TSTP Solution File: SEV157^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV157^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n179.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 300.05s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV157^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 08:15:26 CDT 2014
% % CPUTime : 300.05
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1272ab8>, <kernel.Type object at 0x1272ef0>) 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 (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy)))) ((((and (forall (Xx0:a) (Xy0:a), (((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((R Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((S Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xy0) Xz))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xz))))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy))))->False))) of role conjecture named cTHM250G_pme
% Conjecture to prove = (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy)))) ((((and (forall (Xx0:a) (Xy0:a), (((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((R Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((S Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xy0) Xz))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xz))))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) 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 (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy)))) ((((and (forall (Xx0:a) (Xy0:a), (((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((R Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((S Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xy0) Xz))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xz))))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy))))->False)))']
% Parameter a:Type.
% Trying to prove (forall (R:(a->(a->Prop))) (S:(a->(a->Prop))) (Xx:a) (Xy:a), ((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy)))) ((((and (forall (Xx0:a) (Xy0:a), (((or (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((R Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((S Xx1) Xy1)->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))->((Xp1 Xx0) Xy0)))))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xy0)))) (forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xy0) Xz))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx1:a) (Xy1:a), (((or ((R Xx1) Xy1)) ((S Xx1) Xy1))->((Xp1 Xx1) Xy1)))) (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xp1 Xx1) Xy1)) ((Xp1 Xy1) Xz0))->((Xp1 Xx1) Xz0))))->((Xp1 Xx0) Xz))))))->(forall (Xp1:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((or ((R Xx0) Xy0)) ((S Xx0) Xy0))->((Xp1 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))))->((Xp1 Xx) Xy))))->False)))
% Found x3:((Xp1 Xy0) Xz)
% Found (fun (x3:((Xp1 Xy0) Xz))=> x3) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz))
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz)))
% Found (and_rect00 (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found ((and_rect0 ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of ((Xp1 Xx0) Xz)
% Found (fun (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))
% Found (fun (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found x3:((Xp1 Xy0) Xz)
% Found (fun (x3:((Xp1 Xy0) Xz))=> x3) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz))
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz)))
% Found (and_rect00 (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found ((and_rect0 ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of ((Xp1 Xx0) Xz)
% Found (fun (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))
% Found (fun (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found x3:((Xp1 Xy0) Xz)
% Found (fun (x3:((Xp1 Xy0) Xz))=> x3) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz))
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz)))
% Found (and_rect00 (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found ((and_rect0 ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of ((Xp1 Xx0) Xz)
% Found (fun (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz))
% Found (fun (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz))->((Xp1 Xx0) Xz)))
% Found x3:((Xp1 Xy0) Xz)
% Found (fun (x3:((Xp1 Xy0) Xz))=> x3) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz))
% Found (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3) as proof of (((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->((Xp1 Xx0) Xz)))
% Found (and_rect00 (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found ((and_rect0 ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (((fun (P:Type) (x2:(((Xp1 Xx0) Xy0)->(((Xp1 Xy0) Xz)->P)))=> (((((and_rect ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)) P) x2) x1)) ((Xp1 Xx0) Xz)) (fun (x2:((Xp1 Xx0) Xy0)) (x3:((Xp1 Xy0) Xz))=> x3)) as proof of ((Xp1 Xx0) Xz)
% Found (fun (x1:((and ((Xp1 Xx0) Xy0)) ((Xp1 Xy0) Xz)))=> (((fun (P:Type) (x2:(((Xp1 Xx0) Xy
% EOF
%------------------------------------------------------------------------------