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