TSTP Solution File: SEV154^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV154^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n189.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 : SEV154^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.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 08:14:46 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 0x18a8fc8>, <kernel.Type object at 0x18a87a0>) 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 (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))))))->(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))) of role conjecture named cTHM251G_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 (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))))))->(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))):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 (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))))))->(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)))']
% 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 (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))))))->(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)))
% Found x2:(Xq Xu)
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (Xq Xv)
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (fun (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(Xq Xu)
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (Xq Xv)
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (fun (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(Xq Xu)
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (Xq Xv)
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (fun (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(Xq Xu)
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (Xq Xv)
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (fun (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x3:(Xq Xu)
% Found (fun (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (Xq Xv)
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (fun (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x3:(Xq Xu)
% Found (fun (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (Xq Xv)
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (fun (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x3:(Xq Xu)
% Found (fun (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (Xq Xv)
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3)) as proof of (Xq Xv)
% Found (fun (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x2:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x3:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x3) x2)) (Xq Xv)) (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x2:(Xq Xu)
% Found (fun (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (Xq Xv)
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found ((and_rect0 (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2)) as proof of (Xq Xv)
% Found (fun (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (Xq Xv)
% Found (fun (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found (fun (Xu:a) (Xv:a) (x1:((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))))=> (((fun (P:Type) (x2:((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->P)))=> (((((and_rect (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv))) P) x2) x1)) (Xq Xv)) (fun (x2:(Xq Xu)) (x3:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x2))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x3:(Xq Xu)
% Found (fun (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (Xq Xv)
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of (((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv))
% Found (fun (x3:(Xq Xu)) (x4:((or ((R Xu) Xv)) ((S Xu) Xv)))=> x3) as proof of ((Xq Xu)->(((or ((R Xu) Xv)) ((S Xu) Xv))->(Xq Xv)))
% Found (and_rect00 (fun (x3:(
% EOF
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