TSTP Solution File: SEV070^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV070^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n094.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 13:33:42 EDT 2014
% Result : Theorem 1.88s
% Output : Proof 1.88s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV070^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.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 07:54:56 CDT 2014
% % CPUTime : 1.88
% 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 0x1526c20>, <kernel.DependentProduct object at 0x1526560>) of role type named cS
% Using role type
% Declaring cS:(fofType->fofType)
% FOF formula (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) of role conjecture named cTHM577_pme
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))))']
% Parameter fofType:Type.
% Parameter cS:(fofType->fofType).
% Trying to prove (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))))
% Found x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found x0 as proof of ((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found x100:=(x10 x0):(Xp Xy)
% Found (x10 x0) as proof of (Xp Xy)
% Found ((x1 Xp) x0) as proof of (Xp Xy)
% Found ((x1 Xp) x0) as proof of (Xp Xy)
% Found x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))
% Found x2 as proof of (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))
% Found x4:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))
% Found x4 as proof of (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))
% Found x300:=(x30 x0):(Xp Xy)
% Found (x30 x0) as proof of (Xp Xy)
% Found ((x3 Xp) x0) as proof of (Xp Xy)
% Found ((x3 Xp) x0) as proof of (Xp Xy)
% Found ((conj00 ((x3 Xp) x0)) x2) as proof of ((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found (((conj0 (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2) as proof of ((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2) as proof of ((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2) as proof of ((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))
% Found (x40 ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)) as proof of (Xp Xz)
% Found ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)) as proof of (Xp Xz)
% Found (fun (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))) as proof of (Xp Xz)
% Found (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))) as proof of ((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->(Xp Xz))
% Found (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))) as proof of ((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->(Xp Xz)))
% Found (and_rect10 (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))) as proof of (Xp Xz)
% Found ((and_rect1 (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))) as proof of (Xp Xz)
% Found (((fun (P:Type) (x3:((forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))->((forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))->P)))=> (((((and_rect (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))) as proof of (Xp Xz)
% Found (fun (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))->((forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))->P)))=> (((((and_rect (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))) as proof of (Xp Xz)
% Found (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))->((forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))->P)))=> (((((and_rect (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))) as proof of ((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->(Xp Xz))
% Found (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))->((forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))->P)))=> (((((and_rect (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))) as proof of ((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->(Xp Xz)))
% Found (and_rect00 (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))->((forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))->P)))=> (((((and_rect (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))))) as proof of (Xp Xz)
% Found ((and_rect0 (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))))) as proof of (Xp Xz)
% Found (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))))) as proof of (Xp Xz)
% Found (fun (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (Xp Xz)
% Found (fun (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))
% Found (fun (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))
% Found (fun (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))
% Found (fun (Xy:fofType) (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (forall (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))))
% Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (forall (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))))
% Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2))))))) as proof of (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))->(forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz)))))
% Got proof (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))))))
% Time elapsed = 1.551668s
% node=284 cost=664.000000 depth=27
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xy)))) (forall (Xp:(fofType->Prop)), (((and (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))->(Xp Xz))))) (Xp:(fofType->Prop)) (x0:((and (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))))=> (((fun (P:Type) (x1:((Xp Xx)->((forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) P) x1) x0)) (Xp Xz)) (fun (x1:(Xp Xx)) (x2:(forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn)))))=> (((fun (P:Type) (x3:((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))->((forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))->P)))=> (((((and_rect (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz)))) P) x3) x)) (Xp Xz)) (fun (x3:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xx)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xy)))) (x4:(forall (Xp0:(fofType->Prop)), (((and (Xp0 Xy)) (forall (Xn:fofType), ((Xp0 Xn)->(Xp0 (cS Xn)))))->(Xp0 Xz))))=> ((x4 Xp) ((((conj (Xp Xy)) (forall (Xn:fofType), ((Xp Xn)->(Xp (cS Xn))))) ((x3 Xp) x0)) x2)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
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