%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU970^5 : TPTP v6.1.0. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n106.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 13:33:27 EDT 2014 % Result : Theorem 5.61s % Output : Proof 5.61s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU970^5 : TPTP v6.1.0. Bugfixed v5.2.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n106.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 11:46:46 CDT 2014 % % CPUTime : 5.61 % 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 0x1622cf8>, <kernel.DependentProduct object at 0x1803908>) of role type named s_type % Using role type % Declaring s:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x1805170>, <kernel.DependentProduct object at 0x1803638>) 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) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) of role conjecture named cCKB_L34000_pme % Conjecture to prove = (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))'] % 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) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) % Found x0:((cCKB_E2 Xx) Xy) % Found x0 as proof of ((cCKB_E2 Xx) Xy) % Found x00:=(x0 Xp):(((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)) % Found (x0 Xp) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)) % Found (x0 Xp) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)) % Found x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found x2 as proof of ((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found x0:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found x0 as proof of ((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found x000:=(x00 x2):(Xp Xy) % Found (x00 x2) as proof of (Xp Xy) % Found ((x0 Xp) x2) as proof of (Xp Xy) % Found ((x0 Xp) x2) as proof of (Xp Xy) % 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 x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))) % Found x4 as proof of (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))) % Found x000:=(x00 x2):(Xp Xy) % Found (x00 x2) as proof of (Xp Xy) % Found ((x0 Xp) x2) as proof of (Xp Xy) % Found ((x0 Xp) x2) as proof of (Xp Xy) % Found ((conj00 ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found (((conj0 (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) % Found (x10 ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)) as proof of (Xp Xz) % Found ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)) as proof of (Xp Xz) % Found (fun (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of (Xp Xz) % Found (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of ((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp Xz)) % Found (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of ((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp Xz))) % Found (and_rect10 (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz) % Found ((and_rect1 (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz) % Found (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz) % Found (fun (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (Xp Xz) % Found (fun (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xz)) % Found (fun (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of ((cCKB_E2 Xx) Xz) % Found (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((cCKB_E2 Xy) Xz)->((cCKB_E2 Xx) Xz)) % Found (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->((cCKB_E2 Xx) Xz))) % Found (and_rect00 (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz) % Found ((and_rect0 ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz) % Found (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz) % Found (fun (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of ((cCKB_E2 Xx) Xz) % Found (fun (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)) % Found (fun (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) % Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) % Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) % Got proof (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) % Time elapsed = 5.229947s % node=926 cost=595.000000 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 ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------