TSTP Solution File: SEV149^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV149^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n180.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 13:33:48 EDT 2014
% Result : Timeout 300.01s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV149^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n180.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 08:13:56 CDT 2014
% % CPUTime : 300.01
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1b48c20>, <kernel.Type object at 0x1b48e60>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy)))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((R Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((R Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((S Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((S Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw))))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((R Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((R Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((S Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((S Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))))->(Xq Xv))))->(Xq Xy))))) of role conjecture named cTHM251B_pme
% Conjecture to prove = (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy)))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((R Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((R Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((S Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((S Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw))))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((R Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((R Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((S Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((S Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))))->(Xq Xv))))->(Xq Xy))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy)))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((R Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((R Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((S Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((S Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw))))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((R Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((R Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((S Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((S Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))))->(Xq Xv))))->(Xq Xy)))))']
% Parameter a:Type.
% Trying to prove (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy)))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((R Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((R Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw0:a), (((S Xx) Xw0)->(Xq0 Xw0)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((S Xu) Xv))->(Xq0 Xv))))->(Xq0 Xw))))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((R Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((R Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((S Xu) Xw)->(Xq0 Xw)))) (forall (Xu0:a) (Xv0:a), (((and (Xq0 Xu0)) ((S Xu0) Xv0))->(Xq0 Xv0))))->(Xq0 Xv)))))->(Xq Xv))))->(Xq Xy)))))
% Found x40:=(x4 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x400:=(x40 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x400:=(x40 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x40:=(x4 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x40:=(x4 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found x60:=(x6 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x60:=(x6 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x400:=(x40 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x400:=(x40 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x40 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x7:((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of ((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x7:((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of ((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x6:((S Xx) Xw)
% Found (fun (x6:((S Xx) Xw))=> x6) as proof of ((S Xx) Xw)
% Found (fun (x6:((S Xx) Xw))=> x6) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x6:((R Xx) Xw)
% Found (fun (x6:((R Xx) Xw))=> x6) as proof of ((R Xx) Xw)
% Found (fun (x6:((R Xx) Xw))=> x6) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x40:=(x4 x20):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x4 x20) as proof of (Xq Xu0)
% Found (x4 x20) as proof of (Xq Xu0)
% Found x60:=(x6 Xw):(((S Xx) Xw)->(Xq00 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found x60:=(x6 Xw):(((R Xx) Xw)->(Xq00 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found x40:=(x4 x20):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x4 x20) as proof of (Xq Xu0)
% Found (x4 x20) as proof of (Xq Xu0)
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x5:(Xq Xu)
% Found (fun (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5) as proof of (Xq Xu)
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5) as proof of (((or ((R Xu0) Xv)) ((S Xu0) Xv))->(Xq Xu))
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5) as proof of ((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->(Xq Xu)))
% Found (and_rect10 (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5)) as proof of (Xq Xu)
% Found ((and_rect1 (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5)) as proof of (Xq Xu)
% Found (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))) P) x5) x4)) (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5)) as proof of (Xq Xu)
% Found (fun (x4:((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))))=> (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))) P) x5) x4)) (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5))) as proof of (Xq Xu)
% Found (fun (Xv:a) (x4:((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))))=> (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))) P) x5) x4)) (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5))) as proof of (((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv)))->(Xq Xu))
% Found (fun (Xu0:a) (Xv:a) (x4:((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))))=> (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))) P) x5) x4)) (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv)))->(Xq Xu)))
% Found (fun (Xu0:a) (Xv:a) (x4:((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))))=> (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu0) Xv)) ((S Xu0) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv))) P) x5) x4)) (Xq Xu)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu0) Xv)) ((S Xu0) Xv)))=> x5))) as proof of (forall (Xu0:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu0) Xv)) ((S Xu0) Xv)))->(Xq Xu)))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (fun (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of (Xq Xu0)
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0))
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0)))
% Found (and_rect10 (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found ((and_rect1 (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x5) x4)) (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x5) x4)) (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found x60:=(x6 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x60:=(x6 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x60:=(x6 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x60:=(x6 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (fun (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of (Xq Xu0)
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0))
% Found (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0)))
% Found (and_rect10 (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found ((and_rect1 (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x5) x4)) (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x5:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x5) x4)) (Xq Xu0)) (fun (x5:(Xq Xu)) (x6:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x5)) as proof of (Xq Xu0)
% Found x60:=(x6 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x60:=(x6 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x6 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x300:=(x30 x20):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x30 x20) as proof of (Xq Xu0)
% Found ((x3 x10) x20) as proof of (Xq Xu0)
% Found ((x3 x10) x20) as proof of (Xq Xu0)
% Found x50:=(x5 Xw):(((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x50:=(x5 Xw):(((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found (x5 Xw) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x7:((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of ((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x7:((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of ((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x3:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x3 as proof of (Xq Xu0)
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x7:(Xq Xu)
% Found x7 as proof of (Xq Xu)
% Found x300:=(x30 x20):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x30 x20) as proof of (Xq Xu0)
% Found ((x3 x10) x20) as proof of (Xq Xu0)
% Found ((x3 x10) x20) as proof of (Xq Xu0)
% Found x40:=(x4 Xw):(((R Xx) Xw)->(Xq00 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found (x4 Xw) as proof of (((R Xx) Xw)->(Xq00 Xw))
% Found x40:=(x4 Xw):(((S Xx) Xw)->(Xq00 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found (x4 Xw) as proof of (((S Xx) Xw)->(Xq00 Xw))
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x7:((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of ((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x7:((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of ((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x5:(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found x5 as proof of (Xq Xu0)
% Found x7:((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of ((S Xx) Xw)
% Found (fun (x7:((S Xx) Xw))=> x7) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x7:((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of ((R Xx) Xw)
% Found (fun (x7:((R Xx) Xw))=> x7) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of ((R Xx) Xw)
% Found (fun (x8:((R Xx) Xw))=> x8) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x8:((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of ((S Xx) Xw)
% Found (fun (x8:((S Xx) Xw))=> x8) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x20:=(x2 x00):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x2 x00) as proof of (Xq Xu0)
% Found (x2 x00) as proof of (Xq Xu0)
% Found x40:=(x4 x00):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x4 x00) as proof of (Xq Xu0)
% Found (x4 x00) as proof of (Xq Xu0)
% Found x6:((S Xx) Xw)
% Found (fun (x6:((S Xx) Xw))=> x6) as proof of ((S Xx) Xw)
% Found (fun (x6:((S Xx) Xw))=> x6) as proof of (((S Xx) Xw)->((S Xx) Xw))
% Found x6:((R Xx) Xw)
% Found (fun (x6:((R Xx) Xw))=> x6) as proof of ((R Xx) Xw)
% Found (fun (x6:((R Xx) Xw))=> x6) as proof of (((R Xx) Xw)->((R Xx) Xw))
% Found x40:=(x4 x20):(Xq Xu)
% Instantiate: Xu0:=Xu:a
% Found (x4 x20) as proof of (Xq Xu0)
% Found (fun (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20)) as proof of (Xq Xu0)
% Found (fun (x4:((forall (Xu00:a) (Xv:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((R Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((S Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20)) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0))
% Found (fun (x4:((forall (Xu00:a) (Xv:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((R Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((S Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20)) as proof of (((forall (Xu00:a) (Xv:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((R Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((S Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xu0)))
% Found (and_rect10 (fun (x4:((forall (Xu00:a) (Xv:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((R Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((S Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20))) as proof of (Xq Xu0)
% Found ((and_rect1 (Xq Xu0)) (fun (x4:((forall (Xu00:a) (Xv:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((R Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv0:a), (((and (Xq00 Xu000)) ((S Xu000) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20))) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x4:(((forall (Xu0:a) (Xv:a), (((and (Xq Xu0)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv0:a), (((and (Xq00 Xu00)) ((R Xu00) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv0:a), (((and (Xq00 Xu00)) ((S Xu00) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect ((forall (Xu0:a) (Xv0:a), (((and (Xq Xu0)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv00:a), (((and (Xq00 Xu00)) ((R Xu00) Xv00))->(Xq00 Xv00))))->(Xq00 Xv0)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv00:a), (((and (Xq00 Xu00)) ((S Xu00) Xv00))->(Xq00 Xv00))))->(Xq00 Xv0)))))->(Xq Xv0)))->(Xq Xu))) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xu0)) (fun (x4:((forall (Xu00:a) (Xv0:a), (((and (Xq Xu00)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv00:a), (((and (Xq00 Xu000)) ((R Xu000) Xv00))->(Xq00 Xv00))))->(Xq00 Xv0)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu00) Xw)->(Xq00 Xw)))) (forall (Xu000:a) (Xv00:a), (((and (Xq00 Xu000)) ((S Xu000) Xv00))->(Xq00 Xv00))))->(Xq00 Xv0)))))->(Xq Xv0)))->(Xq Xu))) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> (x4 x20))) as proof of (Xq Xu0)
% Found (((fun (P:Type) (x4:(((forall (Xu0:a) (Xv:a), (((and (Xq Xu0)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv0:a), (((and (Xq00 Xu00)) ((R Xu00) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv0:a), (((and (Xq00 Xu00)) ((S Xu00) Xv0))->(Xq00 Xv0))))->(Xq00 Xv)))))->(Xq Xv)))->(Xq Xu))->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect ((forall (Xu0:a) (Xv0:a), (((and (Xq Xu0)) ((or (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((R Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv00:a), (((and (Xq00 Xu00)) ((R Xu00) Xv00))->(Xq00 Xv00))))->(Xq00 Xv0)))) (forall (Xq00:(a->Prop)), (((and (forall (Xw:a), (((S Xu0) Xw)->(Xq00 Xw)))) (forall (Xu00:a) (Xv00:a),
% EOF
%------------------------------------------------------------------------------