%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV045^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n110.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 13:33:39 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV045^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n110.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 07:42:41 CDT 2014
% % CPUTime  : 300.03 
% 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 0x12739e0>, <kernel.Type object at 0x1273d88>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0xf5fc20>, <kernel.Type object at 0x1273710>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1273560>, <kernel.DependentProduct object at 0x1273a70>) of role type named g
% Using role type
% Declaring g:(a->b)
% FOF formula (<kernel.Constant object at 0x1273d88>, <kernel.DependentProduct object at 0x1273d40>) of role type named f
% Using role type
% Declaring f:(a->b)
% FOF formula (<kernel.Constant object at 0x12739e0>, <kernel.DependentProduct object at 0x1273200>) of role type named cQ
% Using role type
% Declaring cQ:(a->(b->(b->Prop)))
% FOF formula (<kernel.Constant object at 0x1273a70>, <kernel.DependentProduct object at 0x1273cb0>) of role type named cP
% Using role type
% Declaring cP:(a->(a->Prop))
% FOF formula ((forall (Xx:a), (((cP Xx) Xx)->(((cQ Xx) (f Xx)) (g Xx))))->((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (f Xy))))->(((and (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))->(((and (forall (Xx:a), (((cP Xx) Xx)->((and (forall (Xx0:b) (Xy:b), ((((cQ Xx) Xx0) Xy)->(((cQ Xx) Xy) Xx0)))) (forall (Xx0:b) (Xy:b) (Xz:b), (((and (((cQ Xx) Xx0) Xy)) (((cQ Xx) Xy) Xz))->(((cQ Xx) Xx0) Xz))))))) (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((eq (b->(b->Prop))) (cQ Xx)) (cQ Xy)))))->(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (g Xy)))))))) of role conjecture named cTHM509_pme
% Conjecture to prove = ((forall (Xx:a), (((cP Xx) Xx)->(((cQ Xx) (f Xx)) (g Xx))))->((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (f Xy))))->(((and (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))->(((and (forall (Xx:a), (((cP Xx) Xx)->((and (forall (Xx0:b) (Xy:b), ((((cQ Xx) Xx0) Xy)->(((cQ Xx) Xy) Xx0)))) (forall (Xx0:b) (Xy:b) (Xz:b), (((and (((cQ Xx) Xx0) Xy)) (((cQ Xx) Xy) Xz))->(((cQ Xx) Xx0) Xz))))))) (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((eq (b->(b->Prop))) (cQ Xx)) (cQ Xy)))))->(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (g Xy)))))))):Prop
% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
% We need to prove ['((forall (Xx:a), (((cP Xx) Xx)->(((cQ Xx) (f Xx)) (g Xx))))->((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (f Xy))))->(((and (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))->(((and (forall (Xx:a), (((cP Xx) Xx)->((and (forall (Xx0:b) (Xy:b), ((((cQ Xx) Xx0) Xy)->(((cQ Xx) Xy) Xx0)))) (forall (Xx0:b) (Xy:b) (Xz:b), (((and (((cQ Xx) Xx0) Xy)) (((cQ Xx) Xy) Xz))->(((cQ Xx) Xx0) Xz))))))) (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((eq (b->(b->Prop))) (cQ Xx)) (cQ Xy)))))->(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (g Xy))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter g:(a->b).
% Parameter f:(a->b).
% Parameter cQ:(a->(b->(b->Prop))).
% Parameter cP:(a->(a->Prop)).
% Trying to prove ((forall (Xx:a), (((cP Xx) Xx)->(((cQ Xx) (f Xx)) (g Xx))))->((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (f Xy))))->(((and (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))->(((and (forall (Xx:a), (((cP Xx) Xx)->((and (forall (Xx0:b) (Xy:b), ((((cQ Xx) Xx0) Xy)->(((cQ Xx) Xy) Xx0)))) (forall (Xx0:b) (Xy:b) (Xz:b), (((and (((cQ Xx) Xx0) Xy)) (((cQ Xx) Xy) Xz))->(((cQ Xx) Xx0) Xz))))))) (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((eq (b->(b->Prop))) (cQ Xx)) (cQ Xy)))))->(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->(((cQ Xx) (f Xx)) (g Xy))))))))
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found (fun (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of (P b0)
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P b0))
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P b0)))
% Found (and_rect00 (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P b0)
% Found ((and_rect0 (P b0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P b0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P b0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found (fun (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of (P (g a0))
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P (g a0)))
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P (g a0))))
% Found (and_rect00 (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found ((and_rect0 (P (g a0))) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P (g a0))) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P (g a0))) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P b0)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found ((and_rect1 (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P (g a0))
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (g a0))
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P (g a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P (g a0)))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P (g a0))))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found ((and_rect1 (P (g a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P (g a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P (g a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (g a0))
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xx:a;b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0))
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0)))
% Found (and_rect00 (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect0 (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x6 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0))
% Found (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0)))
% Found (and_rect00 (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect0 (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x4) x1)) (P a0)) (fun (x4:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x5:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))))) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((cP Xx) Xy0)
% Found x4000:=(x400 x3):((cP Xy0) Xx)
% Found (x400 x3) as proof of ((cP Xy0) Xx)
% Found ((x40 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x4 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x5000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x4 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x500 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x50 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x5 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x4 Xx) Xy) x3)))) as proof of (P a0)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x6000:=(x600 x3):((cP Xy0) Xx)
% Found (x600 x3) as proof of ((cP Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((cP Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (((conj0 ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((cP Xx) Xy0)) ((cP Xy0) Xx))
% Found (x7000 ((((conj ((cP Xx) Xy0)) ((cP Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((cP Xx) Xx)
% Found ((x700 Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((cP Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P0) x6) x1)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((cP Xx) Xy)) ((cP Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a;Xx00:=Xx:a
% Found x3 as proof of ((cP Xx00) Xx0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq b) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found ((eq_ref b) (g a0)) as proof of (((eq b) (g a0)) b0)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x400 x3) as proof of ((cP Xx0) Xx)
% Found ((x40 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x4 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found x3:((cP Xx) Xy)
% Instantiate: Xx0:=Xy:a
% Found x3 as proof of ((cP Xx) Xx0)
% Found (x600 x3) as proof of ((cP Xx0) Xx)
% Found ((x60 Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (((x6 Xx) Xx0) x3) as proof of ((cP Xx0) Xx)
% Found (fun (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((cP Xx0) Xx)
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx))
% Found (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3)) as proof of ((forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))->((forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz)))->((cP Xx0) Xx)))
% Found (and_rect10 (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found ((and_rect1 ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((cP Xx) Xy)->((cP Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((cP Xx) Xy)) ((cP Xy) Xz))->((cP Xx) Xz)))) P1) x6) x1)) ((cP Xx0) Xx)) (fun (x6:(forall (Xx1:a) (Xy:a), (((cP Xx1) Xy)->((cP Xy) Xx1)))) (x7:(forall (Xx1:a) (Xy:a) (Xz:a), (((and ((cP Xx1) Xy)) ((cP Xy) Xz))->((cP Xx1) Xz))))=> (((x6 Xx) Xx0) x3))) as proof of ((cP Xx0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (g a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (g a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 (g Xy)):(((eq b) (g Xy)) (g Xy))
% Found (eq_ref0 (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found ((eq_ref b) (g Xy)) as proof of (((eq b) (g Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of 
% EOF
%------------------------------------------------------------------------------