%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------