TSTP Solution File: SEV156^5 by cocATP---0.2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV156^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n102.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  : SEV156^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n102.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 08:15:16 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 0x1e448c0>, <kernel.Type object at 0x1e44d88>) 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 ((and ((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)) (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)))))))) of role conjecture named cTHM250H_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 ((and ((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)) (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)))))))):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 ((and ((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)) (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))))))))']
% 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 ((and ((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)) (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))))))))
% Found x5:((Xp1 Xx0) Xz0)
% Found (fun (x5:((Xp1 Xx0) Xz0))=> x5) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0))
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0)))
% Found (and_rect10 (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found ((and_rect1 ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (a->(forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))))
% Found x4:((Xp1 Xx1) Xz)
% Found (fun (x5:((Xp1 Xy1) Xz))=> x4) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz))
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz)))
% Found (and_rect10 (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found ((and_rect1 ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of ((Xp1 Xx1) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xx1:a) (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found x5:((Xp1 Xx0) Xz0)
% Found (fun (x5:((Xp1 Xx0) Xz0))=> x5) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0))
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0)))
% Found (and_rect10 (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found ((and_rect1 ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (a->(forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))))
% Found x4:((Xp1 Xx1) Xz)
% Found (fun (x5:((Xp1 Xy1) Xz))=> x4) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz))
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz)))
% Found (and_rect10 (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found ((and_rect1 ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of ((Xp1 Xx1) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xx1:a) (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found x3:False
% Found (fun (x3:False)=> x3) as proof of False
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->False)
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->(False->False))
% Found (and_rect00 (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (fun (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of False
% Found (fun (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (((and False) False)->False)
% Found (fun (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(((and False) False)->False))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(((and False) False)->False)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(a->(((and False) False)->False))))
% Found x3:False
% Found (fun (x3:False)=> x3) as proof of False
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->False)
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->(False->False))
% Found (and_rect00 (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (fun (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of False
% Found (fun (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (((and False) False)->False)
% Found (fun (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(((and False) False)->False))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(((and False) False)->False)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(a->(((and False) False)->False))))
% Found x4:((Xp1 Xx1) Xz)
% Found (fun (x5:((Xp1 Xy1) Xz))=> x4) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz))
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz)))
% Found (and_rect10 (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found ((and_rect1 ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of ((Xp1 Xx1) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xx1:a) (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found x5:((Xp1 Xx0) Xz0)
% Found (fun (x5:((Xp1 Xx0) Xz0))=> x5) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0))
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0)))
% Found (and_rect10 (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found ((and_rect1 ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (a->(forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))))
% Found x4:((Xp1 Xx1) Xz)
% Found (fun (x5:((Xp1 Xy1) Xz))=> x4) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz))
% Found (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4) as proof of (((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->((Xp1 Xx1) Xz)))
% Found (and_rect10 (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found ((and_rect1 ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4)) as proof of ((Xp1 Xx1) Xz)
% Found (fun (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of ((Xp1 Xx1) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)))=> (((fun (P:Type) (x4:(((Xp1 Xx1) Xz)->(((Xp1 Xy1) Xz)->P)))=> (((((and_rect ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz)) P) x4) x3)) ((Xp1 Xx1) Xz)) (fun (x4:((Xp1 Xx1) Xz)) (x5:((Xp1 Xy1) Xz))=> x4))) as proof of (forall (Xx1:a) (Xy1:a), (a->(((and ((Xp1 Xx1) Xz)) ((Xp1 Xy1) Xz))->((Xp1 Xx1) Xz))))
% Found x5:((Xp1 Xx0) Xz0)
% Found (fun (x5:((Xp1 Xx0) Xz0))=> x5) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0))
% Found (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5) as proof of (((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->((Xp1 Xx0) Xz0)))
% Found (and_rect10 (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found ((and_rect1 ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5)) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of ((Xp1 Xx0) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))
% Found (fun (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy1:a) (Xz0:a) (x3:((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)))=> (((fun (P:Type) (x4:(((Xp1 Xx0) Xy1)->(((Xp1 Xx0) Xz0)->P)))=> (((((and_rect ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0)) P) x4) x3)) ((Xp1 Xx0) Xz0)) (fun (x4:((Xp1 Xx0) Xy1)) (x5:((Xp1 Xx0) Xz0))=> x5))) as proof of (a->(forall (Xy1:a) (Xz0:a), (((and ((Xp1 Xx0) Xy1)) ((Xp1 Xx0) Xz0))->((Xp1 Xx0) Xz0))))
% Found x3:False
% Found (fun (x3:False)=> x3) as proof of False
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->False)
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->(False->False))
% Found (and_rect00 (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found ((and_rect0 False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3)) as proof of False
% Found (fun (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of False
% Found (fun (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (((and False) False)->False)
% Found (fun (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(((and False) False)->False))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(((and False) False)->False)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x1:((and False) False))=> (((fun (P:Type) (x2:(False->(False->P)))=> (((((and_rect False) False) P) x2) x1)) False) (fun (x2:False) (x3:False)=> x3))) as proof of (a->(a->(a->(((and False) False)->False))))
% Found x3:False
% Found (fun (x3:False)=> x3) as proof of False
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->False)
% Found (fun (x2:False) (x3:False)=> x3) as proof of (False->(False->False))
% Fou
% EOF
%------------------------------------------------------------------------------