TSTP Solution File: SEV152^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV152^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n098.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 300.04s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV152^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.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 08:14:21 CDT 2014
% % CPUTime : 300.04
% 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 0x145f5f0>, <kernel.Type object at 0x145fe18>) 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), ((((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))))->(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))))) of role conjecture named cTHM251D_pme
% Conjecture to prove = (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((((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))))->(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))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((((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))))->(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)))))']
% Parameter a:Type.
% Trying to prove (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((((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))))->(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)))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x1:((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))))
% Found x1 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x4:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (Xq0 Xw)
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x100:=(x10 x0):(Xq Xy)
% Found (x10 x0) as proof of (Xq Xy)
% Found ((x1 Xq) x0) as proof of (Xq Xy)
% Found (fun (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0)) as proof of (Xq Xy)
% Found (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0)) as proof of ((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))->(Xq Xy))
% Found (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0)) as proof of ((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)))
% Found (and_rect00 (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0))) as proof of (Xq Xy)
% Found ((and_rect0 (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0))) as proof of (Xq Xy)
% Found (((fun (P:Type) (x2:((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)))->P)))=> (((((and_rect (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)))) P) x2) x0)) (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0))) as proof of (Xq Xy)
% Found (((fun (P:Type) (x2:((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)))->P)))=> (((((and_rect (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)))) P) x2) x0)) (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x1 Xq) x0))) as proof of (Xq Xy)
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x000:=(x00 x1):(Xq Xy)
% Found (x00 x1) as proof of (Xq Xy)
% Found ((x0 Xq) x1) as proof of (Xq Xy)
% Found (fun (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1)) as proof of (Xq Xy)
% Found (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1)) as proof of ((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))->(Xq Xy))
% Found (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1)) as proof of ((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)))
% Found (and_rect00 (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1))) as proof of (Xq Xy)
% Found ((and_rect0 (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1))) as proof of (Xq Xy)
% Found (((fun (P:Type) (x2:((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)))->P)))=> (((((and_rect (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)))) P) x2) x1)) (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1))) as proof of (Xq Xy)
% Found (fun (x1:((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)))))=> (((fun (P:Type) (x2:((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)))->P)))=> (((((and_rect (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)))) P) x2) x1)) (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1)))) as proof of (Xq Xy)
% Found (fun (x1:((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)))))=> (((fun (P:Type) (x2:((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)))->P)))=> (((((and_rect (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)))) P) x2) x1)) (Xq Xy)) (fun (x2:(forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq Xw)))) (x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv))))=> ((x0 Xq) x1)))) as proof of (((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))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x4:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of ((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw)))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw))))
% Found x4:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of ((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw)))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw))))
% Found x4:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of ((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw)))
% Found (fun (Xw:a) (x4:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x4) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((R Xx) Xw)) ((S Xx) Xw))))
% Found x5:((S Xx) Xw)
% Found (fun (x5:((S Xx) Xw))=> x5) as proof of (Xq0 Xw)
% Found (fun (x5:((S Xx) Xw))=> x5) as proof of (((S Xx) Xw)->(Xq0 Xw))
% Found x5:((R Xx) Xw)
% Found (fun (x5:((R Xx) Xw))=> x5) as proof of (Xq0 Xw)
% Found (fun (x5:((R Xx) Xw))=> x5) as proof of (((R Xx) Xw)->(Xq0 Xw))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x5:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (Xq0 Xw)
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw))))
% Found x5:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (Xq0 Xw)
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x0:((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))))
% Found x0 as proof of ((and (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq0 Xv))))
% Found x3:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((or ((R Xu) Xv)) ((S Xu) Xv)))->(Xq Xv)))
% Found x3 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 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 or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw))))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found x5:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (Xq0 Xw)
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw))))
% Found x5:((or ((R Xx) Xw)) ((S Xx) Xw))
% Found (fun (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (Xq0 Xw)
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw))
% Found (fun (Xw:a) (x5:((or ((R Xx) Xw)) ((S Xx) Xw)))=> x5) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 Xw)))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (fun (Xw:a)=> ((or_comm_i ((R Xx) Xw)) ((S Xx) Xw))) as proof of (forall (Xw:a), (((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw))))
% Found or_comm_i10:=(or_comm_i1 ((S Xx) Xw)):(((or ((R Xx) Xw)) ((S Xx) Xw))->((or ((S Xx) Xw)) ((R Xx) Xw)))
% Found (or_comm_i1 ((S Xx) Xw)) as proof of (((or ((R Xx) Xw)) ((S Xx) Xw))->(Xq0 X
% EOF
%------------------------------------------------------------------------------