TSTP Solution File: SEU452^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU452^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n190.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 13:32:14 EDT 2014
% Result : Timeout 300.08s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU452^1 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.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 10:14:41 CDT 2014
% % CPUTime : 300.08
% 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 0x1649290>, <kernel.DependentProduct object at 0x14fff80>) of role type named r
% Using role type
% Declaring r:(fofType->(fofType->Prop))
% FOF formula (forall (A:fofType) (B:fofType), ((iff (forall (S:(fofType->(fofType->Prop))), (((and (forall (X:fofType) (Y:fofType), (((r X) Y)->((S X) Y)))) (forall (W:fofType) (X:fofType) (Y:fofType) (Z:fofType), (((and ((and ((S X) Y)) ((S Z) Y))) ((S Z) W))->((S X) W))))->((S A) B)))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))->((iff (P A)) (Q B)))))) of role conjecture named thm
% Conjecture to prove = (forall (A:fofType) (B:fofType), ((iff (forall (S:(fofType->(fofType->Prop))), (((and (forall (X:fofType) (Y:fofType), (((r X) Y)->((S X) Y)))) (forall (W:fofType) (X:fofType) (Y:fofType) (Z:fofType), (((and ((and ((S X) Y)) ((S Z) Y))) ((S Z) W))->((S X) W))))->((S A) B)))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))->((iff (P A)) (Q B)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (A:fofType) (B:fofType), ((iff (forall (S:(fofType->(fofType->Prop))), (((and (forall (X:fofType) (Y:fofType), (((r X) Y)->((S X) Y)))) (forall (W:fofType) (X:fofType) (Y:fofType) (Z:fofType), (((and ((and ((S X) Y)) ((S Z) Y))) ((S Z) W))->((S X) W))))->((S A) B)))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))->((iff (P A)) (Q B))))))']
% Parameter fofType:Type.
% Parameter r:(fofType->(fofType->Prop)).
% Trying to prove (forall (A:fofType) (B:fofType), ((iff (forall (S:(fofType->(fofType->Prop))), (((and (forall (X:fofType) (Y:fofType), (((r X) Y)->((S X) Y)))) (forall (W:fofType) (X:fofType) (Y:fofType) (Z:fofType), (((and ((and ((S X) Y)) ((S Z) Y))) ((S Z) W))->((S X) W))))->((S A) B)))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))->((iff (P A)) (Q B))))))
% Found x0:(forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))
% Found x0 as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))
% Found x0:(forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))
% Found x0 as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (P X)) (Q Y))))
% Found x2:((r X) Y)
% Found (fun (x2:((r X) Y))=> x2) as proof of ((r X) Y)
% Found (fun (Y:fofType) (x2:((r X) Y))=> x2) as proof of (((r X) Y)->((r X) Y))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (Y:fofType), (((r X) Y)->((r X) Y)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((r X) Y)))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found x2:((r X) Y)
% Found (fun (x2:((r X) Y))=> x2) as proof of ((r X) Y)
% Found (fun (Y:fofType) (x2:((r X) Y))=> x2) as proof of (((r X) Y)->((r X) Y))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (Y:fofType), (((r X) Y)->((r X) Y)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((r X) Y)))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->(forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found x00000:=(x0000 x1):((iff (P X)) (Q Y))
% Found (x0000 x1) as proof of ((iff (P X)) (Q Y))
% Found ((x000 Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (((x00 X) Y) x1) as proof of ((iff (P X)) (Q Y))
% Found (fun (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((iff (P X)) (Q Y))
% Found (fun (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))
% Found (fun (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))
% Found (fun (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y)))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (Y:fofType), (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found (fun (X:fofType) (Y:fofType) (x1:((r X) Y)) (P:(fofType->Prop)) (Q:(fofType->Prop)) (x00:(forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0)))))=> (((x00 X) Y) x1)) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), ((forall (X0:fofType) (Y0:fofType), (((r X0) Y0)->((iff (P X0)) (Q Y0))))->((iff (P X)) (Q Y))))))
% Found x0000:=(x000 x2):((iff (P X)) (Q Y))
% Found (x000 x2) as proof of ((iff (P X)) (Q Y))
% Found ((x00 Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (((x0 X) Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (((x0 X) Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (iff_sym10 (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found ((iff_sym1 (Q Y)) (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found (fun (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of ((iff (Q Y)) (P X))
% Found (fun (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (((r X) Y)->((iff (Q Y)) (P X)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (forall (Y:fofType), (((r X) Y)->((iff (Q Y)) (P X))))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (Q Y)) (P X))))
% Found x0000:=(x000 x2):((iff (P X)) (Q Y))
% Found (x000 x2) as proof of ((iff (P X)) (Q Y))
% Found ((x00 Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (((x0 X) Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (((x0 X) Y) x2) as proof of ((iff (P X)) (Q Y))
% Found (iff_sym20 (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found ((iff_sym2 (Q Y)) (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2)) as proof of ((iff (Q Y)) (P X))
% Found (fun (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of ((iff (Q Y)) (P X))
% Found (fun (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (((r X) Y)->((iff (Q Y)) (P X)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (forall (Y:fofType), (((r X) Y)->((iff (Q Y)) (P X))))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> (((iff_sym (P X)) (Q Y)) (((x0 X) Y) x2))) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((iff (Q Y)) (P X))))
% Found x2:((r X) Y)
% Found (fun (x2:((r X) Y))=> x2) as proof of ((r X) Y)
% Found (fun (Y:fofType) (x2:((r X) Y))=> x2) as proof of (((r X) Y)->((r X) Y))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (Y:fofType), (((r X) Y)->((r X) Y)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((r X) Y)))
% Found x2:((r X) Y)
% Found (fun (x2:((r X) Y))=> x2) as proof of ((r X) Y)
% Found (fun (Y:fofType) (x2:((r X) Y))=> x2) as proof of (((r X) Y)->((r X) Y))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (Y:fofType), (((r X) Y)->((r X) Y)))
% Found (fun (X:fofType) (Y:fofType) (x2:((r X) Y))=> x2) as proof of (forall (X:fofType) (Y:fofType), (((r X) Y)->((r X) Y)))
% Found x5:(Q W)
% Found (fun (x5:(Q W))=> x5) as proof of (Q W)
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of ((Q W)->(Q W))
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of (((and (Q Y)) (Q Y))->((Q W)->(Q W)))
% Found (and_rect00 (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found ((and_rect0 (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (fun (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (Q W)
% Found (fun (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))
% Found (fun (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W)))
% Found (fun (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))))
% Found (fun (W:fofType) (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (fofType->(forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W)))))
% Found (fun (W:fofType) (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (forall (W:fofType), (fofType->(forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))))))
% Found x5:(Q W)
% Found (fun (x5:(Q W))=> x5) as proof of (Q W)
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of ((Q W)->(Q W))
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of (((and (Q Y)) (Q Y))->((Q W)->(Q W)))
% Found (and_rect00 (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found ((and_rect0 (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (fun (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (Q W)
% Found (fun (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))
% Found (fun (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W)))
% Found (fun (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))))
% Found (fun (W:fofType) (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (fofType->(forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W)))))
% Found (fun (W:fofType) (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (forall (W:fofType), (fofType->(forall (Y:fofType), (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))))))
% Found x50:(Q W)
% Found (fun (x7:(P X))=> x50) as proof of (Q W)
% Found (fun (x7:(P X))=> x50) as proof of ((P X)->(Q W))
% Found x50:(Q W)
% Found (fun (x7:(P X))=> x50) as proof of (Q W)
% Found (fun (x7:(P X))=> x50) as proof of ((P X)->(Q W))
% Found x50:(Q W)
% Found (fun (x7:(P X))=> x50) as proof of (Q W)
% Found (fun (x7:(P X))=> x50) as proof of ((P X)->(Q W))
% Found x50:(Q W)
% Found (fun (x7:(P X))=> x50) as proof of (Q W)
% Found (fun (x7:(P X))=> x50) as proof of ((P X)->(Q W))
% Found x5:(Q W)
% Found (fun (x5:(Q W))=> x5) as proof of (Q W)
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of ((Q W)->(Q W))
% Found (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5) as proof of (((and (Q Y)) (Q Y))->((Q W)->(Q W)))
% Found (and_rect00 (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found ((and_rect0 (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5)) as proof of (Q W)
% Found (fun (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (Q W)
% Found (fun (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (((and ((and (Q Y)) (Q Y))) (Q W))->(Q W))
% Found (fun (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((and (Q Y)) (Q Y))) (Q W)) P0) x4) x3)) (Q W)) (fun (x4:((and (Q Y)) (Q Y))) (x5:(Q W))=> x5))) as proof of (fofType->(((and ((and (Q Y)) (Q Y))) (Q W))->(Q W)))
% Found (fun (X:fofType) (Y:fofType) (Z:fofType) (x3:((and ((and (Q Y)) (Q Y))) (Q W)))=> (((fun (P0:Type) (x4:(((and (Q Y)) (Q Y))->((Q W)->P0)))=> (((((and_rect ((a
% EOF
%------------------------------------------------------------------------------