TSTP Solution File: SEV153^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV153^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n091.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 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV153^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n091.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 08:14:31 CDT 2014
% % CPUTime : 300.10
% 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 0x1bf5830>, <kernel.Type object at 0x1bf5d40>) 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), ((or (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)))) ((and ((and ((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)))->False)) (forall (Xx0:a) (Xy0:a), (((or (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((R Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((R Xu) Xv))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((S Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((S Xu) Xv))->(Xq Xv))))->(Xq Xy0))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0))))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xy0) Xw)) ((S Xy0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz)))))))) of role conjecture named cTHM251H_pme
% Conjecture to prove = (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((or (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)))) ((and ((and ((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)))->False)) (forall (Xx0:a) (Xy0:a), (((or (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((R Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((R Xu) Xv))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((S Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((S Xu) Xv))->(Xq Xv))))->(Xq Xy0))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0))))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xy0) Xw)) ((S Xy0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz)))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((or (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)))) ((and ((and ((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)))->False)) (forall (Xx0:a) (Xy0:a), (((or (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((R Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((R Xu) Xv))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((S Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((S Xu) Xv))->(Xq Xv))))->(Xq Xy0))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0))))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xy0) Xw)) ((S Xy0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))))))']
% Parameter a:Type.
% Trying to prove (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((or (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)))) ((and ((and ((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)))->False)) (forall (Xx0:a) (Xy0:a), (((or (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((R Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((R Xu) Xv))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((S Xx0) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((S Xu) Xv))->(Xq Xv))))->(Xq Xy0))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0))))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xy0)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xy0) Xw)) ((S Xy0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((R Xx0) Xw)) ((S Xx0) Xw))->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))->(Xq Xz))))))))
% Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4:(Xq Xz)
% Found (fun (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (Xq Xz)
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect10 (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (fun (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x4:(Xq Xz)
% Found (fun (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (Xq Xz)
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect10 (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (fun (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x2:False
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of False
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->False)
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (False->(((or ((R Xu) Xv)) ((S Xu) Xv))->False))
% Found (and_rect00 (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (fun (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of False
% Found (fun (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False)
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found x2:False
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of False
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->False)
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (False->(((or ((R Xu) Xv)) ((S Xu) Xv))->False))
% Found (and_rect00 (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (fun (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of False
% Found (fun (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False)
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found x4:(Xq Xz)
% Found (fun (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (Xq Xz)
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect10 (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (fun (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x4:(Xq Xz)
% Found (fun (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (Xq Xz)
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect10 (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4)) as proof of (Xq Xz)
% Found (fun (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x4:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x4))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x2:False
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of False
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->False)
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (False->(((or ((R Xu) Xv)) ((S Xu) Xv))->False))
% Found (and_rect00 (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (fun (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of False
% Found (fun (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False)
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:False
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of False
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->False)
% Found (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (False->(((or ((R Xu) Xv)) ((S Xu) Xv))->False))
% Found (and_rect00 (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of False
% Found (fun (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of False
% Found (fun (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False)
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found (fun (Xu:a) (Xv:a) (x1:((and False) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:(False->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect False) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) False) (fun (x2:False) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and False) ((or ((R Xu) Xv)) ((S Xu) Xv)))->False))
% Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x6:(Xq Xz)
% Found (fun (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (Xq Xz)
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (fun (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x6:(Xq Xz)
% Found (fun (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (Xq Xz)
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (fun (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (Xq Xz)
% Found (fun (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz))
% Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xz)))
% Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x6:(Xq Xz)
% Found (fun (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (Xq Xz)
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz))
% Found (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6) as proof of ((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xz)))
% Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x6)) as proof of (Xq Xz)
% Found (fun (x5:((and (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x6:((Xq Xz)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xz)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((or ((R Xu) Xv)) ((S Xu) Xv)
% EOF
%------------------------------------------------------------------------------