TSTP Solution File: PUZ104^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ104^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n093.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 13:28:59 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 : PUZ104^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:19:21 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 0xed7518>, <kernel.Constant object at 0xed7cb0>) of role type named c1_type
% Using role type
% Declaring c1:fofType
% FOF formula (<kernel.Constant object at 0x10b54d0>, <kernel.DependentProduct object at 0xed74d0>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xed7830>, <kernel.DependentProduct object at 0xed7b48>) of role type named cCKB6_NUM_type
% Using role type
% Declaring cCKB6_NUM:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) cCKB6_NUM) (fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx))))) of role definition named cCKB6_NUM_def
% A new definition: (((eq (fofType->Prop)) cCKB6_NUM) (fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx)))))
% Defined: cCKB6_NUM:=(fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx))))
% FOF formula (forall (Xx:fofType), ((cCKB6_NUM Xx)->(cCKB6_NUM (s (s Xx))))) of role conjecture named cCKB6_L4000
% Conjecture to prove = (forall (Xx:fofType), ((cCKB6_NUM Xx)->(cCKB6_NUM (s (s Xx))))):Prop
% We need to prove ['(forall (Xx:fofType), ((cCKB6_NUM Xx)->(cCKB6_NUM (s (s Xx)))))']
% Parameter fofType:Type.
% Parameter c1:fofType.
% Parameter s:(fofType->fofType).
% Definition cCKB6_NUM:=(fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx)))):(fofType->Prop).
% Trying to prove (forall (Xx:fofType), ((cCKB6_NUM Xx)->(cCKB6_NUM (s (s Xx)))))
% Found x20:=(x2 (s (s Xw))):((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (x2 (s (s Xw))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x2 (s (s Xw)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x2 (s (s Xw)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x30:=(x3 (s (s Xw))):((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (x3 (s (s Xw))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x3 (s (s Xw)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x3 (s (s Xw)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x30:=(x3 x20):(Xp (s (s Xw)))
% Found (x3 x20) as proof of (Xp (s (s Xw)))
% Found (x3 x20) as proof of (Xp (s (s Xw)))
% Found (x200 (x3 x20)) as proof of (Xp (s (s (s Xw))))
% Found ((x20 (s (s Xw))) (x3 x20)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (forall (Xw:fofType), (((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))))
% Found x210:=(x21 x20):(Xp (s (s Xw)))
% Found (x21 x20) as proof of (Xp (s (s Xw)))
% Found ((x2 x10) x20) as proof of (Xp (s (s Xw)))
% Found ((x2 x10) x20) as proof of (Xp (s (s Xw)))
% Found (x200 ((x2 x10) x20)) as proof of (Xp (s (s (s Xw))))
% Found ((x20 (s (s Xw))) ((x2 x10) x20)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))->((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))))
% Found (fun (Xw:fofType) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (forall (Xw:fofType), (((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))->((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))))
% Found x400:=(x40 x2):(Xp (s (s (s Xw))))
% Found (x40 x2) as proof of (Xp (s (s (s Xw))))
% Found ((x4 (s (s Xw))) x2) as proof of (Xp (s (s (s Xw))))
% Found (fun (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (and_rect00 (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found ((and_rect0 (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of (Xp (s (s (s Xw))))
% Found (fun (Xw:fofType) (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x10:=(x1 x00):(Xp (s (s Xw)))
% Found (x1 x00) as proof of (Xp (s (s Xw)))
% Found (x1 x00) as proof of (Xp (s (s Xw)))
% Found (x30 (x1 x00)) as proof of (Xp (s (s (s Xw))))
% Found ((x3 (s (s Xw))) (x1 x00)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (and_rect00 (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found ((and_rect0 (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of ((((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))->(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (forall (Xw:fofType), ((((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))->(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw)))))))
% Found x100:=(x10 x2):(Xp (s (s Xw)))
% Found (x10 x2) as proof of (Xp (s (s Xw)))
% Found ((x1 Xp) x2) as proof of (Xp (s (s Xw)))
% Found ((x1 Xp) x2) as proof of (Xp (s (s Xw)))
% Found (x40 ((x1 Xp) x2)) as proof of (Xp (s (s (s Xw))))
% Found ((x4 (s (s Xw))) ((x1 Xp) x2)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (and_rect00 (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2)))) as proof of (Xp (s (s (s Xw))))
% Found ((and_rect0 (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2)))) as proof of (Xp (s (s (s Xw))))
% Found (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2)))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x2:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))))) as proof of (Xp (s (s (s Xw))))
% Found (fun (Xp:(fofType->Prop)) (x2:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))))) as proof of (((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw)))))
% Found (fun (x1:(cCKB6_NUM (s (s Xw)))) (Xp:(fofType->Prop)) (x2:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))))) as proof of (cCKB6_NUM (s (s (s Xw))))
% Found (fun (Xw:fofType) (x1:(cCKB6_NUM (s (s Xw)))) (Xp:(fofType->Prop)) (x2:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))))) as proof of ((cCKB6_NUM (s (s Xw)))->(cCKB6_NUM (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x1:(cCKB6_NUM (s (s Xw)))) (Xp:(fofType->Prop)) (x2:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x3) x2)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) ((x1 Xp) x2))))) as proof of (forall (Xw:fofType), ((cCKB6_NUM (s (s Xw)))->(cCKB6_NUM (s (s (s Xw))))))
% Found x20:=(x2 (s (s Xw))):((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (x2 (s (s Xw))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x2 (s (s Xw)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x2 (s (s Xw)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x30:=(x3 (s (s Xw))):((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (x3 (s (s Xw))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x3 (s (s Xw)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType)=> (x3 (s (s Xw)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x30:=(x3 x20):(Xp (s (s Xw)))
% Found (x3 x20) as proof of (Xp (s (s Xw)))
% Found (x3 x20) as proof of (Xp (s (s Xw)))
% Found (x200 (x3 x20)) as proof of (Xp (s (s (s Xw))))
% Found ((x20 (s (s Xw))) (x3 x20)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x3:((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) (x3 x20))) as proof of (forall (Xw:fofType), (((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw))))->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))))
% Found x210:=(x21 x20):(Xp (s (s Xw)))
% Found (x21 x20) as proof of (Xp (s (s Xw)))
% Found ((x2 x10) x20) as proof of (Xp (s (s Xw)))
% Found ((x2 x10) x20) as proof of (Xp (s (s Xw)))
% Found (x200 ((x2 x10) x20)) as proof of (Xp (s (s (s Xw))))
% Found ((x20 (s (s Xw))) ((x2 x10) x20)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))->((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))))
% Found (fun (Xw:fofType) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))) (x10:(Xp c1)) (x20:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x20 (s (s Xw))) ((x2 x10) x20))) as proof of (forall (Xw:fofType), (((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s Xw)))))->((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))))
% Found x400:=(x40 x2):(Xp (s (s (s Xw))))
% Found (x40 x2) as proof of (Xp (s (s (s Xw))))
% Found ((x4 (s (s Xw))) x2) as proof of (Xp (s (s (s Xw))))
% Found (fun (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (and_rect00 (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found ((and_rect0 (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of (Xp (s (s (s Xw))))
% Found (fun (Xw:fofType) (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of ((Xp (s (s Xw)))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x2:(Xp (s (s Xw))))=> (((fun (P:Type) (x3:((Xp c1)->((forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw))))) P) x3) x0)) (Xp (s (s (s Xw))))) (fun (x3:(Xp c1)) (x4:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x4 (s (s Xw))) x2)))) as proof of (forall (Xw:fofType), ((Xp (s (s Xw)))->(Xp (s (s (s Xw))))))
% Found x10:=(x1 x00):(Xp (s (s Xw)))
% Found (x1 x00) as proof of (Xp (s (s Xw)))
% Found (x1 x00) as proof of (Xp (s (s Xw)))
% Found (x30 (x1 x00)) as proof of (Xp (s (s (s Xw))))
% Found ((x3 (s (s Xw))) (x1 x00)) as proof of (Xp (s (s (s Xw))))
% Found (fun (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of ((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw)))))
% Found (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))) as proof of ((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->(Xp (s (s (s Xw))))))
% Found (and_rect00 (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found ((and_rect0 (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00)))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (Xp (s (s (s Xw))))
% Found (fun (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw)))))
% Found (fun (Xw:fofType) (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of ((((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))->(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw))))))
% Found (fun (Xw:fofType) (x1:(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))) (x00:((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))))=> (((fun (P:Type) (x2:((Xp c1)->((forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))->P)))=> (((((and_rect (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0))))) P) x2) x00)) (Xp (s (s (s Xw))))) (fun (x2:(Xp c1)) (x3:(forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))=> ((x3 (s (s Xw))) (x1 x00))))) as proof of (forall (Xw:fofType), ((((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s Xw))))->(((and (Xp c1)) (forall (Xw0:fofType), ((Xp Xw0)->(Xp (s Xw0)))))->(Xp (s (s (s Xw)))))))
% Found x100:=(x10 x00):(Xp0 (s (s Xw)))
% Found (x10 x00) as proof of (Xp0 (s (s Xw)))
% Found ((x1 Xp0) x00) as proof of (Xp0 (s (s Xw)))
% Found ((x1 Xp0) x00) as proof of (Xp0 (s (s Xw)))
% Found (x30 ((x1 Xp0) x00)) as proof of (Xp0 (s (s (s Xw))))
% Found ((x3 (s (s Xw))) ((x1 Xp0) x00)) as proof of (Xp0 (s (s (s Xw))))
% Found (fun (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00))) as proof of (Xp0 (s (s (s Xw))))
% Found (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00))) as proof of ((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->(Xp0 (s (s (s Xw)))))
% Found (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00))) as proof of ((Xp0 c1)->((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->(Xp0 (s (s (s Xw))))))
% Found (and_rect00 (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00)))) as proof of (Xp0 (s (s (s Xw))))
% Found ((and_rect0 (Xp0 (s (s (s Xw))))) (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00)))) as proof of (Xp0 (s (s (s Xw))))
% Found (((fun (P:Type) (x2:((Xp0 c1)->((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->P)))=> (((((and_rect (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))) P) x2) x00)) (Xp0 (s (s (s Xw))))) (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00)))) as proof of (Xp0 (s (s (s Xw))))
% Found (fun (x00:((and (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))))=> (((fun (P:Type) (x2:((Xp0 c1)->((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->P)))=> (((((and_rect (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))) P) x2) x00)) (Xp0 (s (s (s Xw))))) (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00))))) as proof of (Xp0 (s (s (s Xw))))
% Found (fun (Xp0:(fofType->Prop)) (x00:((and (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))))=> (((fun (P:Type) (x2:((Xp0 c1)->((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->P)))=> (((((and_rect (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))) P) x2) x00)) (Xp0 (s (s (s Xw))))) (fun (x2:(Xp0 c1)) (x3:(forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))=> ((x3 (s (s Xw))) ((x1 Xp0) x00))))) as proof of (((and (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))->(Xp0 (s (s (s Xw)))))
% Found (fun (x1:(forall (Xp0:(fofType->Prop)), (((and (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0)))))->(Xp0 (s (s Xw)))))) (Xp0:(fofType->Prop)) (x00:((and (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))))=> (((fun (P:Type) (x2:((Xp0 c1)->((forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))->P)))=> (((((and_rect (Xp0 c1)) (forall (Xw0:fofType), ((Xp0 Xw0)->(Xp0 (s Xw0))))) P) x2) x00)) (Xp0 (s (s (s Xw))))) (
% EOF
%------------------------------------------------------------------------------