xp9 Xx0)->False))) ((Xp9 Xx1)->False))) ((Xp9 Xx2)->False))) ((Xp9 Xx3)->False))) ((Xp9 Xx4)->False))) ((Xp9 Xx5)->False))) ((Xp9 Xx6)->False))) ((Xp9 Xx7)->False))) ((Xp9 Xx8)->False))) (Xp9 Xx9))) ((Xp9 Xx10)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((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))) ((G Xx5) Xx0))) ((G Xx5) Xx1))) ((G Xx5) Xx2))) ((G Xx5) Xx3))) ((G Xx5) Xx4))) ((G Xx6) Xx0))) ((G Xx6) Xx1))) ((G Xx6) Xx2))) ((G Xx6) Xx3))) ((G Xx6) Xx4))) ((G Xx6) Xx5))) ((G Xx7) Xx0))) ((G Xx7) Xx1))) ((G Xx7) Xx2))) ((G Xx7) Xx3))) ((G Xx7) Xx4))) ((G Xx7) Xx5))) ((G Xx7) Xx6))) ((G Xx8) Xx0))) ((G Xx8) Xx1))) ((G Xx8) Xx2))) ((G Xx8) Xx3))) ((G Xx8) Xx4))) ((G Xx8) Xx5))) ((G Xx8) Xx6))) ((G Xx8) Xx7))) ((G Xx9) Xx0))) ((G Xx9) Xx1))) ((G Xx9) Xx2))) ((G Xx9) Xx3))) ((G Xx9) Xx4))) ((G Xx9) Xx5))) ((G Xx9) Xx6))) ((G Xx9) Xx7))) ((G Xx9) Xx8))) ((G Xx10) Xx0))) ((G Xx10) Xx1))) ((G Xx10) Xx2))) ((G Xx10) Xx3))) ((G Xx10) Xx4))) ((G Xx10) Xx5))) ((G Xx10) Xx6))) ((G Xx10) Xx7))) ((G Xx10) Xx8))) ((G Xx10) Xx9)))))))
% Found x0000:=(x000 x0):False
% Found (x000 x0) as proof of False
% Found ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0) as proof of False
% Found ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0) as proof of False
% Found (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)) as proof of False
% Found (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)) as proof of (((x Xx5) Xx4)->False)
% Found (or_intror00 (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))
% Found ((or_intror0 (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))
% Found (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))
% Found (fun (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))
% Found (fun (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)))
% Found (fun (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False)))=> (((or_intror ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False)) (fun (x00:((x Xx5) Xx4))=> ((((((((((x00 Xp1) Xx3) Xx1) Xp2) Xp0) Xp4) Xx2) Xx0) Xp3) x0)))) as proof of (forall (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)), (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->False))) ((Xp2 Xx0)->False))) ((Xp2 Xx1)->False))) (Xp2 Xx2))) ((Xp2 Xx3)->False))) ((Xp2 Xx4)->False))) ((Xp2 Xx5)->False))) ((Xp3 Xx0)->False))) ((Xp3 Xx1)->False))) ((Xp3 Xx2)->False))) (Xp3 Xx3))) ((Xp3 Xx4)->False))) ((Xp3 Xx5)->False))) ((Xp4 Xx0)->False))) ((Xp4 Xx1)->False))) ((Xp4 Xx2)->False))) ((Xp4 Xx3)->False))) (Xp4 Xx4))) ((Xp4 Xx5)->False))->((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (((x Xx3) Xx0)->False))) (((x Xx3) Xx1)->False))) (((x Xx3) Xx2)->False))) (((x Xx4) Xx0)->False))) (((x Xx4) Xx1)->False))) (((x Xx4) Xx2)->False))) (((x Xx4) Xx3)->False))) (((x Xx5) Xx0)->False))) (((x Xx5) Xx1)->False))) (((x Xx5) Xx2)->False))) (((x Xx5) Xx3)->False))) (((x Xx5) Xx4)->False))))
% Found (fun (Xx0:(Prop->(Prop->(Prop->Prop)))) (Xx1:(Prop->(Prop->(Prop->Prop)))) (Xx2:(Prop->(Prop->(Prop->Prop)))) (Xx3:(Prop->(Prop->(Prop->Prop)))) (Xx4:(Prop->(Prop->(Prop->Prop)))) (Xx5:(Prop->(Prop->(Prop->Prop)))) (Xp0:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp1:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp2:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp3:((Prop->(Prop->(Prop->Prop)))->Prop)) (Xp4:((Prop->(Prop->(Prop->Prop)))->Prop)) (x0:((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((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))) ((Xp0 Xx5)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))) ((Xp1 Xx3)->False))) ((Xp1 Xx4)->False))) ((Xp1 Xx5)->Fals
% EOF
%------------------------------------------------------------------------------