TSTP Solution File: PUZ108^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ108^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n109.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 : Theorem 0.83s
% Output : Proof 0.83s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : PUZ108^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 08:20:31 CDT 2014
% % CPUTime : 0.83
% 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 0x1734248>, <kernel.DependentProduct object at 0x17343b0>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x198a440>, <kernel.DependentProduct object at 0x1734560>) of role type named cCKB_E2_type
% Using role type
% Declaring cCKB_E2:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) cCKB_E2) (fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))))) of role definition named cCKB_E2_def
% A new definition: (((eq (fofType->(fofType->Prop))) cCKB_E2) (fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)))))
% Defined: cCKB_E2:=(fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))))
% FOF formula (forall (Xx:fofType) (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy)))) of role conjecture named cCKB_L35000
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xx:fofType) (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy))))']
% Parameter fofType:Type.
% Parameter s:(fofType->fofType).
% Definition cCKB_E2:=(fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)))):(fofType->(fofType->Prop)).
% Trying to prove (forall (Xx:fofType) (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy))))
% Found x20:=(x2 (s Xu)):((Xp (s Xu))->(Xp (s (s (s Xu)))))
% Found (x2 (s Xu)) as proof of ((Xp (s Xu))->(Xp (s (s (s Xu)))))
% Found (fun (Xu:fofType)=> (x2 (s Xu))) as proof of ((Xp (s Xu))->(Xp (s (s (s Xu)))))
% Found (fun (Xu:fofType)=> (x2 (s Xu))) as proof of (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))
% Found (conj000 (fun (Xu:fofType)=> (x2 (s Xu)))) as proof of ((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu)))))))
% Found ((conj00 (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))) as proof of ((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu)))))))
% Found (((fun (B:Prop)=> ((conj0 B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))) as proof of ((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu)))))))
% Found (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))) as proof of ((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu)))))))
% Found (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))) as proof of ((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu)))))))
% Found (x3 (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))) as proof of (Xp (s Xy))
% Found ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))) as proof of (Xp (s Xy))
% Found (fun (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))) as proof of (Xp (s Xy))
% Found (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))) as proof of ((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp (s Xy)))
% Found (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))) as proof of ((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp (s Xy))))
% Found (and_rect00 (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))))) as proof of (Xp (s Xy))
% Found ((and_rect0 (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))))) as proof of (Xp (s Xy))
% Found (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))))) as proof of (Xp (s Xy))
% Found (fun (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of (Xp (s Xy))
% Found (fun (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of (((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp (s Xy)))
% Found (fun (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of ((cCKB_E2 (s Xx)) (s Xy))
% Found (fun (Xy:fofType) (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of (forall (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy))))
% Found (fun (Xx:fofType) (Xy:fofType) (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu)))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((cCKB_E2 Xx) Xy)->((cCKB_E2 (s Xx)) (s Xy))))
% Got proof (fun (Xx:fofType) (Xy:fofType) (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))))))
% Time elapsed = 0.504523s
% node=127 cost=298.000000 depth=21
% ::::::::::::::::::::::
% % 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) (x:((cCKB_E2 Xx) Xy)) (Xp:(fofType->Prop)) (x0:((and (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x1:((Xp (s Xx))->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp (s Xx))) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x1) x0)) (Xp (s Xy))) (fun (x1:(Xp (s Xx))) (x2:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x (fun (x4:fofType)=> (Xp (s x4)))) (((fun (B:Prop)=> (((conj (Xp (s Xx))) B) x1)) (forall (Xu:fofType), ((Xp (s Xu))->(Xp (s (s (s Xu))))))) (fun (Xu:fofType)=> (x2 (s Xu))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------